index.xml

<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>natverse</title><link>https://natverse.github.io/</link><description>Recent content on natverse</description><generator>Hugo -- gohugo.io</generator><language>en-us</language><lastBuildDate>Wed, 25 Sep 2019 00:00:00 +0000</lastBuildDate><atom:link href="https://natverse.github.io/index.xml" rel="self" type="application/rss+xml"/><item><title>Introduction to neurons and neuronlists</title><link>https://natverse.github.io/news/2019/09/nat/</link><pubDate>Wed, 25 Sep 2019 00:00:00 +0000</pubDate><guid>https://natverse.github.io/news/2019/09/nat/</guid><description>
&lt;h2 id=&#34;preface&#34;&gt;Preface&lt;/h2&gt;
&lt;p&gt;This vignette is designed to give you a good introduction to some of the key
features of nat by teaching you about how it handles individual neurons and
collections of neurons.&lt;/p&gt;
&lt;p&gt;The source code for this vignette is available at
&lt;a href=&#34;https://github.com/natverse/nat/blob/master/vignettes/neurons-intro.Rmd&#34; target=&#34;_blank&#34;&gt;https://github.com/natverse/nat/blob/master/vignettes/neurons-intro.Rmd&lt;/a&gt;.
If you find something unclear or notice a typo, I would be very happy if you
would click on the Pencil Icon on that page or follow
&lt;a href=&#34;https://github.com/natverse/nat/edit/master/vignettes/neurons-intro.Rmd&#34; target=&#34;_blank&#34;&gt;this link to edit&lt;/a&gt;
and suggest an alternative wording. Don&amp;rsquo;t be shy about doing this; I have to
review any change and even if your suggestion is not perfect it will still
be a prompt for me to improve this document. Thank you!&lt;/p&gt;
&lt;h2 id=&#34;startup&#34;&gt;Startup&lt;/h2&gt;
&lt;p&gt;Install the package if required&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;install.packages(&#39;nat&#39;, dependencies = TRUE)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Load the package&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;library(nat)
&lt;/code&gt;&lt;/pre&gt;
&lt;h2 id=&#34;neurons-and-neuronlists&#34;&gt;Neurons and Neuronlists&lt;/h2&gt;
&lt;p&gt;There are a number of basic built in types of data in R such as vectors and matrices,
but it is also very easy to define new data types with specialised features to
enable powerful and efficient analysis of particular kinds of data. These specialised
data types are called &lt;em&gt;classes&lt;/em&gt; and a specific instance of a class is an &lt;em&gt;object&lt;/em&gt;
(a neuroscience analogy: this is the difference between talking about the
general class of mitral cells and the specific cell that you just sealed onto
with your patch clamp electrode.)&lt;/p&gt;
&lt;p&gt;We will look at two key classes that &lt;strong&gt;nat&lt;/strong&gt; defines for handling 3D structures of neurons&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;code&gt;neuron&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;neuronlist&lt;/code&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;sample-data&#34;&gt;Sample Data&lt;/h3&gt;
&lt;p&gt;As an example we&amp;rsquo;re going to look at a data set of olfactory projection neurons originally
published as Supplemental Information to accompany
&lt;a href=&#34;http://dx.doi.org/10.1016/j.cell.2007.01.040&#34; target=&#34;_blank&#34;&gt;Jefferis, Potter et al, Cell (2007)&lt;/a&gt;.
A subset of the original data are distributed as a sample data object with the
&lt;strong&gt;nat&lt;/strong&gt; package, which we can load like so.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;data(&amp;quot;Cell07PNs&amp;quot;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;For more information about these data see &lt;a href=&#34;https://natverse.github.io/nat/reference/Cell07PNs.html&#34; target=&#34;_blank&#34;&gt;Cell07PNs&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;This &lt;code&gt;Cell07PNs&lt;/code&gt; object has two classes &lt;code&gt;neuronlist&lt;/code&gt; and the base class &lt;code&gt;list&lt;/code&gt;&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;class(Cell07PNs)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] &amp;quot;neuronlist&amp;quot; &amp;quot;list&amp;quot;
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Many R objects inherit from the base class &lt;code&gt;list&lt;/code&gt; (objects can have multiple
classes in the same way that a mitral cell is also neuron) because this is a
convenient container class into which you can put a variety of different kinds
of data. In this case the &lt;code&gt;Cell07PNs&lt;/code&gt; &lt;code&gt;neuronlist&lt;/code&gt; contains 40 objects:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;length(Cell07PNs)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] 40
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# access the first neuron in the neuronlist
class(Cell07PNs[[1]])
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] &amp;quot;neuron&amp;quot; &amp;quot;list&amp;quot;
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;each representing a traced neuron. We will now look in detail at these two classes.&lt;/p&gt;
&lt;h2 id=&#34;neurons&#34;&gt;Neurons&lt;/h2&gt;
&lt;p&gt;We start by extracting the first neuron in Cell07PNs, and assigning it to
a variable. We can then plot the neuron so that we have an image of what we are
talking about.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;n1=Cell07PNs[[1]]
plot(n1)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-6-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;h3 id=&#34;neuron-internal-structure&#34;&gt;Neuron internal structure&lt;/h3&gt;
&lt;p&gt;The &lt;code&gt;str&lt;/code&gt; function (short for structure) allows us to take a look at the internal
structure of this neuron object.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# Use =1 so that we don&#39;t show complete structure
# for objects inside n1
str(n1, max.level=1)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## List of 24
## $ CellType : chr &amp;quot;DA1&amp;quot;
## $ NeuronName : chr &amp;quot;EBH11R&amp;quot;
## $ InputFileName: &#39;AsIs&#39; chr &amp;quot;/GD/projects/PN2/TransformedTraces/DA1/EBH11R.tasc&amp;quot;
## $ CreatedAt : POSIXt[1:1], format: &amp;quot;2006-01-17 15:21:14&amp;quot;
## $ NodeName : Named chr &amp;quot;jefferis.joh.cam.ac.uk&amp;quot;
## ..- attr(*, &amp;quot;names&amp;quot;)= chr &amp;quot;nodename&amp;quot;
## $ InputFileStat:&#39;data.frame&#39;: 1 obs. of 10 variables:
## $ InputFileMD5 : Named chr &amp;quot;fcacee3f874cbe2c6ad96214e6fee337&amp;quot;
## ..- attr(*, &amp;quot;names&amp;quot;)= &#39;AsIs&#39; chr &amp;quot;/GD/projects/PN2/TransformedTraces/DA1/EBH11R.tasc&amp;quot;
## $ NumPoints : int 180
## $ StartPoint : num 1
## $ BranchPoints : num [1:16] 34 48 51 75 78 95 98 99 108 109 ...
## $ EndPoints : num [1:18] 1 42 59 62 80 85 96 100 102 112 ...
## $ NumSegs : int 33
## $ SegList :List of 33
## $ d :&#39;data.frame&#39;: 180 obs. of 7 variables:
## $ OrientInfo :List of 5
## $ SegOrders : num [1:33] 1 2 2 3 4 4 3 4 5 5 ...
## $ MBPoints : int [1:2] 34 48
## $ LHBranchPoint: int 75
## $ SegTypes : num [1:33] 1 3 1 3 3 3 1 2 2 2 ...
## $ AxonSegNos :List of 3
## $ LHSegNos : num [1:26] 8 9 10 11 12 13 14 15 16 17 ...
## $ MBSegNos :List of 2
## $ NumMBBranches: num 2
## $ AxonLHEP : num 72
## - attr(*, &amp;quot;class&amp;quot;)= chr [1:2] &amp;quot;neuron&amp;quot; &amp;quot;list&amp;quot;
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;From this you can see that there are a large number of fields inside the neuron.
Each field can be accessed using the &lt;code&gt;$&lt;/code&gt; or &lt;code&gt;[[&lt;/code&gt; operators&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;n1$NumPoints
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] 180
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;n1[[&amp;quot;NumPoints&amp;quot;]]
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] 180
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;There are a set of core fields (described in &lt;code&gt;?neuron&lt;/code&gt; documentation); the key
ones will be described shortly. However there are also quite a few user fields
in this neuron and you can safely add any field you like so long as its name
does not clash with an existing field. For example:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;n1$Comment=&#39;The sex of this specimen is uncertain&#39;
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;The single most important field in a neuron is the &lt;code&gt;$d&lt;/code&gt; &lt;code&gt;data.frame&lt;/code&gt;. This
contains a block of data closely reminiscent of the SWC data format for traced
neurons:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;str(n1$d)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## &#39;data.frame&#39;: 180 obs. of 7 variables:
## $ PointNo: int 1 2 3 4 5 6 7 8 9 10 ...
## $ Label : num 2 2 2 2 2 2 2 2 2 2 ...
## $ X : num 187 187 188 188 188 ...
## $ Y : num 133 131 130 129 129 ...
## $ Z : num 88.2 90.6 93.1 95 97.5 ...
## $ W : num 1.01 1.27 1.14 1.27 1.27 1.27 1.27 1.27 1.27 1.27 ...
## $ Parent : num -1 1 2 3 4 5 6 7 8 9 ...
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Each row defines a node in a branched tree with a unique integer identifier,
&lt;code&gt;PointNo&lt;/code&gt;, normally but not always sequentially numbered from 1. The &lt;code&gt;X,Y,Z&lt;/code&gt;
columns encode the position of each vertex and the &lt;code&gt;W&lt;/code&gt; column encodes the
diameter of the neurite at that position.&lt;/p&gt;
&lt;h3 id=&#34;methods-for-neurons&#34;&gt;Methods for neurons&lt;/h3&gt;
&lt;p&gt;R&amp;rsquo;s simple &lt;a href=&#34;http://adv-r.had.co.nz/OO-essentials.html&#34; target=&#34;_blank&#34;&gt;S3 object oriented system&lt;/a&gt;
allows specialised functions for particular classes to be defined. These functions
tailored to a particular class are called &lt;em&gt;methods&lt;/em&gt;. Methods can be provided for
pre-existing functions supplied with base R as well as new user-written functions.
The system is quite simple. If a function &lt;code&gt;foo&lt;/code&gt; is defined as a &lt;em&gt;generic&lt;/em&gt; function
then you can define new functions called &lt;code&gt;foo.bar&lt;/code&gt; that will be called when
you write &lt;code&gt;foo(x)&lt;/code&gt; and &lt;code&gt;x&lt;/code&gt; has class `bar.&lt;/p&gt;
&lt;p&gt;We already used one such method without comment, &lt;code&gt;plot.neuron&lt;/code&gt;. There is a base
R function called &lt;code&gt;plot&lt;/code&gt;. nat defines a new function called &lt;code&gt;plot.neuron&lt;/code&gt;, which
R interprets as a &lt;code&gt;plot&lt;/code&gt; method specialised for &lt;code&gt;neuron&lt;/code&gt; objects. When the base
R &lt;code&gt;plot&lt;/code&gt; function is called, it looks at the class of its first object to see
whether a specialised method exists. If there is none, it will use a fallback
method called &lt;code&gt;plot.default&lt;/code&gt;.&lt;/p&gt;
&lt;p&gt;The &lt;code&gt;plot.neuron&lt;/code&gt; method interprets the branching structure of a neuron and
draws line segments joining up the connected nodes at the appropriate 2D positions.
You can compare it with what you would get if you just plotted the XY position
of all nodes joined together by a single line:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(n1$d$X, n1$d$Y, type = &#39;l&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-11-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;You can find out what methods are available for a particular class like so:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;methods(class = &#39;neuron&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] all.equal as.neuron as.ngraph
## [4] as.seglist branchpoints dotprops
## [7] endpoints intersect_plane ndigest
## [10] nvertices Ops plot
## [13] plot3d potential_synapses prune
## [16] resample rootpoints scale
## [19] subset summary write.vtk
## [22] xform xyzmatrix xyzmatrix&amp;lt;-
## see &#39;?methods&#39; for accessing help and source code
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You can then find the help page for any method in the console with &lt;code&gt;?plot.neuron&lt;/code&gt;.
Note that if you write &lt;code&gt;?plot&lt;/code&gt; you will get the documentation for the basic
&lt;code&gt;plot&lt;/code&gt; function supplied with R.&lt;/p&gt;
&lt;p&gt;It is also good idea to look at
&lt;a href=&#34;https://natverse.github.io/nat/reference/index.html&#34; target=&#34;_blank&#34;&gt;nat&amp;rsquo;s function reference page&lt;/a&gt;
which groups available functions into categories that often reflect the class
of object they can work on.&lt;/p&gt;
&lt;p&gt;In R, operators such as &lt;code&gt;*&lt;/code&gt; or &lt;code&gt;+&lt;/code&gt; are actually special functions with two
arguments, so one can add methods for these in the same way. In the following
example we use this arithmetic to shift a neuron by a small amount:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(n1, col = &#39;black&#39;, WithNodes = F, main=&amp;quot;Shifting neurons&amp;quot;)
# shift by 3 microns in x,y,z
plot(n1+3, col = &#39;red&#39;, add = TRUE, WithNodes = F)
# shift by -5 microns in y
plot(n1+c(0,-5,0), col = &#39;blue&#39;, add = TRUE, WithNodes = F)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-13-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;Another specialised method is &lt;code&gt;subset.neuron&lt;/code&gt; which we can use to extract part
of a neuron into a new object. For example, a simple spatial criterion,
X location must be &amp;gt;240, is used to extract the axon terminal arborisation field
in this example&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(n1, col = &#39;black&#39;, WithAllPoints = T, main=&amp;quot;Subsetting a neuron&amp;quot;)
# keep only nodes with X position &amp;gt;20
n1.lh=subset(n1, X&amp;gt;240)
# plot the selected part of the neuron in blue
plot(n1.lh, col=&#39;blue&#39;, lwd=3, add=TRUE)
# add a line illustrating the cut point
abline(v=240, lty=2)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-14-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;We can also summarise the morphological properties of a neuron using the
&lt;code&gt;summary.neuron&lt;/code&gt; method, which allows us to compare measurements for the original
neuron and the axon arbour that we just cut out above.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;summary(n1)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## root nodes segments branchpoints endpoints cable.length
## 1 1 180 33 16 18 297.1763
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;summary(n1.lh)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## root nodes segments branchpoints endpoints cable.length
## 1 1 111 27 13 15 156.7654
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;See &lt;a href=&#34;https://natverse.github.io/nat/reference/index.html&#34; target=&#34;_blank&#34;&gt;nat&amp;rsquo;s function reference page&lt;/a&gt;
for additional functions for working with neurons.&lt;/p&gt;
&lt;h2 id=&#34;neuronlists&#34;&gt;Neuronlists&lt;/h2&gt;
&lt;p&gt;The &lt;code&gt;data&lt;/code&gt; statement above loaded a &lt;code&gt;neuronlist&lt;/code&gt; object called &lt;code&gt;Cell07PNs&lt;/code&gt;
containing 40 &lt;code&gt;neuron&lt;/code&gt; objects. &lt;code&gt;neuronlist&lt;/code&gt; objects are key
data structures in nat for convenient handling of collections of neurons.&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;fig/neuronlist-01.png&#34; alt=&#34;Structure of neuronlist objects&#34; /&gt;&lt;/p&gt;
&lt;p&gt;The diagram above presents the structure of a neuronlist, &lt;code&gt;x&lt;/code&gt;, which contains
5 neurons. The main structure is an R &lt;code&gt;list&lt;/code&gt; object, which in this case contains
5 slots. Each slot contains a neuron with a unique name. In addition to this
list of neurons there is an optional attached &lt;code&gt;data.frame&lt;/code&gt; (another standard R class).
When present, each neuron in the main list must have a matching row in this &lt;code&gt;data.frame&lt;/code&gt;.&lt;/p&gt;
&lt;p&gt;Neuronlists can be manipulated use the square bracket subscript operator to
extract or replace a subset of their elements. Crucially when this happens the
corresponding rows of the attached metadata are also selected as diagrammed for
the result of x&lt;a href=&#34;right hand side of figure above&#34; target=&#34;_blank&#34;&gt;1:3&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;When subscripting any list in R, it is very important to understand the difference
between using the single and double bracket operator. We can illustrate this
difference as follows:&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;fig/neuronlist-subsets-01.png&#34; alt=&#34;The difference between single and double bracket subscript operators&#34; /&gt;&lt;/p&gt;
&lt;p&gt;The single bracket operator makes a new list containing a specified subset of
elements in the original list, while the double bracket operator extracts the
object at the given position. So in the figure &lt;code&gt;x[1]&lt;/code&gt; is a &lt;code&gt;neuronlist&lt;/code&gt; object
of length 1, whereas &lt;code&gt;x[[1]]&lt;/code&gt; is the &lt;code&gt;neuron&lt;/code&gt; object at the first position in
the list.&lt;/p&gt;
&lt;h3 id=&#34;worked-examples&#34;&gt;Worked Examples&lt;/h3&gt;
&lt;p&gt;Let us start by extracting the first five neurons from our sample data.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# we can select neurons by indexing
first5=Cell07PNs[1:5]
summary(first5)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## root nodes segments branchpoints endpoints cable.length
## EBH11R 1 180 33 16 18 297.1763
## EBH20L 1 200 26 12 15 327.0929
## EBH20R 1 199 25 12 14 347.6153
## EBI12L 1 169 23 11 13 294.4680
## EBI22R 1 160 27 13 15 303.0150
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Each neuron in the neuronlist has an associated name which can be used to select
it. We can get the names of all neurons using the &lt;code&gt;names&lt;/code&gt; function.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;names(Cell07PNs)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] &amp;quot;EBH11R&amp;quot; &amp;quot;EBH20L&amp;quot; &amp;quot;EBH20R&amp;quot; &amp;quot;EBI12L&amp;quot; &amp;quot;EBI22R&amp;quot; &amp;quot;EBJ23L&amp;quot; &amp;quot;EBJ3R&amp;quot;
## [8] &amp;quot;EBN19L&amp;quot; &amp;quot;EBO15L&amp;quot; &amp;quot;EBO53L&amp;quot; &amp;quot;ECA34L&amp;quot; &amp;quot;ECB3L&amp;quot; &amp;quot;LI23L&amp;quot; &amp;quot;LIC2R&amp;quot;
## [15] &amp;quot;LJ5L&amp;quot; &amp;quot;MC3B&amp;quot; &amp;quot;MH16L&amp;quot; &amp;quot;MM14L&amp;quot; &amp;quot;NA7L&amp;quot; &amp;quot;NH15L&amp;quot; &amp;quot;NH29B&amp;quot;
## [22] &amp;quot;NI16L&amp;quot; &amp;quot;NIA8L&amp;quot; &amp;quot;NIA8R&amp;quot; &amp;quot;NNA9L&amp;quot; &amp;quot;NNC4R&amp;quot; &amp;quot;NNE1L&amp;quot; &amp;quot;OFD2L&amp;quot;
## [29] &amp;quot;OKC9R&amp;quot; &amp;quot;SDD8L&amp;quot; &amp;quot;SH21L&amp;quot; &amp;quot;SL20L&amp;quot; &amp;quot;TKC8R&amp;quot; &amp;quot;TL4R&amp;quot; &amp;quot;TS7L&amp;quot;
## [36] &amp;quot;TT27R&amp;quot; &amp;quot;VA15R&amp;quot; &amp;quot;VA20R&amp;quot; &amp;quot;VB37L&amp;quot; &amp;quot;VB58L&amp;quot;
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;nl3=Cell07PNs[c(&amp;quot;EBH11R&amp;quot;, &amp;quot;EBH20L&amp;quot;, &amp;quot;EBH20R&amp;quot;)]
all.equal(nl3, Cell07PNs[1:3])
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] TRUE
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You can also use the &lt;code&gt;$&lt;/code&gt; operator to access a single neuron e.g. &lt;code&gt;Cell07PNs$EBH11R&lt;/code&gt;.
This can be quite useful when working interactively in the console because
RStudio will offer to autocomplete the neuron name when you start typing past the
&lt;code&gt;$&lt;/code&gt; symbol, but is not recommended for scripts.&lt;/p&gt;
&lt;h3 id=&#34;metadata&#34;&gt;Metadata&lt;/h3&gt;
&lt;p&gt;The names of neurons are also used to index a &lt;code&gt;data.frame&lt;/code&gt; object attached to the
neuronlist with one row for each neuron. You can use the &lt;code&gt;head&lt;/code&gt; function to give
a summary of the attached metadata in this neuronlist. Using the &lt;code&gt;as.data.frame&lt;/code&gt; method on
a neuronlist allows you to extract this attached metadata to a separate object.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;head(Cell07PNs)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## Brain RegistrationScore Notes Glomerulus Batch Directory Traced
## EBH11R EBH11R 4 DA1 PN2 unsure yes
## EBH20L EBH20L 4 DL3 PN2 unsure2 yes
## EBH20R EBH20R 4 DA1 PN2 unsure2 yes
## EBI12L EBI12L 4 DA1 PN2 unsure3 yes
## EBI22R EBI22R 4 DL3 PN2 unsure3 yes
## EBJ23L EBJ23L 4 DL3 PN2 unsure4 yes
## Scored.By Sex Include ID HaveWarp HaveAsc
## EBH11R ACH M EBH11R TRUE TRUE
## EBH20L ACH EBH20L TRUE TRUE
## EBH20R ACH M EBH20R TRUE TRUE
## EBI12L ACH F EBI12L TRUE TRUE
## EBI22R ACH EBI22R TRUE TRUE
## EBJ23L ACH EBJ23L TRUE TRUE
## TraceFile AscBatch Status
## EBH11R /GD/projects/PN2/TransformedTraces/DA1/EBH11R.tasc New
## EBH20L /GD/projects/PN2/TransformedTraces/DL3/EBH20L.tasc New
## EBH20R /GD/projects/PN2/TransformedTraces/DA1/EBH20R.tasc New
## EBI12L /GD/projects/PN2/TransformedTraces/DA1/EBI12L.tasc New
## EBI22R /GD/projects/PN2/TransformedTraces/DL3/EBI22R.tasc New
## EBJ23L /GD/projects/PN2/TransformedTraces/DL3/EBJ23L.tasc New
## GlomSeq NumNAs MBP1 MBP2 LHBP PNType Seq nTrees StartPoint
## EBH11R 1 0 34 48 75 iPN 13 1 1
## EBH20L 1 0 29 29 77 iPN 15 1 1
## EBH20R 2 0 24 80 147 iPN 16 1 1
## EBI12L 3 0 29 59 89 iPN 18 1 1
## EBI22R 2 0 34 34 56 iPN 20 1 1
## EBJ23L 3 0 23 23 52 iPN 21 1 1
## CreatedAt
## EBH11R 2006-01-17 15:21:14
## EBH20L 2006-01-17 15:21:14
## EBH20R 2006-01-17 15:21:14
## EBI12L 2006-01-17 15:21:15
## EBI22R 2006-01-17 15:21:15
## EBJ23L 2006-01-17 15:21:15
## WarpFile
## EBH11R /GD/projects/PN2/allreg/warp/unsure/average-goodbrains_EBH11R101_warp_m0g40c4e1e-1x16r3.list
## EBH20L /GD/projects/PN2/allreg/warp/unsure2/average-goodbrains_EBH20L101_warp_m0g40c4e1e-1x16r3.list
## EBH20R /GD/projects/PN2/allreg/warp/unsure2/average-goodbrains_EBH20R101_warp_m0g40c4e1e-1x16r3.list
## EBI12L /GD/projects/PN2/allreg/warp/unsure3/average-goodbrains_EBI12L101_warp_m0g40c4e1e-1x16r3.list
## EBI22R /GD/projects/PN2/allreg/warp/unsure3/average-goodbrains_EBI22R101_warp_m0g40c4e1e-1x16r3.list
## EBJ23L /GD/projects/PN2/allreg/warp/unsure4/average-goodbrains_EBJ23L101_warp_m0g40c4e1e-1x16r3.list
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;df=as.data.frame(Cell07PNs)
nrow(df)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] 40
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# rownames of data.frame are the same as names of Cell07PNs list.
all.equal(rownames(df), names(Cell07PNs))
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] TRUE
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You can use columns in the attached metadata in expressions that select or
operate on the neurons in the list. In the next two examples we&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;code&gt;subset&lt;/code&gt; the neurons in a neuronlist based on a metadata column&lt;/li&gt;
&lt;li&gt;use the &lt;code&gt;with&lt;/code&gt; function to carry out a calculation using column(s)
of metadata.&lt;/li&gt;
&lt;/ul&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# subset.neuronlist method (which you call using the subset function)
da1n=subset(Cell07PNs, Glomerulus==&amp;quot;DA1&amp;quot;)
# with.neuronlist method
with(Cell07PNs, table(Glomerulus))
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## Glomerulus
## DA1 DL3 DP1m VA1d
## 11 10 8 11
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;There is a second approach to accessing this attached metadata data.frame, using
the square bracket operator with two arguments as used for subscripting (2D)
matrices or &lt;code&gt;data.frames&lt;/code&gt;. For example we can access the &lt;code&gt;Glomerulus&lt;/code&gt; column
like so:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;Cell07PNs[, &#39;Glomerulus&#39;]
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] DA1 DL3 DA1 DA1 DL3 DL3 VA1d VA1d VA1d VA1d DP1m DP1m DA1 DL3
## [15] VA1d VA1d DL3 DA1 DA1 VA1d VA1d VA1d DL3 VA1d DP1m DP1m DP1m DP1m
## [29] DP1m DP1m DA1 DL3 DL3 DL3 VA1d DA1 DA1 DA1 DL3 DA1
## Levels: DA1 DL3 DP1m VA1d
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;This approach has some features that make for additional flexibility. For example
you can access the whole data.frame like so:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;summary(Cell07PNs[,])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;The form &lt;code&gt;[,]&lt;/code&gt; which includes a comma implies two (missing) arguments.
&lt;strong&gt;nat&lt;/strong&gt; therefore interprets this as request for the 2D data.frame
attached to Cell07PNs rather than the neuronlist itself. You can also use this
notation to add new columns or modify existing columns in place.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;Cell07PNs[, &#39;NewColumn&#39;] = somevariable
Cell07PNs[, &amp;quot;Sex&amp;quot;] = sub(&amp;quot;F&amp;quot;, &amp;quot;female&amp;quot;, Cell07PNs[, &amp;quot;Sex&amp;quot;])
Cell07PNs[, &amp;quot;Sex&amp;quot;] = sub(&amp;quot;M&amp;quot;, &amp;quot;male&amp;quot;, Cell07PNs[, &amp;quot;Sex&amp;quot;])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You can also access selected rows of the data.frame in the normal way:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;Cell07PNs[1:5, &amp;quot;Glomerulus&amp;quot;]
Cell07PNs[Cell07PNs[, &amp;quot;Sex&amp;quot;]==&amp;quot;F&amp;quot;, &amp;quot;Glomerulus&amp;quot;]
&lt;/code&gt;&lt;/pre&gt;
&lt;h3 id=&#34;working-on-all-the-neurons-in-a-neuronlist&#34;&gt;Working on all the neurons in a neuronlist&lt;/h3&gt;
&lt;p&gt;There are quite a few methods defined for the &lt;code&gt;neuronlist&lt;/code&gt; class:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;methods(class = &amp;quot;neuronlist&amp;quot;)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] - [ [&amp;lt;-
## [4] * / +
## [7] as.data.frame as.neuronlistfh c
## [10] data.frame&amp;lt;- dimnames dotprops
## [13] droplevels head intersect
## [16] mirror nvertices plot
## [19] plot3d potential_synapses prune
## [22] setdiff subset summary
## [25] tail union with
## [28] xform xyzmatrix xyzmatrix&amp;lt;-
## see &#39;?methods&#39; for accessing help and source code
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;For example we can scale the position (and diameter) of all of the neurons in a
neuronlist using the &lt;code&gt;*&lt;/code&gt; operator:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# convert from microns to nm
Cell07PNs.nm = Cell07PNs*1e3
plot(Cell07PNs.nm)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-25-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;There is also a more powerful &lt;code&gt;xform&lt;/code&gt; function that allows arbitrary
transformations to be applied. For example here we apply a 3D rotation expressed
as a homogeneous affine matrix:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# define a 180 degree rotation around the x axis
rotm=cmtkparams2affmat(rx=180)
# remove tiny values due to rounding errors
rotm=zapsmall(rotm)
plot(xform(Cell07PNs, rotm))
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-26-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;More generally any function that works on a neuron can be applied to a
neuronlist by using the function &lt;code&gt;nlapply&lt;/code&gt;. This is an analogue to base R&amp;rsquo;s
&lt;code&gt;lapply&lt;/code&gt; function. This will take care of returning a new neuronlist with the
attached metadata and includes additional features such as error tolerance,
progress bars and parallelisation for multi-core machines. It is worth reviewing
the help and examples for this function carefully if you start to work regularly with
neuronlists.&lt;/p&gt;
&lt;h2 id=&#34;plots&#34;&gt;Plots&lt;/h2&gt;
&lt;p&gt;We have already seen that we can plot a single neuron (the first) like so:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs[[1]])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-27-1.png&#34; width=&#34;768&#34; /&gt;&lt;/p&gt;
&lt;p&gt;The purple node highlights the root or soma of the neuron, red nodes are branch
points, green nodes are end points. We can also label each node with its &lt;code&gt;PointNo&lt;/code&gt; index.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs[[1]], col=&#39;red&#39;, WithText=T)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-28-1.png&#34; width=&#34;768&#34; /&gt;&lt;/p&gt;
&lt;p&gt;Multiple neurons can be plotted by passing a whole neuronlist or indexing it&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs[1:3])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-29-1.png&#34; width=&#34;768&#34; /&gt;&lt;/p&gt;
&lt;p&gt;More complex subsets are possible by using &lt;code&gt;plot.neuronlist&lt;/code&gt; subset argument
(which works in the same way as the &lt;code&gt;subset.neuronlist&lt;/code&gt; function). For example
here we select neurons by which olfactory glomeruli their dendrites occupy:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs, subset=Glomerulus!=&amp;quot;DA1&amp;quot;, col=&#39;grey&#39;, WithNodes=F, main=&amp;quot;DA1 neurons&amp;quot;)
plot(Cell07PNs, subset=Glomerulus==&amp;quot;DA1&amp;quot;, add=TRUE)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-30-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;h3 id=&#34;3d-plots&#34;&gt;3D plots&lt;/h3&gt;
&lt;p&gt;So far we have only used 2D plots in this document, but especially for
interactive analysis and exploration, it is much more helpful to have
3D plots that can be rotated, zoomed etc. &lt;strong&gt;nat&lt;/strong&gt; provides numerous functions
for &lt;a href=&#34;https://natverse.github.io/nat/reference/index.html#section--d-plotting-of-objects&#34; target=&#34;_blank&#34;&gt;3D plots&lt;/a&gt;
based on the &lt;a href=&#34;https://cran.r-project.org/package=rgl&#34; target=&#34;_blank&#34;&gt;rgl package&lt;/a&gt;. It is
actually possible to embed fully interactive 3d figures in &lt;a href=&#34;http://rmarkdown.rstudio.com/&#34; target=&#34;_blank&#34;&gt;rmarkdown&lt;/a&gt; reports
like this one by setting the &lt;a href=&#34;https://CRAN.R-project.org/package=rgl/vignettes/WebGL.html&#34; target=&#34;_blank&#34;&gt;webgl chunk option&lt;/a&gt;.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;clear3d()
plot3d(Cell07PNs[[1]], col=&#39;red&#39;)
# set a grey background so it&#39;s easier to see extent of the webgl canvas
bg3d(col=&#39;lightgrey&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;script&gt;/*
* Copyright (C) 2009 Apple Inc. All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS&#39;&#39; AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* Copyright (2016) Duncan Murdoch - fixed CanvasMatrix4.ortho,
* cleaned up.
*/
/*
CanvasMatrix4 class
This class implements a 4x4 matrix. It has functions which
duplicate the functionality of the OpenGL matrix stack and
glut functions.
IDL:
[
Constructor(in CanvasMatrix4 matrix), // copy passed matrix into new CanvasMatrix4
Constructor(in sequence&lt;float&gt; array) // create new CanvasMatrix4 with 16 floats (row major)
Constructor() // create new CanvasMatrix4 with identity matrix
]
interface CanvasMatrix4 {
attribute float m11;
attribute float m12;
attribute float m13;
attribute float m14;
attribute float m21;
attribute float m22;
attribute float m23;
attribute float m24;
attribute float m31;
attribute float m32;
attribute float m33;
attribute float m34;
attribute float m41;
attribute float m42;
attribute float m43;
attribute float m44;
void load(in CanvasMatrix4 matrix); // copy the values from the passed matrix
void load(in sequence&lt;float&gt; array); // copy 16 floats into the matrix
sequence&lt;float&gt; getAsArray(); // return the matrix as an array of 16 floats
WebGLFloatArray getAsCanvasFloatArray(); // return the matrix as a WebGLFloatArray with 16 values
void makeIdentity(); // replace the matrix with identity
void transpose(); // replace the matrix with its transpose
void invert(); // replace the matrix with its inverse
void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
void scale(in float x, in float y, in float z); // multiply the matrix by passed scale values on the right
void rotate(in float angle, // multiply the matrix by passed rotation values on the right
in float x, in float y, in float z); // (angle is in degrees)
void multRight(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
void multLeft(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the left
void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
in float bottom, in float top,
in float near, in float far);
void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
in float bottom, in float top,
in float near, in float far);
void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
in float zNear, in float zFar);
void lookat(in float eyex, in float eyey, in float eyez, // multiply the matrix by the passed lookat
in float ctrx, in float ctry, in float ctrz, // values on the right
in float upx, in float upy, in float upz);
}
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return;
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this.makeIdentity();
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this.m13 = matrix[2];
this.m14 = matrix[3];
this.m21 = matrix[4];
this.m22 = matrix[5];
this.m23 = matrix[6];
this.m24 = matrix[7];
this.m31 = matrix[8];
this.m32 = matrix[9];
this.m33 = matrix[10];
this.m34 = matrix[11];
this.m41 = matrix[12];
this.m42 = matrix[13];
this.m43 = matrix[14];
this.m44 = matrix[15];
return;
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if (arguments[0] instanceof CanvasMatrix4) {
this.m11 = matrix.m11;
this.m12 = matrix.m12;
this.m13 = matrix.m13;
this.m14 = matrix.m14;
this.m21 = matrix.m21;
this.m22 = matrix.m22;
this.m23 = matrix.m23;
this.m24 = matrix.m24;
this.m31 = matrix.m31;
this.m32 = matrix.m32;
this.m33 = matrix.m33;
this.m34 = matrix.m34;
this.m41 = matrix.m41;
this.m42 = matrix.m42;
this.m43 = matrix.m43;
this.m44 = matrix.m44;
return;
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this.makeIdentity();
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CanvasMatrix4.prototype.getAsArray = function()
{
return [
this.m11, this.m12, this.m13, this.m14,
this.m21, this.m22, this.m23, this.m24,
this.m31, this.m32, this.m33, this.m34,
this.m41, this.m42, this.m43, this.m44
];
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CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
{
return new WebGLFloatArray(this.getAsArray());
};
CanvasMatrix4.prototype.makeIdentity = function()
{
this.m11 = 1;
this.m12 = 0;
this.m13 = 0;
this.m14 = 0;
this.m21 = 0;
this.m22 = 1;
this.m23 = 0;
this.m24 = 0;
this.m31 = 0;
this.m32 = 0;
this.m33 = 1;
this.m34 = 0;
this.m41 = 0;
this.m42 = 0;
this.m43 = 0;
this.m44 = 1;
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CanvasMatrix4.prototype.transpose = function()
{
var tmp = this.m12;
this.m12 = this.m21;
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tmp = this.m13;
this.m13 = this.m31;
this.m31 = tmp;
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// Calculate the 4x4 determinant
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var det = this._determinant4x4();
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this.m22 /= det;
this.m23 /= det;
this.m24 /= det;
this.m31 /= det;
this.m32 /= det;
this.m33 /= det;
this.m34 /= det;
this.m41 /= det;
this.m42 /= det;
this.m43 /= det;
this.m44 /= det;
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CanvasMatrix4.prototype.translate = function(x,y,z)
{
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var matrix = new CanvasMatrix4();
matrix.m41 = x;
matrix.m42 = y;
matrix.m43 = z;
this.multRight(matrix);
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x = 1;
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matrix.m22 = y;
matrix.m33 = z;
this.multRight(matrix);
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CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
{
// angles are in degrees. Switch to radians
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angle /= 2;
var sinA = Math.sin(angle);
var cosA = Math.cos(angle);
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mat.m44 = 1;
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mat.m21 = -2 * sinA * cosA;
mat.m22 = 1 - 2 * sinA2;
mat.m23 = 0;
mat.m31 = 0;
mat.m32 = 0;
mat.m33 = 1;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else {
var x2 = x*x;
var y2 = y*y;
var z2 = z*z;
mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
}
this.multRight(mat);
};
CanvasMatrix4.prototype.multRight = function(mat)
{
var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21 +
this.m13 * mat.m31 + this.m14 * mat.m41);
var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22 +
this.m13 * mat.m32 + this.m14 * mat.m42);
var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23 +
this.m13 * mat.m33 + this.m14 * mat.m43);
var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24 +
this.m13 * mat.m34 + this.m14 * mat.m44);
var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21 +
this.m23 * mat.m31 + this.m24 * mat.m41);
var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22 +
this.m23 * mat.m32 + this.m24 * mat.m42);
var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23 +
this.m23 * mat.m33 + this.m24 * mat.m43);
var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24 +
this.m23 * mat.m34 + this.m24 * mat.m44);
var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21 +
this.m33 * mat.m31 + this.m34 * mat.m41);
var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22 +
this.m33 * mat.m32 + this.m34 * mat.m42);
var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23 +
this.m33 * mat.m33 + this.m34 * mat.m43);
var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24 +
this.m33 * mat.m34 + this.m34 * mat.m44);
var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21 +
this.m43 * mat.m31 + this.m44 * mat.m41);
var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22 +
this.m43 * mat.m32 + this.m44 * mat.m42);
var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23 +
this.m43 * mat.m33 + this.m44 * mat.m43);
var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24 +
this.m43 * mat.m34 + this.m44 * mat.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.multLeft = function(mat)
{
var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21 +
mat.m13 * this.m31 + mat.m14 * this.m41);
var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22 +
mat.m13 * this.m32 + mat.m14 * this.m42);
var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23 +
mat.m13 * this.m33 + mat.m14 * this.m43);
var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24 +
mat.m13 * this.m34 + mat.m14 * this.m44);
var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21 +
mat.m23 * this.m31 + mat.m24 * this.m41);
var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22 +
mat.m23 * this.m32 + mat.m24 * this.m42);
var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23 +
mat.m23 * this.m33 + mat.m24 * this.m43);
var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24 +
mat.m23 * this.m34 + mat.m24 * this.m44);
var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21 +
mat.m33 * this.m31 + mat.m34 * this.m41);
var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22 +
mat.m33 * this.m32 + mat.m34 * this.m42);
var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23 +
mat.m33 * this.m33 + mat.m34 * this.m43);
var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24 +
mat.m33 * this.m34 + mat.m34 * this.m44);
var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21 +
mat.m43 * this.m31 + mat.m44 * this.m41);
var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22 +
mat.m43 * this.m32 + mat.m44 * this.m42);
var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23 +
mat.m43 * this.m33 + mat.m44 * this.m43);
var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24 +
mat.m43 * this.m34 + mat.m44 * this.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
{
var tx = (left + right) / (left - right);
var ty = (top + bottom) / (bottom - top);
var tz = (far + near) / (near - far);
var matrix = new CanvasMatrix4();
matrix.m11 = 2 / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = 0;
matrix.m32 = 0;
matrix.m33 = -2 / (far - near);
matrix.m34 = 0;
matrix.m41 = tx;
matrix.m42 = ty;
matrix.m43 = tz;
matrix.m44 = 1;
this.multRight(matrix);
};
CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
{
var matrix = new CanvasMatrix4();
var A = (right + left) / (right - left);
var B = (top + bottom) / (top - bottom);
var C = -(far + near) / (far - near);
var D = -(2 * far * near) / (far - near);
matrix.m11 = (2 * near) / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 * near / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = A;
matrix.m32 = B;
matrix.m33 = C;
matrix.m34 = -1;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = D;
matrix.m44 = 0;
this.multRight(matrix);
};
CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
{
var top = Math.tan(fovy * Math.PI / 360) * zNear;
var bottom = -top;
var left = aspect * bottom;
var right = aspect * top;
this.frustum(left, right, bottom, top, zNear, zFar);
};
CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
{
var matrix = new CanvasMatrix4();
// Make rotation matrix
// Z vector
var zx = eyex - centerx;
var zy = eyey - centery;
var zz = eyez - centerz;
var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
if (mag) {
zx /= mag;
zy /= mag;
zz /= mag;
}
// Y vector
var yx = upx;
var yy = upy;
var yz = upz;
// X vector = Y cross Z
xx = yy * zz - yz * zy;
xy = -yx * zz + yz * zx;
xz = yx * zy - yy * zx;
// Recompute Y = Z cross X
yx = zy * xz - zz * xy;
yy = -zx * xz + zz * xx;
yx = zx * xy - zy * xx;
// cross product gives area of parallelogram, which is &lt; 1.0 for
// non-perpendicular unit-length vectors; so normalize x, y here
mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
if (mag) {
xx /= mag;
xy /= mag;
xz /= mag;
}
mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
if (mag) {
yx /= mag;
yy /= mag;
yz /= mag;
}
matrix.m11 = xx;
matrix.m12 = xy;
matrix.m13 = xz;
matrix.m14 = 0;
matrix.m21 = yx;
matrix.m22 = yy;
matrix.m23 = yz;
matrix.m24 = 0;
matrix.m31 = zx;
matrix.m32 = zy;
matrix.m33 = zz;
matrix.m34 = 0;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = 0;
matrix.m44 = 1;
matrix.translate(-eyex, -eyey, -eyez);
this.multRight(matrix);
};
// Support functions
CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
{
return a * d - b * c;
};
CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
{
return a1 * this._determinant2x2(b2, b3, c2, c3) -
b1 * this._determinant2x2(a2, a3, c2, c3) +
c1 * this._determinant2x2(a2, a3, b2, b3);
};
CanvasMatrix4.prototype._determinant4x4 = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
};
CanvasMatrix4.prototype._makeAdjoint = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
// Row column labeling reversed since we transpose rows &amp; columns
this.m11 = this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
this.m21 = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
this.m31 = this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
this.m41 = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
this.m12 = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
this.m22 = this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
this.m32 = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
this.m42 = this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
this.m13 = this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
this.m23 = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
this.m33 = this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
this.m43 = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
this.m14 = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
this.m24 = this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
this.m34 = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
this.m44 = this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
};&lt;/script&gt;
&lt;script&gt;// To generate the help pages for this library, use
// jsdoc --destination ../../../doc/rglwidgetClass --template ~/node_modules/jsdoc-baseline rglClass.src.js
// To validate, use
// setwd(&#34;.../inst/htmlwidgets/lib/rglClass&#34;)
// hints &lt;- js::jshint(readLines(&#34;rglClass.src.js&#34;))
// hints[, c(&#34;line&#34;, &#34;reason&#34;)]
/**
* The class of an rgl widget
* @class
*/
rglwidgetClass = function() {
this.canvas = null;
this.userMatrix = new CanvasMatrix4();
this.types = [];
this.prMatrix = new CanvasMatrix4();
this.mvMatrix = new CanvasMatrix4();
this.vp = null;
this.prmvMatrix = null;
this.origs = null;
this.gl = null;
this.scene = null;
this.select = {state: &#34;inactive&#34;, subscene: null, region: {p1: {x:0, y:0}, p2: {x:0, y:0}}};
this.drawing = false;
};
/**
* Multiply matrix by vector
* @returns {number[]}
* @param M {number[][]} Left operand
* @param v {number[]} Right operand
*/
rglwidgetClass.prototype.multMV = function(M, v) {
return [ M.m11 * v[0] + M.m12 * v[1] + M.m13 * v[2] + M.m14 * v[3],
M.m21 * v[0] + M.m22 * v[1] + M.m23 * v[2] + M.m24 * v[3],
M.m31 * v[0] + M.m32 * v[1] + M.m33 * v[2] + M.m34 * v[3],
M.m41 * v[0] + M.m42 * v[1] + M.m43 * v[2] + M.m44 * v[3]
];
};
/**
* Multiply row vector by Matrix
* @returns {number[]}
* @param v {number[]} left operand
* @param M {number[][]} right operand
*/
rglwidgetClass.prototype.multVM = function(v, M) {
return [ M.m11 * v[0] + M.m21 * v[1] + M.m31 * v[2] + M.m41 * v[3],
M.m12 * v[0] + M.m22 * v[1] + M.m32 * v[2] + M.m42 * v[3],
M.m13 * v[0] + M.m23 * v[1] + M.m33 * v[2] + M.m43 * v[3],
M.m14 * v[0] + M.m24 * v[1] + M.m34 * v[2] + M.m44 * v[3]
];
};
/**
* Euclidean length of a vector
* @returns {number}
* @param v {number[]}
*/
rglwidgetClass.prototype.vlen = function(v) {
return Math.sqrt(this.dotprod(v, v));
};
/**
* Dot product of two vectors
* @instance rglwidgetClass
* @returns {number}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.dotprod = function(a, b) {
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
};
/**
* Cross product of two vectors
* @returns {number[]}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.xprod = function(a, b) {
return [a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0]];
};
/**
* Bind vectors or matrices by columns
* @returns {number[][]}
* @param a {number[]|number[][]}
* @param b {number[]|number[][]}
*/
rglwidgetClass.prototype.cbind = function(a, b) {
if (b.length &lt; a.length)
b = this.repeatToLen(b, a.length);
else if (a.length &lt; b.length)
a = this.repeatToLen(a, b.length);
return a.map(function(currentValue, index, array) {
return currentValue.concat(b[index]);
});
};
/**
* Swap elements
* @returns {any[]}
* @param a {any[]}
* @param i {number} Element to swap
* @param j {number} Other element to swap
*/
rglwidgetClass.prototype.swap = function(a, i, j) {
var temp = a[i];
a[i] = a[j];
a[j] = temp;
};
/**
* Flatten a matrix into a vector
* @returns {any[]}
* @param a {any[][]}
*/
rglwidgetClass.prototype.flatten = function(arr, result) {
var value;
if (typeof result === &#34;undefined&#34;) result = [];
for (var i = 0, length = arr.length; i &lt; length; i++) {
value = arr[i];
if (Array.isArray(value)) {
this.flatten(value, result);
} else {
result.push(value);
}
}
return result;
};
/**
* set element of 1d or 2d array as if it was flattened.
* Column major, zero based!
* @returns {any[]|any[][]}
* @param {any[]|any[][]} a - array
* @param {number} i - element
* @param {any} value
*/
rglwidgetClass.prototype.setElement = function(a, i, value) {
if (Array.isArray(a[0])) {
var dim = a.length,
col = Math.floor(i/dim),
row = i % dim;
a[row][col] = value;
} else {
a[i] = value;
}
};
/**
* Transpose an array
* @returns {any[][]}
* @param {any[][]} a
*/
rglwidgetClass.prototype.transpose = function(a) {
var newArray = [],
n = a.length,
m = a[0].length,
i;
for(i = 0; i &lt; m; i++){
newArray.push([]);
}
for(i = 0; i &lt; n; i++){
for(var j = 0; j &lt; m; j++){
newArray[j].push(a[i][j]);
}
}
return newArray;
};
/**
* Calculate sum of squares of a numeric vector
* @returns {number}
* @param {number[]} x
*/
rglwidgetClass.prototype.sumsq = function(x) {
var result = 0, i;
for (i=0; i &lt; x.length; i++)
result += x[i]*x[i];
return result;
};
/**
* Convert a matrix to a CanvasMatrix4
* @returns {CanvasMatrix4}
* @param {number[][]|number[]} mat
*/
rglwidgetClass.prototype.toCanvasMatrix4 = function(mat) {
if (mat instanceof CanvasMatrix4)
return mat;
var result = new CanvasMatrix4();
mat = this.flatten(this.transpose(mat));
result.load(mat);
return result;
};
/**
* Convert an R-style numeric colour string to an rgb vector
* @returns {number[]}
* @param {string} s
*/
rglwidgetClass.prototype.stringToRgb = function(s) {
s = s.replace(&#34;#&#34;, &#34;&#34;);
var bigint = parseInt(s, 16);
return [((bigint &gt;&gt; 16) &amp; 255)/255,
((bigint &gt;&gt; 8) &amp; 255)/255,
(bigint &amp; 255)/255];
};
/**
* Take a component-by-component product of two 3 vectors
* @returns {number[]}
* @param {number[]} x
* @param {number[]} y
*/
rglwidgetClass.prototype.componentProduct = function(x, y) {
if (typeof y === &#34;undefined&#34;) {
this.alertOnce(&#34;Bad arg to componentProduct&#34;);
}
var result = new Float32Array(3), i;
for (i = 0; i&lt;3; i++)
result[i] = x[i]*y[i];
return result;
};
/**
* Get next higher power of two
* @returns { number }
* @param { number } value - input value
*/
rglwidgetClass.prototype.getPowerOfTwo = function(value) {
var pow = 1;
while(pow&lt;value) {
pow *= 2;
}
return pow;
};
/**
* Unique entries
* @returns { any[] }
* @param { any[] } arr - An array
*/
rglwidgetClass.prototype.unique = function(arr) {
arr = [].concat(arr);
return arr.filter(function(value, index, self) {
return self.indexOf(value) === index;
});
};
/**
* Shallow compare of arrays
* @returns { boolean }
* @param { any[] } a - An array
* @param { any[] } b - Another array
*/
rglwidgetClass.prototype.equalArrays = function(a, b) {
return a === b || (a &amp;&amp; b &amp;&amp;
a.length === b.length &amp;&amp;
a.every(function(v, i) {return v === b[i];}));
};
/**
* Repeat an array to a desired length
* @returns {any[]}
* @param {any | any[]} arr The input array
* @param {number} len The desired output length
*/
rglwidgetClass.prototype.repeatToLen = function(arr, len) {
arr = [].concat(arr);
while (arr.length &lt; len/2)
arr = arr.concat(arr);
return arr.concat(arr.slice(0, len - arr.length));
};
/**
* Give a single alert message, not to be repeated.
* @param {string} msg The message to give.
*/
rglwidgetClass.prototype.alertOnce = function(msg) {
if (typeof this.alerted !== &#34;undefined&#34;)
return;
this.alerted = true;
alert(msg);
};
rglwidgetClass.prototype.f_is_lit = 1;
rglwidgetClass.prototype.f_is_smooth = 2;
rglwidgetClass.prototype.f_has_texture = 4;
rglwidgetClass.prototype.f_depth_sort = 8;
rglwidgetClass.prototype.f_fixed_quads = 16;
rglwidgetClass.prototype.f_is_transparent = 32;
rglwidgetClass.prototype.f_is_lines = 64;
rglwidgetClass.prototype.f_sprites_3d = 128;
rglwidgetClass.prototype.f_sprite_3d = 256;
rglwidgetClass.prototype.f_is_subscene = 512;
rglwidgetClass.prototype.f_is_clipplanes = 1024;
rglwidgetClass.prototype.f_fixed_size = 2048;
rglwidgetClass.prototype.f_is_points = 4096;
rglwidgetClass.prototype.f_is_twosided = 8192;
rglwidgetClass.prototype.f_fat_lines = 16384;
rglwidgetClass.prototype.f_is_brush = 32768;
/**
* Which list does a particular id come from?
* @returns { string }
* @param {number} id The id to look up.
*/
rglwidgetClass.prototype.whichList = function(id) {
var obj = this.getObj(id),
flags = obj.flags;
if (obj.type === &#34;light&#34;)
return &#34;lights&#34;;
if (flags &amp; this.f_is_subscene)
return &#34;subscenes&#34;;
if (flags &amp; this.f_is_clipplanes)
return &#34;clipplanes&#34;;
if (flags &amp; this.f_is_transparent)
return &#34;transparent&#34;;
return &#34;opaque&#34;;
};
/**
* Get an object by id number.
* @returns { Object }
* @param {number} id
*/
rglwidgetClass.prototype.getObj = function(id) {
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;getObj id is &#34;+typeof id);
}
return this.scene.objects[id];
};
/**
* Get ids of a particular type from a subscene or the whole scene
* @returns { number[] }
* @param {string} type What type of object?
* @param {number} subscene Which subscene? If not given, find in the whole scene
*/
rglwidgetClass.prototype.getIdsByType = function(type, subscene) {
var
result = [], i, self = this;
if (typeof subscene === &#34;undefined&#34;) {
Object.keys(this.scene.objects).forEach(
function(key) {
key = parseInt(key, 10);
if (self.getObj(key).type === type)
result.push(key);
});
} else {
ids = this.getObj(subscene).objects;
for (i=0; i &lt; ids.length; i++) {
if (this.getObj(ids[i]).type === type) {
result.push(ids[i]);
}
}
}
return result;
};
/**
* Get a particular material property for an id
* @returns { any }
* @param {number} id Which object?
* @param {string} property Which material property?
*/
rglwidgetClass.prototype.getMaterial = function(id, property) {
var obj = this.getObj(id), mat;
if (typeof obj.material === &#34;undefined&#34;)
console.error(&#34;material undefined&#34;);
mat = obj.material[property];
if (typeof mat === &#34;undefined&#34;)
mat = this.scene.material[property];
return mat;
};
/**
* Is a particular id in a subscene?
* @returns { boolean }
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.inSubscene = function(id, subscene) {
return this.getObj(subscene).objects.indexOf(id) &gt; -1;
};
/**
* Add an id to a subscene.
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.addToSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
ids = [id],
obj = this.getObj(id), i;
if (typeof obj != &#34;undefined&#34; &amp;&amp; typeof (obj.newIds) !== &#34;undefined&#34;) {
ids = ids.concat(obj.newIds);
}
thesub.objects = [].concat(thesub.objects);
for (i = 0; i &lt; ids.length; i++) {
id = ids[i];
if (thesub.objects.indexOf(id) == -1) {
thelist = this.whichList(id);
thesub.objects.push(id);
thesub[thelist].push(id);
}
}
};
/**
* Delete an id from a subscene
* @param { number } id - the id to add
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.delFromSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
obj = this.getObj(id),
ids = [id], i;
if (typeof obj !== &#34;undefined&#34; &amp;&amp; typeof (obj.newIds) !== &#34;undefined&#34;)
ids = ids.concat(obj.newIds);
thesub.objects = [].concat(thesub.objects); // It might be a scalar
for (j=0; j&lt;ids.length;j++) {
id = ids[j];
i = thesub.objects.indexOf(id);
if (i &gt; -1) {
thesub.objects.splice(i, 1);
thelist = this.whichList(id);
i = thesub[thelist].indexOf(id);
thesub[thelist].splice(i, 1);
}
}
};
/**
* Set the ids in a subscene
* @param { number[] } ids - the ids to set
* @param { number } subsceneid - the id of the subscene
*/
rglwidgetClass.prototype.setSubsceneEntries = function(ids, subsceneid) {
var sub = this.getObj(subsceneid);
sub.objects = ids;
this.initSubscene(subsceneid);
};
/**
* Get the ids in a subscene
* @returns {number[]}
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getSubsceneEntries = function(subscene) {
return this.getObj(subscene).objects;
};
/**
* Get the ids of the subscenes within a subscene
* @returns { number[] }
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getChildSubscenes = function(subscene) {
return this.getObj(subscene).subscenes;
};
/**
* Start drawing
* @returns { boolean } Previous state
*/
rglwidgetClass.prototype.startDrawing = function() {
var value = this.drawing;
this.drawing = true;
return value;
};
/**
* Stop drawing and check for context loss
* @param { boolean } saved - Previous state
*/
rglwidgetClass.prototype.stopDrawing = function(saved) {
this.drawing = saved;
if (!saved &amp;&amp; this.gl &amp;&amp; this.gl.isContextLost())
this.restartCanvas();
};
/**
* Generate the vertex shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getVertexShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userVertexShader,
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
nclipplanes = this.countClipplanes(),
fixed_size = flags &amp; this.f_fixed_size,
is_points = flags &amp; this.f_is_points,
is_twosided = flags &amp; this.f_is_twosided,
fat_lines = flags &amp; this.f_fat_lines,
is_brush = flags &amp; this.f_is_brush,
result;
if (type === &#34;clipplanes&#34; || sprites_3d) return;
if (typeof userShader !== &#34;undefined&#34;) return userShader;
result = &#34; /* ****** &#34;+type+&#34; object &#34;+id+&#34; vertex shader ****** */\n&#34;+
&#34; attribute vec3 aPos;\n&#34;+
&#34; attribute vec4 aCol;\n&#34;+
&#34; uniform mat4 mvMatrix;\n&#34;+
&#34; uniform mat4 prMatrix;\n&#34;+
&#34; varying vec4 vCol;\n&#34;+
&#34; varying vec4 vPosition;\n&#34;;
if ((is_lit &amp;&amp; !fixed_quads &amp;&amp; !is_brush) || sprite_3d)
result = result + &#34; attribute vec3 aNorm;\n&#34;+
&#34; uniform mat4 normMatrix;\n&#34;+
&#34; varying vec3 vNormal;\n&#34;;
if (has_texture || type === &#34;text&#34;)
result = result + &#34; attribute vec2 aTexcoord;\n&#34;+
&#34; varying vec2 vTexcoord;\n&#34;;
if (fixed_size)
result = result + &#34; uniform vec2 textScale;\n&#34;;
if (fixed_quads)
result = result + &#34; attribute vec2 aOfs;\n&#34;;
else if (sprite_3d)
result = result + &#34; uniform vec3 uOrig;\n&#34;+
&#34; uniform float uSize;\n&#34;+
&#34; uniform mat4 usermat;\n&#34;;
if (is_twosided)
result = result + &#34; attribute vec3 aPos1;\n&#34;+
&#34; attribute vec3 aPos2;\n&#34;+
&#34; varying float normz;\n&#34;;
if (fat_lines) {
result = result + &#34; attribute vec3 aNext;\n&#34;+
&#34; attribute vec2 aPoint;\n&#34;+
&#34; varying vec2 vPoint;\n&#34;+
&#34; varying float vLength;\n&#34;+
&#34; uniform float uAspect;\n&#34;+
&#34; uniform float uLwd;\n&#34;;
}
result = result + &#34; void main(void) {\n&#34;;
if ((nclipplanes || (!fixed_quads &amp;&amp; !sprite_3d)) &amp;&amp; !is_brush)
result = result + &#34; vPosition = mvMatrix * vec4(aPos, 1.);\n&#34;;
if (!fixed_quads &amp;&amp; !sprite_3d &amp;&amp; !is_brush)
result = result + &#34; gl_Position = prMatrix * vPosition;\n&#34;;
if (is_points) {
var size = this.getMaterial(id, &#34;size&#34;);
result = result + &#34; gl_PointSize = &#34;+size.toFixed(1)+&#34;;\n&#34;;
}
result = result + &#34; vCol = aCol;\n&#34;;
if (is_lit &amp;&amp; !fixed_quads &amp;&amp; !sprite_3d &amp;&amp; !is_brush)
result = result + &#34; vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n&#34;;
if (has_texture || type == &#34;text&#34;)
result = result + &#34; vTexcoord = aTexcoord;\n&#34;;
if (fixed_size)
result = result + &#34; vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n&#34;+
&#34; pos = pos/pos.w;\n&#34;+
&#34; gl_Position = pos + vec4(aOfs*textScale, 0.,0.);\n&#34;;
if (type == &#34;sprites&#34; &amp;&amp; !fixed_size)
result = result + &#34; vec4 pos = mvMatrix * vec4(aPos, 1.);\n&#34;+
&#34; pos = pos/pos.w + vec4(aOfs, 0., 0.);\n&#34;+
&#34; gl_Position = prMatrix*pos;\n&#34;;
if (sprite_3d)
result = result + &#34; vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n&#34;+
&#34; vec4 pos = mvMatrix * vec4(uOrig, 1.);\n&#34;+
&#34; vPosition = pos/pos.w + vec4(uSize*(vec4(aPos, 1.)*usermat).xyz,0.);\n&#34;+
&#34; gl_Position = prMatrix * vPosition;\n&#34;;
if (is_twosided)
result = result + &#34; vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n&#34;+
&#34; pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n&#34;+
&#34; vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n&#34;+
&#34; pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n&#34;+
&#34; normz = pos1.x*pos2.y - pos1.y*pos2.x;\n&#34;;
if (fat_lines)
/* This code was inspired by Matt Deslauriers&#39; code in https://mattdesl.svbtle.com/drawing-lines-is-hard */
result = result + &#34; vec2 aspectVec = vec2(uAspect, 1.0);\n&#34;+
&#34; mat4 projViewModel = prMatrix * mvMatrix;\n&#34;+
&#34; vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n&#34;+
&#34; currentProjected = currentProjected/currentProjected.w;\n&#34;+
&#34; vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n&#34;+
&#34; vec2 currentScreen = currentProjected.xy * aspectVec;\n&#34;+
&#34; vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n&#34;+
&#34; float len = uLwd;\n&#34;+
&#34; vec2 dir = vec2(1.0, 0.0);\n&#34;+
&#34; vPoint = aPoint;\n&#34;+
&#34; vLength = length(nextScreen - currentScreen)/2.0;\n&#34;+
&#34; vLength = vLength/(vLength + len);\n&#34;+
&#34; if (vLength &gt; 0.0) {\n&#34;+
&#34; dir = normalize(nextScreen - currentScreen);\n&#34;+
&#34; }\n&#34;+
&#34; vec2 normal = vec2(-dir.y, dir.x);\n&#34;+
&#34; dir.x /= uAspect;\n&#34;+
&#34; normal.x /= uAspect;\n&#34;+
&#34; vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n&#34;+
&#34; gl_Position = currentProjected + offset;\n&#34;;
if (is_brush)
result = result + &#34; gl_Position = vec4(aPos, 1.);\n&#34;;
result = result + &#34; }\n&#34;;
// console.log(result);
return result;
};
/**
* Generate the fragment shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getFragmentShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userFragmentShader,
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
sprites_3d = flags &amp; this.f_sprites_3d,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
fat_lines = flags &amp; this.f_fat_lines,
is_transparent = flags &amp; this.f_is_transparent,
nclipplanes = this.countClipplanes(), i,
texture_format, nlights,
result;
if (type === &#34;clipplanes&#34; || sprites_3d) return;
if (typeof userShader !== &#34;undefined&#34;) return userShader;
if (has_texture)
texture_format = this.getMaterial(id, &#34;textype&#34;);
result = &#34;/* ****** &#34;+type+&#34; object &#34;+id+&#34; fragment shader ****** */\n&#34;+
&#34;#ifdef GL_ES\n&#34;+
&#34;#ifdef GL_FRAGMENT_PRECISION_HIGH\n&#34;+
&#34; precision highp float;\n&#34;+
&#34;#else\n&#34;+
&#34; precision mediump float;\n&#34;+
&#34;#endif\n&#34;+
&#34;#endif\n&#34;+
&#34; varying vec4 vCol; // carries alpha\n&#34;+
&#34; varying vec4 vPosition;\n&#34;;
if (has_texture || type === &#34;text&#34;)
result = result + &#34; varying vec2 vTexcoord;\n&#34;+
&#34; uniform sampler2D uSampler;\n&#34;;
if (is_lit &amp;&amp; !fixed_quads)
result = result + &#34; varying vec3 vNormal;\n&#34;;
for (i = 0; i &lt; nclipplanes; i++)
result = result + &#34; uniform vec4 vClipplane&#34;+i+&#34;;\n&#34;;
if (is_lit) {
nlights = this.countLights();
if (nlights)
result = result + &#34; uniform mat4 mvMatrix;\n&#34;;
else
is_lit = false;
}
if (is_lit) {
result = result + &#34; uniform vec3 emission;\n&#34;+
&#34; uniform float shininess;\n&#34;;
for (i=0; i &lt; nlights; i++) {
result = result + &#34; uniform vec3 ambient&#34; + i + &#34;;\n&#34;+
&#34; uniform vec3 specular&#34; + i +&#34;; // light*material\n&#34;+
&#34; uniform vec3 diffuse&#34; + i + &#34;;\n&#34;+
&#34; uniform vec3 lightDir&#34; + i + &#34;;\n&#34;+
&#34; uniform bool viewpoint&#34; + i + &#34;;\n&#34;+
&#34; uniform bool finite&#34; + i + &#34;;\n&#34;;
}
}
if (is_twosided)
result = result + &#34; uniform bool front;\n&#34;+
&#34; varying float normz;\n&#34;;
if (fat_lines)
result = result + &#34; varying vec2 vPoint;\n&#34;+
&#34; varying float vLength;\n&#34;;
result = result + &#34; void main(void) {\n&#34;;
if (fat_lines) {
result = result + &#34; vec2 point = vPoint;\n&#34;+
&#34; bool neg = point.y &lt; 0.0;\n&#34;+
&#34; point.y = neg ? &#34;+
&#34; (point.y + vLength)/(1.0 - vLength) :\n&#34;+
&#34; -(point.y - vLength)/(1.0 - vLength);\n&#34;;
if (is_transparent &amp;&amp; type == &#34;linestrip&#34;)
result = result+&#34; if (neg &amp;&amp; length(point) &lt;= 1.0) discard;\n&#34;;
result = result + &#34; point.y = min(point.y, 0.0);\n&#34;+
&#34; if (length(point) &gt; 1.0) discard;\n&#34;;
}
for (i=0; i &lt; nclipplanes;i++)
result = result + &#34; if (dot(vPosition, vClipplane&#34;+i+&#34;) &lt; 0.0) discard;\n&#34;;
if (fixed_quads) {
result = result + &#34; vec3 n = vec3(0., 0., 1.);\n&#34;;
} else if (is_lit) {
result = result + &#34; vec3 n = normalize(vNormal);\n&#34;;
}
if (is_twosided) {
result = result + &#34; if ((normz &lt;= 0.) != front) discard;\n&#34;;
}
if (is_lit) {
result = result + &#34; vec3 eye = normalize(-vPosition.xyz);\n&#34;+
&#34; vec3 lightdir;\n&#34;+
&#34; vec4 colDiff;\n&#34;+
&#34; vec3 halfVec;\n&#34;+
&#34; vec4 lighteffect = vec4(emission, 0.);\n&#34;+
&#34; vec3 col;\n&#34;+
&#34; float nDotL;\n&#34;;
if (!fixed_quads) {
result = result + &#34; n = -faceforward(n, n, eye);\n&#34;;
}
for (i=0; i &lt; nlights; i++) {
result = result + &#34; colDiff = vec4(vCol.rgb * diffuse&#34; + i + &#34;, vCol.a);\n&#34;+
&#34; lightdir = lightDir&#34; + i + &#34;;\n&#34;+
&#34; if (!viewpoint&#34; + i +&#34;)\n&#34;+
&#34; lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n&#34;+
&#34; if (!finite&#34; + i + &#34;) {\n&#34;+
&#34; halfVec = normalize(lightdir + eye);\n&#34;+
&#34; } else {\n&#34;+
&#34; lightdir = normalize(lightdir - vPosition.xyz);\n&#34;+
&#34; halfVec = normalize(lightdir + eye);\n&#34;+
&#34; }\n&#34;+
&#34; col = ambient&#34; + i + &#34;;\n&#34;+
&#34; nDotL = dot(n, lightdir);\n&#34;+
&#34; col = col + max(nDotL, 0.) * colDiff.rgb;\n&#34;+
&#34; col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular&#34; + i + &#34;;\n&#34;+
&#34; lighteffect = lighteffect + vec4(col, colDiff.a);\n&#34;;
}
} else {
result = result + &#34; vec4 colDiff = vCol;\n&#34;+
&#34; vec4 lighteffect = colDiff;\n&#34;;
}
if (type === &#34;text&#34;)
result = result + &#34; vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n&#34;;
if (has_texture) {
result = result + {
rgb: &#34; vec4 textureColor = lighteffect*vec4(texture2D(uSampler, vTexcoord).rgb, 1.);\n&#34;,
rgba: &#34; vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n&#34;,
alpha: &#34; vec4 textureColor = texture2D(uSampler, vTexcoord);\n&#34;+
&#34; float luminance = dot(vec3(1.,1.,1.), textureColor.rgb)/3.;\n&#34;+
&#34; textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n&#34;,
luminance: &#34; vec4 textureColor = vec4(lighteffect.rgb*dot(texture2D(uSampler, vTexcoord).rgb, vec3(1.,1.,1.))/3., lighteffect.a);\n&#34;,
&#34;luminance.alpha&#34;:&#34; vec4 textureColor = texture2D(uSampler, vTexcoord);\n&#34;+
&#34; float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n&#34;+
&#34; textureColor = vec4(lighteffect.rgb*luminance, lighteffect.a*textureColor.a);\n&#34;
}[texture_format]+
&#34; gl_FragColor = textureColor;\n&#34;;
} else if (type === &#34;text&#34;) {
result = result + &#34; if (textureColor.a &lt; 0.1)\n&#34;+
&#34; discard;\n&#34;+
&#34; else\n&#34;+
&#34; gl_FragColor = textureColor;\n&#34;;
} else
result = result + &#34; gl_FragColor = lighteffect;\n&#34;;
//if (fat_lines)
// result = result + &#34; gl_FragColor = vec4(0.0, abs(point.x), abs(point.y), 1.0);&#34;
result = result + &#34; }\n&#34;;
// console.log(result);
return result;
};
/**
* Call gl functions to create and compile shader
* @returns {Object}
* @param { number } shaderType - gl code for shader type
* @param { string } code - code for the shader
*/
rglwidgetClass.prototype.getShader = function(shaderType, code) {
var gl = this.gl, shader;
shader = gl.createShader(shaderType);
gl.shaderSource(shader, code);
gl.compileShader(shader);
if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS) &amp;&amp; !gl.isContextLost())
alert(gl.getShaderInfoLog(shader));
return shader;
};
/**
* Handle a texture after its image has been loaded
* @param { Object } texture - the gl texture object
* @param { Object } textureCanvas - the canvas holding the image
*/
rglwidgetClass.prototype.handleLoadedTexture = function(texture, textureCanvas) {
var gl = this.gl || this.initGL();
gl.pixelStorei(gl.UNPACK_FLIP_Y_WEBGL, true);
gl.bindTexture(gl.TEXTURE_2D, texture);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, textureCanvas);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR_MIPMAP_NEAREST);
gl.generateMipmap(gl.TEXTURE_2D);
gl.bindTexture(gl.TEXTURE_2D, null);
};
/**
* Get maximum dimension of texture in current browser.
* @returns {number}
*/
rglwidgetClass.prototype.getMaxTexSize = function() {
var gl = this.gl || this.initGL();
return Math.min(4096, gl.getParameter(gl.MAX_TEXTURE_SIZE));
};
/**
* Load an image to a texture
* @param { string } uri - The image location
* @param { Object } texture - the gl texture object
*/
rglwidgetClass.prototype.loadImageToTexture = function(uri, texture) {
var canvas = this.textureCanvas,
ctx = canvas.getContext(&#34;2d&#34;),
image = new Image(),
self = this;
image.onload = function() {
var w = image.width,
h = image.height,
canvasX = self.getPowerOfTwo(w),
canvasY = self.getPowerOfTwo(h),
gl = self.gl || self.initGL(),
maxTexSize = self.getMaxTexSize();
while (canvasX &gt; 1 &amp;&amp; canvasY &gt; 1 &amp;&amp; (canvasX &gt; maxTexSize || canvasY &gt; maxTexSize)) {
canvasX /= 2;
canvasY /= 2;
}
canvas.width = canvasX;
canvas.height = canvasY;
ctx.imageSmoothingEnabled = true;
ctx.drawImage(image, 0, 0, canvasX, canvasY);
self.handleLoadedTexture(texture, canvas);
self.drawScene();
};
image.src = uri;
};
/**
* Draw text to the texture canvas
* @returns { Object } object with text measurements
* @param { string } text - the text
* @param { number } cex - expansion
* @param { string } family - font family
* @param { number } font - font number
*/
rglwidgetClass.prototype.drawTextToCanvas = function(text, cex, family, font) {
var canvasX, canvasY,
textY,
scaling = 20,
textColour = &#34;white&#34;,
backgroundColour = &#34;rgba(0,0,0,0)&#34;,
canvas = this.textureCanvas,
ctx = canvas.getContext(&#34;2d&#34;),
i, textHeight = 0, textHeights = [], width, widths = [],
offsetx, offsety = 0, line, lines = [], offsetsx = [],
offsetsy = [], lineoffsetsy = [], fontStrings = [],
maxTexSize = this.getMaxTexSize(),
getFontString = function(i) {
textHeights[i] = scaling*cex[i];
var fontString = textHeights[i] + &#34;px&#34;,
family0 = family[i],
font0 = font[i];
if (family0 === &#34;sans&#34;)
family0 = &#34;sans-serif&#34;;
else if (family0 === &#34;mono&#34;)
family0 = &#34;monospace&#34;;
fontString = fontString + &#34; &#34; + family0;
if (font0 === 2 || font0 === 4)
fontString = &#34;bold &#34; + fontString;
if (font0 === 3 || font0 === 4)
fontString = &#34;italic &#34; + fontString;
return fontString;
};
cex = this.repeatToLen(cex, text.length);
family = this.repeatToLen(family, text.length);
font = this.repeatToLen(font, text.length);
canvasX = 1;
line = -1;
offsetx = maxTexSize;
for (i = 0; i &lt; text.length; i++) {
ctx.font = fontStrings[i] = getFontString(i);
width = widths[i] = ctx.measureText(text[i]).width;
if (offsetx + width &gt; maxTexSize) {
line += 1;
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
if (offsety &gt; maxTexSize)
console.error(&#34;Too many strings for texture.&#34;);
textHeight = 0;
offsetx = 0;
}
textHeight = Math.max(textHeight, textHeights[i]);
offsetsx[i] = offsetx;
offsetx += width;
canvasX = Math.max(canvasX, offsetx);
lines[i] = line;
}
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
for (i = 0; i &lt; text.length; i++) {
offsetsy[i] = lineoffsetsy[lines[i]];
}
canvasX = this.getPowerOfTwo(canvasX);
canvasY = this.getPowerOfTwo(offsety);
canvas.width = canvasX;
canvas.height = canvasY;
ctx.fillStyle = backgroundColour;
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.textBaseline = &#34;alphabetic&#34;;
for(i = 0; i &lt; text.length; i++) {
ctx.font = fontStrings[i];
ctx.fillStyle = textColour;
ctx.textAlign = &#34;left&#34;;
ctx.fillText(text[i], offsetsx[i], offsetsy[i]);
}
return {canvasX:canvasX, canvasY:canvasY,
widths:widths, textHeights:textHeights,
offsetsx:offsetsx, offsetsy:offsetsy};
};
/**
* Set the gl viewport and scissor test
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setViewport = function(id) {
var gl = this.gl || this.initGL(),
vp = this.getObj(id).par3d.viewport,
x = vp.x*this.canvas.width,
y = vp.y*this.canvas.height,
width = vp.width*this.canvas.width,
height = vp.height*this.canvas.height;
this.vp = {x:x, y:y, width:width, height:height};
gl.viewport(x, y, width, height);
gl.scissor(x, y, width, height);
gl.enable(gl.SCISSOR_TEST);
};
/**
* Set the projection matrix for a subscene
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setprMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.projection;
if (embedding === &#34;replace&#34;)
this.prMatrix.makeIdentity();
else
this.setprMatrix(subscene.parent);
if (embedding === &#34;inherit&#34;)
return;
// This is based on the Frustum::enclose code from geom.cpp
var bbox = subscene.par3d.bbox,
scale = subscene.par3d.scale,
ranges = [(bbox[1]-bbox[0])*scale[0]/2,
(bbox[3]-bbox[2])*scale[1]/2,
(bbox[5]-bbox[4])*scale[2]/2],
radius = Math.sqrt(this.sumsq(ranges))*1.1; // A bit bigger to handle labels
if (radius &lt;= 0) radius = 1;
var observer = subscene.par3d.observer,
distance = observer[2],
FOV = subscene.par3d.FOV, ortho = FOV === 0,
t = ortho ? 1 : Math.tan(FOV*Math.PI/360),
near = distance - radius,
far = distance + radius,
hlen,
aspect = this.vp.width/this.vp.height,
z = subscene.par3d.zoom,
userProjection = subscene.par3d.userProjection;
if (far &lt; 0.0)
far = 1.0;
if (near &lt; far/100.0)
near = far/100.0;
hlen = t*near;
if (ortho) {
if (aspect &gt; 1)
this.prMatrix.ortho(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.ortho(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
} else {
if (aspect &gt; 1)
this.prMatrix.frustum(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.frustum(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
}
this.prMatrix.multRight(userProjection);
};
/**
* Set the model-view matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmvMatrix = function(id) {
var observer = this.getObj(id).par3d.observer;
this.mvMatrix.makeIdentity();
this.setmodelMatrix(id);
this.mvMatrix.translate(-observer[0], -observer[1], -observer[2]);
};
/**
* Set the model matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmodelMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.model;
if (embedding !== &#34;inherit&#34;) {
var scale = subscene.par3d.scale,
bbox = subscene.par3d.bbox,
center = [(bbox[0]+bbox[1])/2,
(bbox[2]+bbox[3])/2,
(bbox[4]+bbox[5])/2];
this.mvMatrix.translate(-center[0], -center[1], -center[2]);
this.mvMatrix.scale(scale[0], scale[1], scale[2]);
this.mvMatrix.multRight( subscene.par3d.userMatrix );
}
if (embedding !== &#34;replace&#34;)
this.setmodelMatrix(subscene.parent);
};
/**
* Set the normals matrix for a subscene
* @param { number } subsceneid - id of the subscene
*/
rglwidgetClass.prototype.setnormMatrix = function(subsceneid) {
var self = this,
recurse = function(id) {
var sub = self.getObj(id),
embedding = sub.embeddings.model;
if (embedding !== &#34;inherit&#34;) {
var scale = sub.par3d.scale;
self.normMatrix.scale(1/scale[0], 1/scale[1], 1/scale[2]);
self.normMatrix.multRight(sub.par3d.userMatrix);
}
if (embedding !== &#34;replace&#34;)
recurse(sub.parent);
};
self.normMatrix.makeIdentity();
recurse(subsceneid);
};
/**
* Set the combined projection-model-view matrix
*/
rglwidgetClass.prototype.setprmvMatrix = function() {
this.prmvMatrix = new CanvasMatrix4( this.mvMatrix );
this.prmvMatrix.multRight( this.prMatrix );
};
/**
* Count clipping planes in a scene
* @returns {number}
*/
rglwidgetClass.prototype.countClipplanes = function() {
return this.countObjs(&#34;clipplanes&#34;);
};
/**
* Count lights in a scene
* @returns { number }
*/
rglwidgetClass.prototype.countLights = function() {
return this.countObjs(&#34;light&#34;);
};
/**
* Count objects of specific type in a scene
* @returns { number }
* @param { string } type - Type of object to count
*/
rglwidgetClass.prototype.countObjs = function(type) {
var self = this,
bound = 0;
Object.keys(this.scene.objects).forEach(
function(key) {
if (self.getObj(parseInt(key, 10)).type === type)
bound = bound + 1;
});
return bound;
};
/**
* Initialize a subscene
* @param { number } id - id of subscene.
*/
rglwidgetClass.prototype.initSubscene = function(id) {
var sub = this.getObj(id),
i, obj;
if (sub.type !== &#34;subscene&#34;)
return;
sub.par3d.userMatrix = this.toCanvasMatrix4(sub.par3d.userMatrix);
sub.par3d.userProjection = this.toCanvasMatrix4(sub.par3d.userProjection);
sub.par3d.userProjection.transpose();
sub.par3d.listeners = [].concat(sub.par3d.listeners);
sub.backgroundId = undefined;
sub.subscenes = [];
sub.clipplanes = [];
sub.transparent = [];
sub.opaque = [];
sub.lights = [];
for (i=0; i &lt; sub.objects.length; i++) {
obj = this.getObj(sub.objects[i]);
if (typeof obj === &#34;undefined&#34;) {
sub.objects.splice(i, 1);
i--;
} else if (obj.type === &#34;background&#34;)
sub.backgroundId = obj.id;
else
sub[this.whichList(obj.id)].push(obj.id);
}
};
/**
* Copy object
* @param { number } id - id of object to copy
* @param { string } reuse - Document id of scene to reuse
*/
rglwidgetClass.prototype.copyObj = function(id, reuse) {
var obj = this.getObj(id),
prev = document.getElementById(reuse);
if (prev !== null) {
prev = prev.rglinstance;
var
prevobj = prev.getObj(id),
fields = [&#34;flags&#34;, &#34;type&#34;,
&#34;colors&#34;, &#34;vertices&#34;, &#34;centers&#34;,
&#34;normals&#34;, &#34;offsets&#34;,
&#34;texts&#34;, &#34;cex&#34;, &#34;family&#34;, &#34;font&#34;, &#34;adj&#34;,
&#34;material&#34;,
&#34;radii&#34;,
&#34;texcoords&#34;,
&#34;userMatrix&#34;, &#34;ids&#34;,
&#34;dim&#34;,
&#34;par3d&#34;, &#34;userMatrix&#34;,
&#34;viewpoint&#34;, &#34;finite&#34;,
&#34;pos&#34;],
i;
for (i = 0; i &lt; fields.length; i++) {
if (typeof prevobj[fields[i]] !== &#34;undefined&#34;)
obj[fields[i]] = prevobj[fields[i]];
}
} else
console.warn(&#34;copyObj failed&#34;);
};
/**
* Update the triangles used to display a plane
* @param { number } id - id of the plane
* @param { Object } bbox - bounding box in which to display the plane
*/
rglwidgetClass.prototype.planeUpdateTriangles = function(id, bbox) {
var perms = [[0,0,1], [1,2,2], [2,1,0]],
x, xrow, elem, A, d, nhits, i, j, k, u, v, w, intersect, which, v0, v2, vx, reverse,
face1 = [], face2 = [], normals = [],
obj = this.getObj(id),
nPlanes = obj.normals.length;
obj.bbox = bbox;
obj.vertices = [];
obj.initialized = false;
for (elem = 0; elem &lt; nPlanes; elem++) {
// Vertex Av = normal.getRecycled(elem);
x = [];
A = obj.normals[elem];
d = obj.offsets[elem][0];
nhits = 0;
for (i=0; i&lt;3; i++)
for (j=0; j&lt;2; j++)
for (k=0; k&lt;2; k++) {
u = perms[0][i];
v = perms[1][i];
w = perms[2][i];
if (A[w] !== 0.0) {
intersect = -(d + A[u]*bbox[j+2*u] + A[v]*bbox[k+2*v])/A[w];
if (bbox[2*w] &lt; intersect &amp;&amp; intersect &lt; bbox[1+2*w]) {
xrow = [];
xrow[u] = bbox[j+2*u];
xrow[v] = bbox[k+2*v];
xrow[w] = intersect;
x.push(xrow);
face1[nhits] = j + 2*u;
face2[nhits] = k + 2*v;
nhits++;
}
}
}
if (nhits &gt; 3) {
/* Re-order the intersections so the triangles work */
for (i=0; i&lt;nhits-2; i++) {
which = 0; /* initialize to suppress warning */
for (j=i+1; j&lt;nhits; j++) {
if (face1[i] == face1[j] || face1[i] == face2[j] ||
face2[i] == face1[j] || face2[i] == face2[j] ) {
which = j;
break;
}
}
if (which &gt; i+1) {
this.swap(x, i+1, which);
this.swap(face1, i+1, which);
this.swap(face2, i+1, which);
}
}
}
if (nhits &gt;= 3) {
/* Put in order so that the normal points out the FRONT of the faces */
v0 = [x[0][0] - x[1][0] , x[0][1] - x[1][1], x[0][2] - x[1][2]];
v2 = [x[2][0] - x[1][0] , x[2][1] - x[1][1], x[2][2] - x[1][2]];
/* cross-product */
vx = this.xprod(v0, v2);
reverse = this.dotprod(vx, A) &gt; 0;
for (i=0; i&lt;nhits-2; i++) {
obj.vertices.push(x[0]);
normals.push(A);
for (j=1; j&lt;3; j++) {
obj.vertices.push(x[i + (reverse ? 3-j : j)]);
normals.push(A);
}
}
}
}
obj.pnormals = normals;
};
rglwidgetClass.prototype.getAdj = function (pos, offset, text) {
switch(pos) {
case 1: return [0.5, 1 + offset];
case 2: return [1 + offset/text.length, 0.5];
case 3: return [0.5, -offset];
case 4: return [-offset/text.length, 0.5];
}
}
/**
* Initialize object for display
* @param { number } id - id of object to initialize
*/
rglwidgetClass.prototype.initObj = function(id) {
var obj = this.getObj(id),
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
is_lines = flags &amp; this.f_is_lines,
fat_lines = flags &amp; this.f_fat_lines,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
is_transparent = obj.is_transparent,
depth_sort = flags &amp; this.f_depth_sort,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
fixed_size = flags &amp; this.f_fixed_size,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
is_brush = flags &amp; this.f_is_brush,
gl = this.gl || this.initGL(),
polygon_offset,
texinfo, drawtype, nclipplanes, f, nrows, oldrows,
i,j,v,v1,v2, mat, uri, matobj, pass, passes, pmode,
dim, nx, nz, attr;
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;initObj id is &#34;+typeof id);
}
obj.initialized = true;
if (type === &#34;bboxdeco&#34; || type === &#34;subscene&#34;)
return;
if (type === &#34;light&#34;) {
obj.ambient = new Float32Array(obj.colors[0].slice(0,3));
obj.diffuse = new Float32Array(obj.colors[1].slice(0,3));
obj.specular = new Float32Array(obj.colors[2].slice(0,3));
obj.lightDir = new Float32Array(obj.vertices[0]);
return;
}
if (type === &#34;clipplanes&#34;) {
obj.vClipplane = this.flatten(this.cbind(obj.normals, obj.offsets));
return;
}
if (type === &#34;background&#34; &amp;&amp; typeof obj.ids !== &#34;undefined&#34;) {
obj.quad = this.flatten([].concat(obj.ids));
return;
}
polygon_offset = this.getMaterial(id, &#34;polygon_offset&#34;);
if (polygon_offset[0] != 0 || polygon_offset[1] != 0)
obj.polygon_offset = polygon_offset;
if (is_transparent) {
depth_sort = [&#34;triangles&#34;, &#34;quads&#34;, &#34;surface&#34;,
&#34;spheres&#34;, &#34;sprites&#34;, &#34;text&#34;].indexOf(type) &gt;= 0;
}
if (is_brush)
this.initSelection(id);
if (typeof obj.vertices === &#34;undefined&#34;)
obj.vertices = [];
v = obj.vertices;
obj.vertexCount = v.length;
if (!obj.vertexCount) return;
if (is_twosided) {
if (typeof obj.userAttributes === &#34;undefined&#34;)
obj.userAttributes = {};
v1 = Array(v.length);
v2 = Array(v.length);
if (obj.type == &#34;triangles&#34; || obj.type == &#34;quads&#34;) {
if (obj.type == &#34;triangles&#34;)
nrow = 3;
else
nrow = 4;
for (i=0; i&lt;Math.floor(v.length/nrow); i++)
for (j=0; j&lt;nrow; j++) {
v1[nrow*i + j] = v[nrow*i + ((j+1) % nrow)];
v2[nrow*i + j] = v[nrow*i + ((j+2) % nrow)];
}
} else if (obj.type == &#34;surface&#34;) {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
for (j=0; j&lt;nx; j++) {
for (i=0; i&lt;nz; i++) {
if (i+1 &lt; nz &amp;&amp; j+1 &lt; nx) {
v2[j + nx*i] = v[j + nx*(i+1)];
v1[j + nx*i] = v[j+1 + nx*(i+1)];
} else if (i+1 &lt; nz) {
v2[j + nx*i] = v[j-1 + nx*i];
v1[j + nx*i] = v[j + nx*(i+1)];
} else {
v2[j + nx*i] = v[j + nx*(i-1)];
v1[j + nx*i] = v[j-1 + nx*(i-1)];
}
}
}
}
obj.userAttributes.aPos1 = v1;
obj.userAttributes.aPos2 = v2;
}
if (!sprites_3d) {
if (gl.isContextLost()) return;
obj.prog = gl.createProgram();
gl.attachShader(obj.prog, this.getShader( gl.VERTEX_SHADER,
this.getVertexShader(id) ));
gl.attachShader(obj.prog, this.getShader( gl.FRAGMENT_SHADER,
this.getFragmentShader(id) ));
// Force aPos to location 0, aCol to location 1
gl.bindAttribLocation(obj.prog, 0, &#34;aPos&#34;);
gl.bindAttribLocation(obj.prog, 1, &#34;aCol&#34;);
gl.linkProgram(obj.prog);
var linked = gl.getProgramParameter(obj.prog, gl.LINK_STATUS);
if (!linked) {
// An error occurred while linking
var lastError = gl.getProgramInfoLog(obj.prog);
console.warn(&#34;Error in program linking:&#34; + lastError);
gl.deleteProgram(obj.prog);
return;
}
}
if (type === &#34;text&#34;) {
texinfo = this.drawTextToCanvas(obj.texts,
this.flatten(obj.cex),
this.flatten(obj.family),
this.flatten(obj.family));
}
if (fixed_quads &amp;&amp; !sprites_3d) {
obj.ofsLoc = gl.getAttribLocation(obj.prog, &#34;aOfs&#34;);
}
if (sprite_3d) {
obj.origLoc = gl.getUniformLocation(obj.prog, &#34;uOrig&#34;);
obj.sizeLoc = gl.getUniformLocation(obj.prog, &#34;uSize&#34;);
obj.usermatLoc = gl.getUniformLocation(obj.prog, &#34;usermat&#34;);
}
if (has_texture || type == &#34;text&#34;) {
if (!obj.texture)
obj.texture = gl.createTexture();
obj.texLoc = gl.getAttribLocation(obj.prog, &#34;aTexcoord&#34;);
obj.sampler = gl.getUniformLocation(obj.prog, &#34;uSampler&#34;);
}
if (has_texture) {
mat = obj.material;
if (typeof mat.uri !== &#34;undefined&#34;)
uri = mat.uri;
else if (typeof mat.uriElementId === &#34;undefined&#34;) {
matobj = this.getObj(mat.uriId);
if (typeof matobj !== &#34;undefined&#34;) {
uri = matobj.material.uri;
} else {
uri = &#34;&#34;;
}
} else
uri = document.getElementById(mat.uriElementId).rglinstance.getObj(mat.uriId).material.uri;
this.loadImageToTexture(uri, obj.texture);
}
if (type === &#34;text&#34;) {
this.handleLoadedTexture(obj.texture, this.textureCanvas);
}
var stride = 3, nc, cofs, nofs, radofs, oofs, tofs, vnew, fnew,
nextofs = -1, pointofs = -1, alias, colors, key, selection, filter, adj, pos, offset;
obj.alias = undefined;
colors = obj.colors;
j = this.scene.crosstalk.id.indexOf(id);
if (j &gt;= 0) {
key = this.scene.crosstalk.key[j];
options = this.scene.crosstalk.options[j];
colors = colors.slice(0);
for (i = 0; i &lt; v.length; i++)
colors[i] = obj.colors[i % obj.colors.length].slice(0);
if ( (selection = this.scene.crosstalk.selection) &amp;&amp;
(selection.length || !options.selectedIgnoreNone) )
for (i = 0; i &lt; v.length; i++) {
if (!selection.includes(key[i])) {
if (options.deselectedColor)
colors[i] = options.deselectedColor.slice(0);
colors[i][3] = colors[i][3]*options.deselectedFade; /* default: mostly transparent if not selected */
} else if (options.selectedColor)
colors[i] = options.selectedColor.slice(0);
}
if ( (filter = this.scene.crosstalk.filter) )
for (i = 0; i &lt; v.length; i++)
if (!filter.includes(key[i])) {
if (options.filteredColor)
colors[i] = options.filteredColor.slice(0);
colors[i][3] = colors[i][3]*options.filteredFade; /* default: completely hidden if filtered */
}
}
nc = obj.colorCount = colors.length;
if (nc &gt; 1) {
cofs = stride;
stride = stride + 4;
v = this.cbind(v, colors);
} else {
cofs = -1;
obj.onecolor = this.flatten(colors);
}
if (typeof obj.normals !== &#34;undefined&#34;) {
nofs = stride;
stride = stride + 3;
v = this.cbind(v, typeof obj.pnormals !== &#34;undefined&#34; ? obj.pnormals : obj.normals);
} else
nofs = -1;
if (typeof obj.radii !== &#34;undefined&#34;) {
radofs = stride;
stride = stride + 1;
// FIXME: always concat the radii?
if (obj.radii.length === v.length) {
v = this.cbind(v, obj.radii);
} else if (obj.radii.length === 1) {
v = v.map(function(row, i, arr) { return row.concat(obj.radii[0]);});
}
} else
radofs = -1;
// Add default indices
f = Array(v.length);
for (i = 0; i &lt; v.length; i++)
f[i] = i;
obj.f = [f,f];
if (type == &#34;sprites&#34; &amp;&amp; !sprites_3d) {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
fnew = new Array(4*v.length);
alias = new Array(v.length);
var rescale = fixed_size ? 72 : 1,
size = obj.radii, s = rescale*size[0]/2;
last = v.length;
f = obj.f[0];
for (i=0; i &lt; v.length; i++) {
if (size.length &gt; 1)
s = rescale*size[i]/2;
vnew[i] = v[i].concat([0,0,-s,-s]);
fnew[4*i] = f[i];
vnew[last]= v[i].concat([1,0, s,-s]);
fnew[4*i+1] = last++;
vnew[last]= v[i].concat([1,1, s, s]);
fnew[4*i+2] = last++;
vnew[last]= v[i].concat([0,1,-s, s]);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (type === &#34;text&#34;) {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
f = obj.f[0];
fnew = new Array(4*f.length);
alias = new Array(v.length);
last = v.length;
adj = this.flatten(obj.adj);
if (typeof obj.pos !== &#34;undefined&#34;) {
pos = this.flatten(obj.pos);
offset = adj[0];
}
for (i=0; i &lt; v.length; i++) {
if (typeof pos !== &#34;undefined&#34;)
adj = this.getAdj(pos[i % pos.length], offset, obj.texts[i]);
vnew[i] = v[i].concat([0,-0.5]).concat(adj);
fnew[4*i] = f[i];
vnew[last] = v[i].concat([1,-0.5]).concat(adj);
fnew[4*i+1] = last++;
vnew[last] = v[i].concat([1, 1.5]).concat(adj);
fnew[4*i+2] = last++;
vnew[last] = v[i].concat([0, 1.5]).concat(adj);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
for (j=0; j &lt; 4; j++) {
v1 = vnew[fnew[4*i+j]];
v1[tofs+2] = 2*(v1[tofs]-v1[tofs+2])*texinfo.widths[i];
v1[tofs+3] = 2*(v1[tofs+1]-v1[tofs+3])*texinfo.textHeights[i];
v1[tofs] = (texinfo.offsetsx[i] + v1[tofs]*texinfo.widths[i])/texinfo.canvasX;
v1[tofs+1] = 1.0-(texinfo.offsetsy[i] -
v1[tofs+1]*texinfo.textHeights[i])/texinfo.canvasY;
vnew[fnew[4*i+j]] = v1;
}
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (typeof obj.texcoords !== &#34;undefined&#34;) {
tofs = stride;
stride += 2;
oofs = -1;
v = this.cbind(v, obj.texcoords);
} else {
tofs = -1;
oofs = -1;
}
obj.alias = alias;
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
obj.userAttribOffsets = {};
obj.userAttribLocations = {};
obj.userAttribSizes = {};
for (attr in obj.userAttributes) {
obj.userAttribLocations[attr] = gl.getAttribLocation(obj.prog, attr);
if (obj.userAttribLocations[attr] &gt;= 0) { // Attribute may not have been used
obj.userAttribOffsets[attr] = stride;
v = this.cbind(v, obj.userAttributes[attr]);
stride = v[0].length;
obj.userAttribSizes[attr] = stride - obj.userAttribOffsets[attr];
}
}
}
if (typeof obj.userUniforms !== &#34;undefined&#34;) {
obj.userUniformLocations = {};
for (attr in obj.userUniforms)
obj.userUniformLocations[attr] = gl.getUniformLocation(obj.prog, attr);
}
if (sprites_3d) {
obj.userMatrix = new CanvasMatrix4(obj.userMatrix);
obj.objects = this.flatten([].concat(obj.ids));
is_lit = false;
for (i=0; i &lt; obj.objects.length; i++)
this.initObj(obj.objects[i]);
}
if (is_lit &amp;&amp; !fixed_quads) {
obj.normLoc = gl.getAttribLocation(obj.prog, &#34;aNorm&#34;);
}
nclipplanes = this.countClipplanes();
if (nclipplanes &amp;&amp; !sprites_3d) {
obj.clipLoc = [];
for (i=0; i &lt; nclipplanes; i++)
obj.clipLoc[i] = gl.getUniformLocation(obj.prog,&#34;vClipplane&#34; + i);
}
if (is_lit) {
obj.emissionLoc = gl.getUniformLocation(obj.prog, &#34;emission&#34;);
obj.emission = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;emission&#34;)));
obj.shininessLoc = gl.getUniformLocation(obj.prog, &#34;shininess&#34;);
obj.shininess = this.getMaterial(id, &#34;shininess&#34;);
obj.nlights = this.countLights();
obj.ambientLoc = [];
obj.ambient = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;ambient&#34;)));
obj.specularLoc = [];
obj.specular = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;specular&#34;)));
obj.diffuseLoc = [];
obj.lightDirLoc = [];
obj.viewpointLoc = [];
obj.finiteLoc = [];
for (i=0; i &lt; obj.nlights; i++) {
obj.ambientLoc[i] = gl.getUniformLocation(obj.prog, &#34;ambient&#34; + i);
obj.specularLoc[i] = gl.getUniformLocation(obj.prog, &#34;specular&#34; + i);
obj.diffuseLoc[i] = gl.getUniformLocation(obj.prog, &#34;diffuse&#34; + i);
obj.lightDirLoc[i] = gl.getUniformLocation(obj.prog, &#34;lightDir&#34; + i);
obj.viewpointLoc[i] = gl.getUniformLocation(obj.prog, &#34;viewpoint&#34; + i);
obj.finiteLoc[i] = gl.getUniformLocation(obj.prog, &#34;finite&#34; + i);
}
}
obj.passes = is_twosided + 1;
obj.pmode = new Array(obj.passes);
for (pass = 0; pass &lt; obj.passes; pass++) {
if (type === &#34;triangles&#34; || type === &#34;quads&#34; || type === &#34;surface&#34;)
pmode = this.getMaterial(id, (pass === 0) ? &#34;front&#34; : &#34;back&#34;);
else pmode = &#34;filled&#34;;
obj.pmode[pass] = pmode;
}
obj.f.length = obj.passes;
for (pass = 0; pass &lt; obj.passes; pass++) {
f = fnew = obj.f[pass];
pmode = obj.pmode[pass];
if (pmode === &#34;culled&#34;)
f = [];
else if (pmode === &#34;points&#34;) {
// stay with default
} else if ((type === &#34;quads&#34; || type === &#34;text&#34; ||
type === &#34;sprites&#34;) &amp;&amp; !sprites_3d) {
nrows = Math.floor(obj.vertexCount/4);
if (pmode === &#34;filled&#34;) {
fnew = Array(6*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[6*i] = f[4*i];
fnew[6*i+1] = f[4*i + 1];
fnew[6*i+2] = f[4*i + 2];
fnew[6*i+3] = f[4*i];
fnew[6*i+4] = f[4*i + 2];
fnew[6*i+5] = f[4*i + 3];
}
} else {
fnew = Array(8*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[8*i] = f[4*i];
fnew[8*i+1] = f[4*i + 1];
fnew[8*i+2] = f[4*i + 1];
fnew[8*i+3] = f[4*i + 2];
fnew[8*i+4] = f[4*i + 2];
fnew[8*i+5] = f[4*i + 3];
fnew[8*i+6] = f[4*i + 3];
fnew[8*i+7] = f[4*i];
}
}
} else if (type === &#34;triangles&#34;) {
nrows = Math.floor(obj.vertexCount/3);
if (pmode === &#34;filled&#34;) {
fnew = Array(3*nrows);
for (i=0; i &lt; fnew.length; i++) {
fnew[i] = f[i];
}
} else if (pmode === &#34;lines&#34;) {
fnew = Array(6*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[6*i] = f[3*i];
fnew[6*i + 1] = f[3*i + 1];
fnew[6*i + 2] = f[3*i + 1];
fnew[6*i + 3] = f[3*i + 2];
fnew[6*i + 4] = f[3*i + 2];
fnew[6*i + 5] = f[3*i];
}
}
} else if (type === &#34;spheres&#34;) {
// default
} else if (type === &#34;surface&#34;) {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
if (pmode === &#34;filled&#34;) {
fnew = [];
for (j=0; j&lt;nx-1; j++) {
for (i=0; i&lt;nz-1; i++) {
fnew.push(f[j + nx*i],
f[j + nx*(i+1)],
f[j + 1 + nx*(i+1)],
f[j + nx*i],
f[j + 1 + nx*(i+1)],
f[j + 1 + nx*i]);
}
}
} else if (pmode === &#34;lines&#34;) {
fnew = [];
for (j=0; j&lt;nx; j++) {
for (i=0; i&lt;nz; i++) {
if (i+1 &lt; nz)
fnew.push(f[j + nx*i],
f[j + nx*(i+1)]);
if (j+1 &lt; nx)
fnew.push(f[j + nx*i],
f[j+1 + nx*i]);
}
}
}
}
obj.f[pass] = fnew;
if (depth_sort) {
drawtype = &#34;DYNAMIC_DRAW&#34;;
} else {
drawtype = &#34;STATIC_DRAW&#34;;
}
}
if (fat_lines) {
alias = undefined;
obj.nextLoc = gl.getAttribLocation(obj.prog, &#34;aNext&#34;);
obj.pointLoc = gl.getAttribLocation(obj.prog, &#34;aPoint&#34;);
obj.aspectLoc = gl.getUniformLocation(obj.prog, &#34;uAspect&#34;);
obj.lwdLoc = gl.getUniformLocation(obj.prog, &#34;uLwd&#34;);
// Expand vertices to turn each segment into a pair of triangles
for (pass = 0; pass &lt; obj.passes; pass++) {
f = obj.f[pass];
oldrows = f.length;
if (obj.pmode[pass] === &#34;lines&#34;)
break;
}
if (type === &#34;linestrip&#34;)
nrows = 4*(oldrows - 1);
else
nrows = 2*oldrows;
vnew = new Array(nrows);
fnew = new Array(1.5*nrows);
var fnext = new Array(nrows),
fpt = new Array(nrows),
pt, start, gap = type === &#34;linestrip&#34; ? 3 : 1;
// We&#39;re going to turn each pair of vertices into 4 new ones, with the &#34;next&#34; and &#34;pt&#34; attributes
// added.
// We do this by copying the originals in the first pass, adding the new attributes, then in a
// second pass add new vertices at the end.
for (i = 0; i &lt; v.length; i++) {
vnew[i] = v[i].concat([0,0,0,0,0]);
}
nextofs = stride;
pointofs = stride + 3;
stride = stride + 5;
// Now add the extras
last = v.length - 1;
ind = 0;
alias = new Array(f.length);
for (i = 0; i &lt; f.length; i++)
alias[i] = [];
for (i = 0; i &lt; f.length - 1; i++) {
if (type !== &#34;linestrip&#34; &amp;&amp; i % 2 == 1)
continue;
k = ++last;
vnew[k] = vnew[f[i]].slice();
for (j=0; j&lt;3; j++)
vnew[k][nextofs + j] = vnew[f[i+1]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = -1;
fnew[ind] = k;
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+1] = last;
alias[f[i]].push(last-1, last);
last++;
k = last;
vnew[k] = vnew[f[i+1]].slice();
for (j=0; j&lt;3; j++)
vnew[k][nextofs + j] = vnew[f[i]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = 1;
fnew[ind+2] = k;
fnew[ind+3] = fnew[ind+1];
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+4] = last;
fnew[ind+5] = fnew[ind+2];
ind += 6;
alias[f[i+1]].push(last-1, last);
}
vnew.length = last+1;
v = vnew;
obj.vertexCount = v.length;
if (typeof alias !== &#34;undefined&#34; &amp;&amp; typeof obj.alias !== &#34;undefined&#34;) { // Already have aliases from previous section?
var oldalias = obj.alias, newalias = Array(obj.alias.length);
for (i = 0; i &lt; newalias.length; i++) {
newalias[i] = oldalias[i].slice();
for (j = 0; j &lt; oldalias[i].length; j++)
Array.prototype.push.apply(newalias[i], alias[oldalias[j]]); // pushes each element
}
obj.alias = newalias;
} else
obj.alias = alias;
for (pass = 0; pass &lt; obj.passes; pass++)
if (type === &#34;lines&#34; || type === &#34;linestrip&#34; || obj.pmode[pass] == &#34;lines&#34;) {
obj.f[pass] = fnew;
}
if (depth_sort)
drawtype = &#34;DYNAMIC_DRAW&#34;;
else
drawtype = &#34;STATIC_DRAW&#34;;
}
for (pass = 0; pass &lt; obj.passes; pass++) {
if (obj.vertexCount &gt; 65535) {
if (this.index_uint) {
obj.f[pass] = new Uint32Array(obj.f[pass]);
obj.index_uint = true;
} else
this.alertOnce(&#34;Object has &#34;+obj.vertexCount+&#34; vertices, not supported in this browser.&#34;);
} else {
obj.f[pass] = new Uint16Array(obj.f[pass]);
obj.index_uint = false;
}
}
if (stride !== v[0].length) {
this.alertOnce(&#34;problem in stride calculation&#34;);
}
obj.vOffsets = {vofs:0, cofs:cofs, nofs:nofs, radofs:radofs, oofs:oofs, tofs:tofs,
nextofs:nextofs, pointofs:pointofs, stride:stride};
obj.values = new Float32Array(this.flatten(v));
if (type !== &#34;spheres&#34; &amp;&amp; !sprites_3d) {
obj.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW); //
obj.ibuf = Array(obj.passes);
obj.ibuf[0] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[0]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[0], gl[drawtype]);
if (is_twosided) {
obj.ibuf[1] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[1]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[1], gl[drawtype]);
}
}
if (!sprites_3d) {
obj.mvMatLoc = gl.getUniformLocation(obj.prog, &#34;mvMatrix&#34;);
obj.prMatLoc = gl.getUniformLocation(obj.prog, &#34;prMatrix&#34;);
}
if (fixed_size) {
obj.textScaleLoc = gl.getUniformLocation(obj.prog, &#34;textScale&#34;);
}
if (is_lit &amp;&amp; !sprites_3d) {
obj.normMatLoc = gl.getUniformLocation(obj.prog, &#34;normMatrix&#34;);
}
if (is_twosided) {
obj.frontLoc = gl.getUniformLocation(obj.prog, &#34;front&#34;);
}
};
/**
* Set gl depth test based on object&#39;s material
* @param { number } id - object to use
*/
rglwidgetClass.prototype.setDepthTest = function(id) {
var gl = this.gl || this.initGL(),
tests = {never: gl.NEVER,
less: gl.LESS,
equal: gl.EQUAL,
lequal:gl.LEQUAL,
greater: gl.GREATER,
notequal: gl.NOTEQUAL,
gequal: gl.GEQUAL,
always: gl.ALWAYS},
test = tests[this.getMaterial(id, &#34;depth_test&#34;)];
gl.depthFunc(test);
};
rglwidgetClass.prototype.mode4type = {points : &#34;POINTS&#34;,
linestrip : &#34;LINE_STRIP&#34;,
abclines : &#34;LINES&#34;,
lines : &#34;LINES&#34;,
sprites : &#34;TRIANGLES&#34;,
planes : &#34;TRIANGLES&#34;,
text : &#34;TRIANGLES&#34;,
quads : &#34;TRIANGLES&#34;,
surface : &#34;TRIANGLES&#34;,
triangles : &#34;TRIANGLES&#34;};
/**
* Sort objects from back to front
* @returns { number[] }
* @param { Object } obj - object to sort
*/
rglwidgetClass.prototype.depthSort = function(obj) {
var n = obj.centers.length,
depths = new Float32Array(n),
result = new Array(n),
compare = function(i,j) { return depths[j] - depths[i]; },
z, w;
for(i=0; i&lt;n; i++) {
z = this.prmvMatrix.m13*obj.centers[i][0] +
this.prmvMatrix.m23*obj.centers[i][1] +
this.prmvMatrix.m33*obj.centers[i][2] +
this.prmvMatrix.m43;
w = this.prmvMatrix.m14*obj.centers[i][0] +
this.prmvMatrix.m24*obj.centers[i][1] +
this.prmvMatrix.m34*obj.centers[i][2] +
this.prmvMatrix.m44;
depths[i] = z/w;
result[i] = i;
}
result.sort(compare);
return result;
};
rglwidgetClass.prototype.disableArrays = function(obj, enabled) {
var gl = this.gl || this.initGL(),
objLocs = [&#34;normLoc&#34;, &#34;texLoc&#34;, &#34;ofsLoc&#34;, &#34;pointLoc&#34;, &#34;nextLoc&#34;],
thisLocs = [&#34;posLoc&#34;, &#34;colLoc&#34;], i, attr;
for (i = 0; i &lt; objLocs.length; i++)
if (enabled[objLocs[i]]) gl.disableVertexAttribArray(obj[objLocs[i]]);
for (i = 0; i &lt; thisLocs.length; i++)
if (enabled[thisLocs[i]]) gl.disableVertexAttribArray(this[objLocs[i]]);
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
for (attr in obj.userAttribSizes) { // Not all attributes may have been used
gl.disableVertexAttribArray( obj.userAttribLocations[attr] );
}
}
}
/**
* Draw an object in a subscene
* @param { number } id - object to draw
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawObj = function(id, subsceneid) {
var obj = this.getObj(id),
subscene = this.getObj(subsceneid),
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
is_transparent = flags &amp; this.f_is_transparent,
depth_sort = flags &amp; this.f_depth_sort,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
is_lines = flags &amp; this.f_is_lines,
fat_lines = flags &amp; this.f_fat_lines,
is_points = flags &amp; this.f_is_points,
fixed_size = flags &amp; this.f_fixed_size,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
gl = this.gl || this.initGL(),
mat,
sphereMV, baseofs, ofs, sscale, i, count, light,
pass, mode, pmode, attr,
enabled = {};
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;drawObj id is &#34;+typeof id);
}
if (type === &#34;planes&#34;) {
if (obj.bbox !== subscene.par3d.bbox || !obj.initialized) {
this.planeUpdateTriangles(id, subscene.par3d.bbox);
}
}
if (!obj.initialized)
this.initObj(id);
if (type === &#34;clipplanes&#34;) {
count = obj.offsets.length;
var IMVClip = [];
for (i=0; i &lt; count; i++) {
IMVClip[i] = this.multMV(this.invMatrix, obj.vClipplane.slice(4*i, 4*(i+1)));
}
obj.IMVClip = IMVClip;
return;
}
if (type === &#34;light&#34; || type === &#34;bboxdeco&#34; || !obj.vertexCount)
return;
if (!is_transparent &amp;&amp;
obj.someHidden) {
is_transparent = true;
depth_sort = [&#34;triangles&#34;, &#34;quads&#34;, &#34;surface&#34;,
&#34;spheres&#34;, &#34;sprites&#34;, &#34;text&#34;].indexOf(type) &gt;= 0;
}
this.setDepthTest(id);
if (sprites_3d) {
var norigs = obj.vertices.length,
savenorm = new CanvasMatrix4(this.normMatrix);
this.origs = obj.vertices;
this.usermat = new Float32Array(obj.userMatrix.getAsArray());
this.radii = obj.radii;
this.normMatrix = subscene.spriteNormmat;
for (this.iOrig=0; this.iOrig &lt; norigs; this.iOrig++) {
for (i=0; i &lt; obj.objects.length; i++) {
this.drawObj(obj.objects[i], subsceneid);
}
}
this.normMatrix = savenorm;
return;
} else {
gl.useProgram(obj.prog);
}
if (typeof obj.polygon_offset !== &#34;undefined&#34;) {
gl.polygonOffset(obj.polygon_offset[0],
obj.polygon_offset[1]);
gl.enable(gl.POLYGON_OFFSET_FILL);
}
if (sprite_3d) {
gl.uniform3fv(obj.origLoc, new Float32Array(this.origs[this.iOrig]));
if (this.radii.length &gt; 1) {
gl.uniform1f(obj.sizeLoc, this.radii[this.iOrig][0]);
} else {
gl.uniform1f(obj.sizeLoc, this.radii[0][0]);
}
gl.uniformMatrix4fv(obj.usermatLoc, false, this.usermat);
}
if (type === &#34;spheres&#34;) {
gl.bindBuffer(gl.ARRAY_BUFFER, this.sphere.buf);
} else {
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
}
gl.uniformMatrix4fv( obj.prMatLoc, false, new Float32Array(this.prMatrix.getAsArray()) );
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(this.mvMatrix.getAsArray()) );
var clipcheck = 0,
clipplaneids = subscene.clipplanes,
clip, j;
for (i=0; i &lt; clipplaneids.length; i++) {
clip = this.getObj(clipplaneids[i]);
for (j=0; j &lt; clip.offsets.length; j++) {
gl.uniform4fv(obj.clipLoc[clipcheck + j], clip.IMVClip[j]);
}
clipcheck += clip.offsets.length;
}
if (typeof obj.clipLoc !== &#34;undefined&#34;)
for (i=clipcheck; i &lt; obj.clipLoc.length; i++)
gl.uniform4f(obj.clipLoc[i], 0,0,0,0);
if (is_lit) {
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(this.normMatrix.getAsArray()) );
gl.uniform3fv( obj.emissionLoc, obj.emission);
gl.uniform1f( obj.shininessLoc, obj.shininess);
for (i=0; i &lt; subscene.lights.length; i++) {
light = this.getObj(subscene.lights[i]);
if (!light.initialized) this.initObj(subscene.lights[i]);
gl.uniform3fv( obj.ambientLoc[i], this.componentProduct(light.ambient, obj.ambient));
gl.uniform3fv( obj.specularLoc[i], this.componentProduct(light.specular, obj.specular));
gl.uniform3fv( obj.diffuseLoc[i], light.diffuse);
gl.uniform3fv( obj.lightDirLoc[i], light.lightDir);
gl.uniform1i( obj.viewpointLoc[i], light.viewpoint);
gl.uniform1i( obj.finiteLoc[i], light.finite);
}
for (i=subscene.lights.length; i &lt; obj.nlights; i++) {
gl.uniform3f( obj.ambientLoc[i], 0,0,0);
gl.uniform3f( obj.specularLoc[i], 0,0,0);
gl.uniform3f( obj.diffuseLoc[i], 0,0,0);
}
}
if (fixed_size) {
gl.uniform2f( obj.textScaleLoc, 0.75/this.vp.width, 0.75/this.vp.height);
}
gl.enableVertexAttribArray( this.posLoc );
enabled.posLoc = true;
var nc = obj.colorCount;
count = obj.vertexCount;
if (type === &#34;spheres&#34;) {
subscene = this.getObj(subsceneid);
var scale = subscene.par3d.scale,
scount = count, indices;
gl.vertexAttribPointer(this.posLoc, 3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 0);
gl.enableVertexAttribArray(obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 0);
gl.disableVertexAttribArray( this.colLoc );
var sphereNorm = new CanvasMatrix4();
sphereNorm.scale(scale[0], scale[1], scale[2]);
sphereNorm.multRight(this.normMatrix);
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(sphereNorm.getAsArray()) );
if (nc == 1) {
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
}
if (has_texture) {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*this.sphere.vOffsets.stride,
4*this.sphere.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (depth_sort)
indices = this.depthSort(obj);
for (i = 0; i &lt; scount; i++) {
sphereMV = new CanvasMatrix4();
if (depth_sort) {
baseofs = indices[i]*obj.vOffsets.stride;
} else {
baseofs = i*obj.vOffsets.stride;
}
ofs = baseofs + obj.vOffsets.radofs;
sscale = obj.values[ofs];
sphereMV.scale(sscale/scale[0], sscale/scale[1], sscale/scale[2]);
sphereMV.translate(obj.values[baseofs],
obj.values[baseofs+1],
obj.values[baseofs+2]);
sphereMV.multRight(this.mvMatrix);
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(sphereMV.getAsArray()) );
if (nc &gt; 1) {
ofs = baseofs + obj.vOffsets.cofs;
gl.vertexAttrib4f( this.colLoc, obj.values[ofs],
obj.values[ofs+1],
obj.values[ofs+2],
obj.values[ofs+3] );
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.sphere.ibuf);
gl.drawElements(gl.TRIANGLES, this.sphere.sphereCount, gl.UNSIGNED_SHORT, 0);
}
this.disableArrays(obj, enabled);
if (typeof obj.polygon_offset !== &#34;undefined&#34;)
gl.disable(gl.POLYGON_OFFSET_FILL);
return;
} else {
if (obj.colorCount === 1) {
gl.disableVertexAttribArray( this.colLoc );
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
} else {
gl.enableVertexAttribArray( this.colLoc );
enabled.colLoc = true;
gl.vertexAttribPointer(this.colLoc, 4, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.cofs);
}
}
if (is_lit &amp;&amp; obj.vOffsets.nofs &gt; 0) {
gl.enableVertexAttribArray( obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nofs);
}
if (has_texture || type === &#34;text&#34;) {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (fixed_quads) {
gl.enableVertexAttribArray( obj.ofsLoc );
enabled.ofsLoc = true;
gl.vertexAttribPointer(obj.ofsLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.oofs);
}
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
for (attr in obj.userAttribSizes) { // Not all attributes may have been used
gl.enableVertexAttribArray( obj.userAttribLocations[attr] );
gl.vertexAttribPointer( obj.userAttribLocations[attr], obj.userAttribSizes[attr],
gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.userAttribOffsets[attr]);
}
}
if (typeof obj.userUniforms !== &#34;undefined&#34;) {
for (attr in obj.userUniformLocations) {
var loc = obj.userUniformLocations[attr];
if (loc !== null) {
var uniform = obj.userUniforms[attr];
if (typeof uniform.length === &#34;undefined&#34;)
gl.uniform1f(loc, uniform);
else if (typeof uniform[0].length === &#34;undefined&#34;) {
uniform = new Float32Array(uniform);
switch(uniform.length) {
case 2: gl.uniform2fv(loc, uniform); break;
case 3: gl.uniform3fv(loc, uniform); break;
case 4: gl.uniform4fv(loc, uniform); break;
default: console.warn(&#34;bad uniform length&#34;);
}
} else if (uniform.length == 4 &amp;&amp; uniform[0].length == 4)
gl.uniformMatrix4fv(loc, false, new Float32Array(uniform.getAsArray()));
else
console.warn(&#34;unsupported uniform matrix&#34;);
}
}
}
for (pass = 0; pass &lt; obj.passes; pass++) {
pmode = obj.pmode[pass];
if (pmode === &#34;culled&#34;)
continue;
mode = fat_lines &amp;&amp; (is_lines || pmode == &#34;lines&#34;) ? &#34;TRIANGLES&#34; : this.mode4type[type];
if (depth_sort &amp;&amp; pmode == &#34;filled&#34;) {// Don&#39;t try depthsorting on wireframe or points
var faces = this.depthSort(obj),
nfaces = faces.length,
frowsize = Math.floor(obj.f[pass].length/nfaces);
if (type !== &#34;spheres&#34;) {
var f = obj.index_uint ? new Uint32Array(obj.f[pass].length) : new Uint16Array(obj.f[pass].length);
for (i=0; i&lt;nfaces; i++) {
for (j=0; j&lt;frowsize; j++) {
f[frowsize*i + j] = obj.f[pass][frowsize*faces[i] + j];
}
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, f, gl.DYNAMIC_DRAW);
}
}
if (is_twosided)
gl.uniform1i(obj.frontLoc, pass !== 0);
if (type !== &#34;spheres&#34;)
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
if (type === &#34;sprites&#34; || type === &#34;text&#34; || type === &#34;quads&#34;) {
count = count * 6/4;
} else if (type === &#34;surface&#34;) {
count = obj.f[pass].length;
}
count = obj.f[pass].length;
if (!is_lines &amp;&amp; pmode === &#34;lines&#34; &amp;&amp; !fat_lines) {
mode = &#34;LINES&#34;;
} else if (pmode === &#34;points&#34;) {
mode = &#34;POINTS&#34;;
}
if ((is_lines || pmode === &#34;lines&#34;) &amp;&amp; fat_lines) {
gl.enableVertexAttribArray(obj.pointLoc);
enabled.pointLoc = true;
gl.vertexAttribPointer(obj.pointLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.pointofs);
gl.enableVertexAttribArray(obj.nextLoc );
enabled.nextLoc = true;
gl.vertexAttribPointer(obj.nextLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nextofs);
gl.uniform1f(obj.aspectLoc, this.vp.width/this.vp.height);
gl.uniform1f(obj.lwdLoc, this.getMaterial(id, &#34;lwd&#34;)/this.vp.height);
}
gl.vertexAttribPointer(this.posLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.vofs);
gl.drawElements(gl[mode], count, obj.index_uint ? gl.UNSIGNED_INT : gl.UNSIGNED_SHORT, 0);
this.disableArrays(obj, enabled);
}
if (typeof obj.polygon_offset !== &#34;undefined&#34;)
gl.disable(gl.POLYGON_OFFSET_FILL);
};
/**
* Draw the background for a subscene
* @param { number } id - id of background object
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawBackground = function(id, subsceneid) {
var gl = this.gl || this.initGL(),
obj = this.getObj(id),
bg, i;
if (!obj.initialized)
this.initObj(id);
if (obj.colors.length) {
bg = obj.colors[0];
gl.clearColor(bg[0], bg[1], bg[2], bg[3]);
gl.depthMask(true);
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
}
if (typeof obj.quad !== &#34;undefined&#34;) {
this.prMatrix.makeIdentity();
this.mvMatrix.makeIdentity();
gl.disable(gl.BLEND);
gl.disable(gl.DEPTH_TEST);
gl.depthMask(false);
for (i=0; i &lt; obj.quad.length; i++)
this.drawObj(obj.quad[i], subsceneid);
}
};
/**
* Draw a subscene
* @param { number } subsceneid - id of subscene
* @param { boolean } opaquePass - is this the opaque drawing pass?
*/
rglwidgetClass.prototype.drawSubscene = function(subsceneid, opaquePass) {
var gl = this.gl || this.initGL(),
sub = this.getObj(subsceneid),
objects = this.scene.objects,
subids = sub.objects,
subscene_has_faces = false,
subscene_needs_sorting = false,
flags, i, obj;
if (sub.par3d.skipRedraw)
return;
for (i=0; i &lt; subids.length; i++) {
obj = objects[subids[i]];
flags = obj.flags;
if (typeof flags !== &#34;undefined&#34;) {
subscene_has_faces |= (flags &amp; this.f_is_lit)
&amp; !(flags &amp; this.f_fixed_quads);
obj.is_transparent = (flags &amp; this.f_is_transparent) || obj.someHidden;
subscene_needs_sorting |= (flags &amp; this.f_depth_sort) || obj.is_transparent;
}
}
this.setViewport(subsceneid);
if (typeof sub.backgroundId !== &#34;undefined&#34; &amp;&amp; opaquePass)
this.drawBackground(sub.backgroundId, subsceneid);
if (subids.length) {
this.setprMatrix(subsceneid);
this.setmvMatrix(subsceneid);
if (subscene_has_faces) {
this.setnormMatrix(subsceneid);
if ((sub.flags &amp; this.f_sprites_3d) &amp;&amp;
typeof sub.spriteNormmat === &#34;undefined&#34;) {
sub.spriteNormmat = new CanvasMatrix4(this.normMatrix);
}
}
if (subscene_needs_sorting)
this.setprmvMatrix();
var clipids = sub.clipplanes;
if (typeof clipids === &#34;undefined&#34;) {
console.warn(&#34;bad clipids&#34;);
}
if (clipids.length &gt; 0) {
this.invMatrix = new CanvasMatrix4(this.mvMatrix);
this.invMatrix.invert();
for (i = 0; i &lt; clipids.length; i++)
this.drawObj(clipids[i], subsceneid);
}
subids = sub.opaque.concat(sub.transparent);
if (opaquePass) {
gl.enable(gl.DEPTH_TEST);
gl.depthMask(true);
gl.disable(gl.BLEND);
for (i = 0; i &lt; subids.length; i++) {
if (!this.getObj(subids[i]).is_transparent)
this.drawObj(subids[i], subsceneid);
}
} else {
gl.depthMask(false);
gl.blendFuncSeparate(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA,
gl.ONE, gl.ONE);
gl.enable(gl.BLEND);
for (i = 0; i &lt; subids.length; i++) {
if (this.getObj(subids[i]).is_transparent)
this.drawObj(subids[i], subsceneid);
}
}
subids = sub.subscenes;
for (i = 0; i &lt; subids.length; i++) {
this.drawSubscene(subids[i], opaquePass);
}
}
};
/**
* Respond to brush change
*/
rglwidgetClass.prototype.selectionChanged = function() {
var i, j, k, id, subid = this.select.subscene, subscene,
objids, obj,
p1 = this.select.region.p1, p2 = this.select.region.p2,
filter, selection = [], handle, keys, xmin, x, xmax, ymin, y, ymax, z, v,
someHidden;
if (!subid)
return;
subscene = this.getObj(subid);
objids = subscene.objects;
filter = this.scene.crosstalk.filter;
this.setmvMatrix(subid);
this.setprMatrix(subid);
this.setprmvMatrix();
xmin = Math.min(p1.x, p2.x);
xmax = Math.max(p1.x, p2.x);
ymin = Math.min(p1.y, p2.y);
ymax = Math.max(p1.y, p2.y);
for (i = 0; i &lt; objids.length; i++) {
id = objids[i];
j = this.scene.crosstalk.id.indexOf(id);
if (j &gt;= 0) {
keys = this.scene.crosstalk.key[j];
obj = this.getObj(id);
someHidden = false;
for (k = 0; k &lt; keys.length; k++) {
if (filter &amp;&amp; filter.indexOf(keys[k]) &lt; 0) {
someHidden = true;
continue;
}
v = [].concat(obj.vertices[k]).concat(1.0);
v = this.multVM(v, this.prmvMatrix);
x = v[0]/v[3];
y = v[1]/v[3];
z = v[2]/v[3];
if (xmin &lt;= x &amp;&amp; x &lt;= xmax &amp;&amp; ymin &lt;= y &amp;&amp; y &lt;= ymax &amp;&amp; -1.0 &lt;= z &amp;&amp; z &lt;= 1.0) {
selection.push(keys[k]);
} else
someHidden = true;
}
obj.someHidden = someHidden &amp;&amp; (filter || selection.length);
obj.initialized = false;
/* Who should we notify? Only shared data in the current subscene, or everyone? */
if (!this.equalArrays(selection, this.scene.crosstalk.selection)) {
handle = this.scene.crosstalk.sel_handle[j];
handle.set(selection, {rglSubsceneId: this.select.subscene});
}
}
}
};
/**
* Respond to selection or filter change from crosstalk
* @param { Object } event - crosstalk event
* @param { boolean } filter - filter or selection?
*/
rglwidgetClass.prototype.selection = function(event, filter) {
var i, j, ids, obj, keys, crosstalk = this.scene.crosstalk,
selection, someHidden;
// Record the message and find out if this event makes some objects have mixed values:
crosstalk = this.scene.crosstalk;
if (filter) {
filter = crosstalk.filter = event.value;
selection = crosstalk.selection;
} else {
selection = crosstalk.selection = event.value;
filter = crosstalk.filter;
}
ids = crosstalk.id;
for (i = 0; i &lt; ids.length ; i++) {
obj = this.getObj(ids[i]);
obj.initialized = false;
keys = crosstalk.key[i];
someHidden = false;
for (j = 0; j &lt; keys.length &amp;&amp; !someHidden; j++) {
if ((filter &amp;&amp; filter.indexOf(keys[j]) &lt; 0) ||
(selection.length &amp;&amp; selection.indexOf(keys[j]) &lt; 0))
someHidden = true;
}
obj.someHidden = someHidden;
}
this.drawScene();
};
/**
* Clear the selection brush
* @param { number } except - Subscene that should ignore this request
*/
rglwidgetClass.prototype.clearBrush = function(except) {
if (this.select.subscene != except) {
this.select.state = &#34;inactive&#34;;
this.delFromSubscene(this.scene.brushId, this.select.subscene);
}
this.drawScene();
};
/**
* Compute mouse coordinates relative to current canvas
* @returns { Object }
* @param { Object } event - event object from mouse click
*/
rglwidgetClass.prototype.relMouseCoords = function(event) {
var totalOffsetX = 0,
totalOffsetY = 0,
currentElement = this.canvas;
do {
totalOffsetX += currentElement.offsetLeft;
totalOffsetY += currentElement.offsetTop;
currentElement = currentElement.offsetParent;
}
while(currentElement);
var canvasX = event.pageX - totalOffsetX,
canvasY = event.pageY - totalOffsetY;
return {x:canvasX, y:canvasY};
};
/**
* Set mouse handlers for the scene
*/
rglwidgetClass.prototype.setMouseHandlers = function() {
var self = this, activeSubscene, handler,
handlers = {}, drag = 0;
handlers.rotBase = 0;
this.screenToVector = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
radius = Math.max(width, height)/2.0,
cx = width/2.0,
cy = height/2.0,
px = (x-cx)/radius,
py = (y-cy)/radius,
plen = Math.sqrt(px*px+py*py);
if (plen &gt; 1.e-6) {
px = px/plen;
py = py/plen;
}
var angle = (Math.SQRT2 - plen)/Math.SQRT2*Math.PI/2,
z = Math.sin(angle),
zlen = Math.sqrt(1.0 - z*z);
px = px * zlen;
py = py * zlen;
return [px, py, z];
};
handlers.trackballdown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
handlers.rotBase = this.screenToVector(x, y);
this.saveMat = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.trackballmove = function(x,y) {
var rotCurrent = this.screenToVector(x,y),
rotBase = handlers.rotBase,
dot = rotBase[0]*rotCurrent[0] +
rotBase[1]*rotCurrent[1] +
rotBase[2]*rotCurrent[2],
angle = Math.acos( dot/this.vlen(rotBase)/this.vlen(rotCurrent) )*180.0/Math.PI,
axis = this.xprod(rotBase, rotCurrent),
objects = this.scene.objects,
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
l = activeModel.par3d.listeners,
i;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(angle, axis[0], axis[1], axis[2]);
}
this.drawScene();
};
handlers.trackballend = 0;
this.clamp = function(x, lo, hi) {
return Math.max(lo, Math.min(x, hi));
};
this.screenToPolar = function(x,y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
r = Math.min(width, height)/2,
dx = this.clamp(x - width/2, -r, r),
dy = this.clamp(y - height/2, -r, r);
return [Math.asin(dx/r), Math.asin(-dy/r)];
};
handlers.polardown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
handlers.dragBase = this.screenToPolar(x, y);
this.saveMat = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
activeSub.camBase = [-Math.atan2(activeSub.saveMat.m13, activeSub.saveMat.m11),
Math.atan2(activeSub.saveMat.m32, activeSub.saveMat.m22)];
}
};
handlers.polarmove = function(x,y) {
var dragCurrent = this.screenToPolar(x,y),
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
objects = this.scene.objects,
l = activeModel.par3d.listeners,
i, changepos = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
for (j=0; j&lt;2; j++)
changepos[j] = -(dragCurrent[j] - handlers.dragBase[j]);
activeSub.par3d.userMatrix.makeIdentity();
activeSub.par3d.userMatrix.rotate(changepos[0]*180/Math.PI, 0,-1,0);
activeSub.par3d.userMatrix.multRight(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(changepos[1]*180/Math.PI, -1,0,0);
}
this.drawScene();
};
handlers.polarend = 0;
handlers.axisdown = function(x,y) {
handlers.rotBase = this.screenToVector(x, this.canvas.height/2);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.axismove = function(x,y) {
var rotCurrent = this.screenToVector(x, this.canvas.height/2),
rotBase = handlers.rotBase,
angle = (rotCurrent[0] - rotBase[0])*180/Math.PI,
rotMat = new CanvasMatrix4();
rotMat.rotate(angle, handlers.axis[0], handlers.axis[1], handlers.axis[2]);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(activeSub.saveMat);
activeSub.par3d.userMatrix.multLeft(rotMat);
}
this.drawScene();
};
handlers.axisend = 0;
handlers.y0zoom = 0;
handlers.zoom0 = 0;
handlers.zoomdown = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
handlers.y0zoom = y;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.zoom0 = Math.log(activeSub.par3d.zoom);
}
};
handlers.zoommove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.zoom = Math.exp(activeSub.zoom0 + (y-handlers.y0zoom)/this.canvas.height);
}
this.drawScene();
};
handlers.zoomend = 0;
handlers.y0fov = 0;
handlers.fovdown = function(x, y) {
handlers.y0fov = y;
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.fov0 = activeSub.par3d.FOV;
}
};
handlers.fovmove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.FOV = Math.max(1, Math.min(179, activeSub.fov0 +
180*(y-handlers.y0fov)/this.canvas.height));
}
this.drawScene();
};
handlers.fovend = 0;
handlers.selectingdown = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
p = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
this.select.region = {p1: p, p2: p};
if (this.select.subscene &amp;&amp; this.select.subscene != activeSubscene)
this.delFromSubscene(this.scene.brushId, this.select.subscene);
this.select.subscene = activeSubscene;
this.addToSubscene(this.scene.brushId, activeSubscene);
this.select.state = &#34;changing&#34;;
if (typeof this.scene.brushId !== &#34;undefined&#34;)
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingmove = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height;
if (this.select.state === &#34;inactive&#34;)
return;
this.select.region.p2 = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
if (typeof this.scene.brushId !== &#34;undefined&#34;)
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingend = 0;
this.canvas.onmousedown = function ( ev ){
if (!ev.which) // Use w3c defns in preference to MS
switch (ev.button) {
case 0: ev.which = 1; break;
case 1:
case 4: ev.which = 2; break;
case 2: ev.which = 3;
}
drag = [&#34;left&#34;, &#34;middle&#34;, &#34;right&#34;][ev.which-1];
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height-coords.y;
activeSubscene = self.whichSubscene(coords);
var sub = self.getObj(activeSubscene), f;
handler = sub.par3d.mouseMode[drag];
switch (handler) {
case &#34;xAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [1.0, 0.0, 0.0];
break;
case &#34;yAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [0.0, 1.0, 0.0];
break;
case &#34;zAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [0.0, 0.0, 1.0];
break;
}
f = handlers[handler + &#34;down&#34;];
if (f) {
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
ev.preventDefault();
} else
console.warn(&#34;Mouse handler &#39;&#34; + handler + &#34;&#39; is not implemented.&#34;);
};
this.canvas.onmouseup = function ( ev ){
if ( drag === 0 ) return;
var f = handlers[handler + &#34;end&#34;];
if (f) {
f.call(self);
ev.preventDefault();
}
drag = 0;
};
this.canvas.onmouseout = this.canvas.onmouseup;
this.canvas.onmousemove = function ( ev ) {
if ( drag === 0 ) return;
var f = handlers[handler + &#34;move&#34;];
if (f) {
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height - coords.y;
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
}
};
handlers.wheelHandler = function(ev) {
var del = 1.02, i;
if (ev.shiftKey) del = 1.002;
var ds = ((ev.detail || ev.wheelDelta) &gt; 0) ? del : (1 / del);
if (typeof activeSubscene === &#34;undefined&#34;)
activeSubscene = self.scene.rootSubscene;
var activeSub = self.getObj(activeSubscene),
activeProjection = self.getObj(self.useid(activeSub.id, &#34;projection&#34;)),
l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = self.getObj(l[i]);
activeSub.par3d.zoom *= ds;
}
self.drawScene();
ev.preventDefault();
};
this.canvas.addEventListener(&#34;DOMMouseScroll&#34;, handlers.wheelHandler, false);
this.canvas.addEventListener(&#34;mousewheel&#34;, handlers.wheelHandler, false);
};
/**
* Find a particular subscene by inheritance
* @returns { number } id of subscene to use
* @param { number } subsceneid - child subscene
* @param { string } type - type of inheritance: &#34;projection&#34; or &#34;model&#34;
*/
rglwidgetClass.prototype.useid = function(subsceneid, type) {
var sub = this.getObj(subsceneid);
if (sub.embeddings[type] === &#34;inherit&#34;)
return(this.useid(sub.parent, type));
else
return subsceneid;
};
/**
* Check whether point is in viewport of subscene
* @returns {boolean}
* @param { Object } coords - screen coordinates of point
* @param { number } subsceneid - subscene to check
*/
rglwidgetClass.prototype.inViewport = function(coords, subsceneid) {
var viewport = this.getObj(subsceneid).par3d.viewport,
x0 = coords.x - viewport.x*this.canvas.width,
y0 = coords.y - viewport.y*this.canvas.height;
return 0 &lt;= x0 &amp;&amp; x0 &lt;= viewport.width*this.canvas.width &amp;&amp;
0 &lt;= y0 &amp;&amp; y0 &lt;= viewport.height*this.canvas.height;
};
/**
* Find which subscene contains a point
* @returns { number } subscene id
* @param { Object } coords - coordinates of point
*/
rglwidgetClass.prototype.whichSubscene = function(coords) {
var self = this,
recurse = function(subsceneid) {
var subscenes = self.getChildSubscenes(subsceneid), i, id;
for (i=0; i &lt; subscenes.length; i++) {
id = recurse(subscenes[i]);
if (typeof(id) !== &#34;undefined&#34;)
return(id);
}
if (self.inViewport(coords, subsceneid))
return(subsceneid);
else
return undefined;
},
rootid = this.scene.rootSubscene,
result = recurse(rootid);
if (typeof(result) === &#34;undefined&#34;)
result = rootid;
return result;
};
/**
* Translate from window coordinates to viewport coordinates
* @returns { Object } translated coordinates
* @param { number } subsceneid - which subscene to use?
* @param { Object } coords - point to translate
*/
rglwidgetClass.prototype.translateCoords = function(subsceneid, coords) {
var viewport = this.getObj(subsceneid).par3d.viewport;
return {x: coords.x - viewport.x*this.canvas.width,
y: coords.y - viewport.y*this.canvas.height};
};
/**
* Initialize the sphere object
*/
rglwidgetClass.prototype.initSphere = function() {
var verts = this.scene.sphereVerts,
reuse = verts.reuse, result;
if (typeof reuse !== &#34;undefined&#34;) {
var prev = document.getElementById(reuse).rglinstance.sphere;
result = {values: prev.values, vOffsets: prev.vOffsets, it: prev.it};
} else
result = {values: new Float32Array(this.flatten(this.cbind(this.transpose(verts.vb),
this.transpose(verts.texcoords)))),
it: new Uint16Array(this.flatten(this.transpose(verts.it))),
vOffsets: {vofs:0, cofs:-1, nofs:-1, radofs:-1, oofs:-1,
tofs:3, nextofs:-1, pointofs:-1, stride:5}};
result.sphereCount = result.it.length;
this.sphere = result;
};
/**
* Set the vertices in the selection box object
*/
rglwidgetClass.prototype.initSelection = function(id) {
if (typeof this.select.region === &#34;undefined&#34;)
return;
var obj = this.getObj(id),
width = this.canvas.width,
height = this.canvas.height,
p1 = this.select.region.p1,
p2 = this.select.region.p2;
obj.vertices = [[p1.x, p1.y, 0.0],
[p2.x, p1.y, 0.0],
[p2.x, p2.y, 0.0],
[p1.x, p2.y, 0.0],
[p1.x, p1.y, 0.0]];
};
/**
* Do the gl part of initializing the sphere
*/
rglwidgetClass.prototype.initSphereGL = function() {
var gl = this.gl || this.initGL(), sphere = this.sphere;
if (gl.isContextLost()) return;
sphere.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, sphere.buf);
gl.bufferData(gl.ARRAY_BUFFER, sphere.values, gl.STATIC_DRAW);
sphere.ibuf = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, sphere.ibuf);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, sphere.it, gl.STATIC_DRAW);
return;
};
/**
* Initialize the DOM object
* @param { Object } el - the DOM object
* @param { Object } x - the scene data sent by JSON from R
*/
rglwidgetClass.prototype.initialize = function(el, x) {
this.textureCanvas = document.createElement(&#34;canvas&#34;);
this.textureCanvas.style.display = &#34;block&#34;;
this.scene = x;
this.normMatrix = new CanvasMatrix4();
this.saveMat = {};
this.distance = null;
this.posLoc = 0;
this.colLoc = 1;
if (el) {
el.rglinstance = this;
this.el = el;
this.webGLoptions = el.rglinstance.scene.webGLoptions;
this.initCanvas();
}
if (typeof Shiny !== &#34;undefined&#34;) {
var self = this;
Shiny.addCustomMessageHandler(&#34;shinyGetPar3d&#34;,
function(message) {
var i, param,
subscene = self.getObj(message.subscene),
parameters = [].concat(message.parameters),
result = {tag: message.tag, subscene: message.subscene};
if (typeof subscene !== &#34;undefined&#34;) {
for (i = 0; i &lt; parameters.length; i++) {
param = parameters[i];
result[param] = subscene.par3d[param];
};
} else {
console.log(&#34;subscene &#34;+message.subscene+&#34; undefined.&#34;)
}
Shiny.setInputValue(&#34;par3d:shinyPar3d&#34;, result, {priority: &#34;event&#34;});
});
Shiny.addCustomMessageHandler(&#34;shinySetPar3d&#34;,
function(message) {
var param = message.parameter,
subscene = self.getObj(message.subscene);
if (typeof subscene !== &#34;undefined&#34;) {
subscene.par3d[param] = message.value;
subscene.initialized = false;
self.drawScene();
} else {
console.log(&#34;subscene &#34;+message.subscene+&#34; undefined.&#34;)
}
})
}
};
/**
* Restart the WebGL canvas
*/
rglwidgetClass.prototype.restartCanvas = function() {
var newcanvas = document.createElement(&#34;canvas&#34;),
self = this;
newcanvas.width = this.el.width;
newcanvas.height = this.el.height;
newcanvas.addEventListener(&#34;webglcontextrestored&#34;,
this.onContextRestored, false);
newcanvas.addEventListener(&#34;webglcontextlost&#34;,
this.onContextLost, false);
while (this.el.firstChild) {
this.el.removeChild(this.el.firstChild);
}
this.el.appendChild(newcanvas);
this.canvas = newcanvas;
this.setMouseHandlers();
if (this.gl)
Object.keys(this.scene.objects).forEach(function(key){
self.getObj(parseInt(key, 10)).texture = undefined;
});
this.gl = null;
};
/**
* Initialize the WebGL canvas
*/
rglwidgetClass.prototype.initCanvas = function() {
this.restartCanvas();
var objs = this.scene.objects,
self = this;
Object.keys(objs).forEach(function(key){
var id = parseInt(key, 10),
obj = self.getObj(id);
if (typeof obj.reuse !== &#34;undefined&#34;)
self.copyObj(id, obj.reuse);
});
Object.keys(objs).forEach(function(key){
self.initSubscene(parseInt(key, 10));
});
this.setMouseHandlers();
this.initSphere();
this.onContextRestored = function(event) {
self.initGL();
self.drawScene();
};
this.onContextLost = function(event) {
if (!self.drawing)
this.gl = null;
event.preventDefault();
};
this.initGL0();
this.lazyLoadScene = function() {
if (typeof self.slide === &#34;undefined&#34;)
self.slide = self.getSlide();
if (self.isInBrowserViewport()) {
if (!self.gl || self.gl.isContextLost())
self.initGL();
self.drawScene();
}
};
window.addEventListener(&#34;DOMContentLoaded&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;load&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;resize&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;scroll&#34;, this.lazyLoadScene, false);
this.slide = this.getSlide();
if (this.slide) {
if (typeof this.slide.rgl === &#34;undefined&#34;)
this.slide.rgl = [this];
else
this.slide.rgl.push(this);
if (this.scene.context.rmarkdown)
if (this.scene.context.rmarkdown === &#34;ioslides_presentation&#34;) {
this.slide.setAttribute(&#34;slideenter&#34;, &#34;this.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window);})&#34;);
} else if (this.scene.context.rmarkdown === &#34;slidy_presentation&#34;) {
// This method would also work in ioslides, but it gets triggered
// something like 5 times per slide for every slide change, so
// you&#39;d need a quicker function than lazyLoadScene.
var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver,
observer = new MutationObserver(function(mutations) {
mutations.forEach(function(mutation) {
self.slide.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window); });});});
observer.observe(this.slide, { attributes: true, attributeFilter:[&#34;class&#34;] });
}
}
};
/**
* Start the writeWebGL scene. This is only used by writeWebGL; rglwidget has
no debug element and does the drawing in rglwidget.js.
*/
rglwidgetClass.prototype.start = function() {
if (typeof this.prefix !== &#34;undefined&#34;) {
this.debugelement = document.getElementById(this.prefix + &#34;debug&#34;);
this.debug(&#34;&#34;);
}
this.drag = 0;
this.drawScene();
};
/**
* Display a debug message
* @param { string } msg - The message to display
* @param { Object } [img] - Image to insert before message
*/
rglwidgetClass.prototype.debug = function(msg, img) {
if (typeof this.debugelement !== &#34;undefined&#34; &amp;&amp; this.debugelement !== null) {
this.debugelement.innerHTML = msg;
if (typeof img !== &#34;undefined&#34;) {
this.debugelement.insertBefore(img, this.debugelement.firstChild);
}
} else if (msg !== &#34;&#34;)
alert(msg);
};
/**
* Get the snapshot image of this scene
* @returns { Object } The img DOM element
*/
rglwidgetClass.prototype.getSnapshot = function() {
var img;
if (typeof this.scene.snapshot !== &#34;undefined&#34;) {
img = document.createElement(&#34;img&#34;);
img.src = this.scene.snapshot;
img.alt = &#34;Snapshot&#34;;
}
return img;
};
/**
* Initial test for WebGL
*/
rglwidgetClass.prototype.initGL0 = function() {
if (!window.WebGLRenderingContext){
alert(&#34;Your browser does not support WebGL. See http://get.webgl.org&#34;);
return;
}
};
/**
* If we are in an ioslides or slidy presentation, get the
* DOM element of the current slide
* @returns { Object }
*/
rglwidgetClass.prototype.getSlide = function() {
var result = this.el, done = false;
while (result &amp;&amp; !done &amp;&amp; this.scene.context.rmarkdown) {
switch(this.scene.context.rmarkdown) {
case &#34;ioslides_presentation&#34;:
if (result.tagName === &#34;SLIDE&#34;) return result;
break;
case &#34;slidy_presentation&#34;:
if (result.tagName === &#34;DIV&#34; &amp;&amp; result.classList.contains(&#34;slide&#34;))
return result;
break;
default: return null;
}
result = result.parentElement;
}
return null;
};
/**
* Is this scene visible in the browser?
* @returns { boolean }
*/
rglwidgetClass.prototype.isInBrowserViewport = function() {
var rect = this.canvas.getBoundingClientRect(),
windHeight = (window.innerHeight || document.documentElement.clientHeight),
windWidth = (window.innerWidth || document.documentElement.clientWidth);
if (this.scene.context &amp;&amp; this.scene.context.rmarkdown !== null) {
if (this.slide)
return (this.scene.context.rmarkdown === &#34;ioslides_presentation&#34; &amp;&amp;
this.slide.classList.contains(&#34;current&#34;)) ||
(this.scene.context.rmarkdown === &#34;slidy_presentation&#34; &amp;&amp;
!this.slide.classList.contains(&#34;hidden&#34;));
}
return (
rect.top &gt;= -windHeight &amp;&amp;
rect.left &gt;= -windWidth &amp;&amp;
rect.bottom &lt;= 2*windHeight &amp;&amp;
rect.right &lt;= 2*windWidth);
};
/**
* Initialize WebGL
* @returns { Object } the WebGL context
*/
rglwidgetClass.prototype.initGL = function() {
var self = this;
if (this.gl) {
if (!this.drawing &amp;&amp; this.gl.isContextLost())
this.restartCanvas();
else
return this.gl;
}
// if (!this.isInBrowserViewport()) return; Return what??? At this point we know this.gl is null.
this.canvas.addEventListener(&#34;webglcontextrestored&#34;,
this.onContextRestored, false);
this.canvas.addEventListener(&#34;webglcontextlost&#34;,
this.onContextLost, false);
this.gl = this.canvas.getContext(&#34;webgl&#34;, this.webGLoptions) ||
this.canvas.getContext(&#34;experimental-webgl&#34;, this.webGLoptions);
this.index_uint = this.gl.getExtension(&#34;OES_element_index_uint&#34;);
var save = this.startDrawing();
this.initSphereGL();
Object.keys(this.scene.objects).forEach(function(key){
self.initObj(parseInt(key, 10));
});
this.stopDrawing(save);
return this.gl;
};
/**
* Resize the display to match element
* @param { Object } el - DOM element to match
*/
rglwidgetClass.prototype.resize = function(el) {
this.canvas.width = el.width;
this.canvas.height = el.height;
};
/**
* Draw the whole scene
*/
rglwidgetClass.prototype.drawScene = function() {
var gl = this.gl || this.initGL(),
wasDrawing = this.startDrawing();
if (!wasDrawing) {
if (this.select.state !== &#34;inactive&#34;)
this.selectionChanged();
gl.enable(gl.DEPTH_TEST);
gl.depthFunc(gl.LEQUAL);
gl.clearDepth(1.0);
gl.clearColor(1,1,1,1);
gl.depthMask(true); // Must be true before clearing depth buffer
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
this.drawSubscene(this.scene.rootSubscene, true);
this.drawSubscene(this.scene.rootSubscene, false);
}
this.stopDrawing(wasDrawing);
};
/**
* Change the displayed subset
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The subset control data.
*/
rglwidgetClass.prototype.subsetSetter = function(el, control) {
if (typeof control.subscenes === &#34;undefined&#34; ||
control.subscenes === null)
control.subscenes = this.scene.rootSubscene;
var value = Math.round(control.value),
subscenes = [].concat(control.subscenes),
fullset = [].concat(control.fullset),
i, j, entries, subsceneid,
adds = [], deletes = [],
ismissing = function(x) {
return fullset.indexOf(x) &lt; 0;
},
tointeger = function(x) {
return parseInt(x, 10);
};
if (isNaN(value))
value = control.value = 0;
if (control.accumulate)
for (i=0; i &lt;= value; i++)
adds = adds.concat(control.subsets[i]);
else
adds = adds.concat(control.subsets[value]);
deletes = fullset.filter(function(x) { return adds.indexOf(x) &lt; 0; });
for (i = 0; i &lt; subscenes.length; i++) {
subsceneid = subscenes[i];
if (typeof this.getObj(subsceneid) === &#34;undefined&#34;)
this.alertOnce(&#34;typeof object is undefined&#34;);
for (j = 0; j &lt; adds.length; j++)
this.addToSubscene(adds[j], subsceneid);
for (j = 0; j &lt; deletes.length; j++)
this.delFromSubscene(deletes[j], subsceneid);
}
};
/**
* Change the requested property
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The property setter control data.
*/
rglwidgetClass.prototype.propertySetter = function(el, control) {
var value = control.value,
values = [].concat(control.values),
svals = [].concat(control.param),
direct = values[0] === null,
entries = [].concat(control.entries),
ncol = entries.length,
nrow = values.length/ncol,
properties = this.repeatToLen(control.properties, ncol),
objids = this.repeatToLen(control.objids, ncol),
property, objid = objids[0],
obj = this.getObj(objid),
propvals, i, v1, v2, p, entry, gl, needsBinding,
newprop, newid,
getPropvals = function() {
if (property === &#34;userMatrix&#34;)
return obj.par3d.userMatrix.getAsArray();
else if (property === &#34;scale&#34; || property === &#34;FOV&#34; || property === &#34;zoom&#34;)
return [].concat(obj.par3d[property]);
else
return [].concat(obj[property]);
};
putPropvals = function(newvals) {
if (newvals.length == 1)
newvals = newvals[0];
if (property === &#34;userMatrix&#34;)
obj.par3d.userMatrix.load(newvals);
else if (property === &#34;scale&#34; || property === &#34;FOV&#34; || property === &#34;zoom&#34;)
obj.par3d[property] = newvals;
else
obj[property] = newvals;
};
if (direct &amp;&amp; typeof value === &#34;undefined&#34;)
return;
if (control.interp) {
values = values.slice(0, ncol).concat(values).
concat(values.slice(ncol*(nrow-1), ncol*nrow));
svals = [-Infinity].concat(svals).concat(Infinity);
for (i = 1; i &lt; svals.length; i++) {
if (value &lt;= svals[i]) {
if (svals[i] === Infinity)
p = 1;
else
p = (svals[i] - value)/(svals[i] - svals[i-1]);
break;
}
}
} else if (!direct) {
value = Math.round(value);
}
for (j=0; j&lt;entries.length; j++) {
entry = entries[j];
newprop = properties[j];
newid = objids[j];
if (newprop !== property || newid != objid) {
if (typeof property !== &#34;undefined&#34;)
putPropvals(propvals);
property = newprop;
objid = newid;
obj = this.getObj(objid);
propvals = getPropvals();
}
if (control.interp) {
v1 = values[ncol*(i-1) + j];
v2 = values[ncol*i + j];
this.setElement(propvals, entry, p*v1 + (1-p)*v2);
} else if (!direct) {
this.setElement(propvals, entry, values[ncol*value + j]);
} else {
this.setElement(propvals, entry, value[j]);
}
}
putPropvals(propvals);
needsBinding = [];
for (j=0; j &lt; entries.length; j++) {
if (properties[j] === &#34;values&#34; &amp;&amp;
needsBinding.indexOf(objids[j]) === -1) {
needsBinding.push(objids[j]);
}
}
for (j=0; j &lt; needsBinding.length; j++) {
gl = this.gl || this.initGL();
obj = this.getObj(needsBinding[j]);
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertices
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The vertext setter control data.
*/
rglwidgetClass.prototype.vertexSetter = function(el, control) {
var svals = [].concat(control.param),
j, k, p, a, propvals, stride, ofs, obj, entry,
attrib,
ofss = {x:&#34;vofs&#34;, y:&#34;vofs&#34;, z:&#34;vofs&#34;,
red:&#34;cofs&#34;, green:&#34;cofs&#34;, blue:&#34;cofs&#34;,
alpha:&#34;cofs&#34;, radii:&#34;radofs&#34;,
nx:&#34;nofs&#34;, ny:&#34;nofs&#34;, nz:&#34;nofs&#34;,
ox:&#34;oofs&#34;, oy:&#34;oofs&#34;, oz:&#34;oofs&#34;,
ts:&#34;tofs&#34;, tt:&#34;tofs&#34;},
pos = {x:0, y:1, z:2,
red:0, green:1, blue:2,
alpha:3,radii:0,
nx:0, ny:1, nz:2,
ox:0, oy:1, oz:2,
ts:0, tt:1},
values = control.values,
direct = values === null,
ncol,
interp = control.interp,
vertices = [].concat(control.vertices),
attributes = [].concat(control.attributes),
value = control.value, newval, aliases, alias;
ncol = Math.max(vertices.length, attributes.length);
if (!ncol)
return;
vertices = this.repeatToLen(vertices, ncol);
attributes = this.repeatToLen(attributes, ncol);
if (direct)
interp = false;
/* JSON doesn&#39;t pass Infinity */
svals[0] = -Infinity;
svals[svals.length - 1] = Infinity;
for (j = 1; j &lt; svals.length; j++) {
if (value &lt;= svals[j]) {
if (interp) {
if (svals[j] === Infinity)
p = 1;
else
p = (svals[j] - value)/(svals[j] - svals[j-1]);
} else {
if (svals[j] - value &gt; value - svals[j-1])
j = j - 1;
}
break;
}
}
obj = this.getObj(control.objid);
// First, make sure color attributes vary in original
if (typeof obj.vOffsets !== &#34;undefined&#34;) {
varies = true;
for (k = 0; k &lt; ncol; k++) {
attrib = attributes[k];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[attrib]];
if (ofs &lt; 0) {
switch(attrib) {
case &#34;alpha&#34;:
case &#34;red&#34;:
case &#34;green&#34;:
case &#34;blue&#34;:
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(control.objid);
}
propvals = obj.values;
aliases = obj.alias;
if (typeof aliases === &#34;undefined&#34;)
aliases = [];
for (k=0; k&lt;ncol; k++) {
if (direct) {
newval = value;
} else if (interp) {
newval = p*values[j-1][k] + (1-p)*values[j][k];
} else {
newval = values[j][k];
}
attrib = attributes[k];
vertex = vertices[k];
alias = aliases[vertex];
if (obj.type === &#34;planes&#34; || obj.type === &#34;clipplanes&#34;) {
ofs = [&#34;nx&#34;, &#34;ny&#34;, &#34;nz&#34;, &#34;offset&#34;].indexOf(attrib);
if (ofs &gt;= 0) {
if (ofs &lt; 3) {
if (obj.normals[vertex][ofs] != newval) { // Assume no aliases here...
obj.normals[vertex][ofs] = newval;
obj.initialized = false;
}
} else {
if (obj.offsets[vertex][0] != newval) {
obj.offsets[vertex][0] = newval;
obj.initialized = false;
}
}
continue;
}
}
// Not a plane setting...
ofs = obj.vOffsets[ofss[attrib]];
if (ofs &lt; 0)
this.alertOnce(&#34;Attribute &#39;&#34;+attrib+&#34;&#39; not found in object &#34;+control.objid);
else {
stride = obj.vOffsets.stride;
ofs = ofs + pos[attrib];
entry = vertex*stride + ofs;
propvals[entry] = newval;
if (typeof alias !== &#34;undefined&#34;)
for (a = 0; a &lt; alias.length; a++)
propvals[alias[a]*stride + ofs] = newval;
}
}
if (typeof obj.buf !== &#34;undefined&#34;) {
var gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, propvals, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertex properties by age
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The age setter control data.
*/
rglwidgetClass.prototype.ageSetter = function(el, control) {
var objids = [].concat(control.objids),
nobjs = objids.length,
time = control.value,
births = [].concat(control.births),
ages = [].concat(control.ages),
steps = births.length,
j = Array(steps),
p = Array(steps),
i, k, age, j0, propvals, stride, ofs, objid, obj,
attrib, dim, varies, alias, aliases, a, d,
attribs = [&#34;colors&#34;, &#34;alpha&#34;, &#34;radii&#34;, &#34;vertices&#34;,
&#34;normals&#34;, &#34;origins&#34;, &#34;texcoords&#34;,
&#34;x&#34;, &#34;y&#34;, &#34;z&#34;,
&#34;red&#34;, &#34;green&#34;, &#34;blue&#34;],
ofss = [&#34;cofs&#34;, &#34;cofs&#34;, &#34;radofs&#34;, &#34;vofs&#34;,
&#34;nofs&#34;, &#34;oofs&#34;, &#34;tofs&#34;,
&#34;vofs&#34;, &#34;vofs&#34;, &#34;vofs&#34;,
&#34;cofs&#34;, &#34;cofs&#34;, &#34;cofs&#34;],
dims = [3,1,1,3,
3,2,2,
1,1,1,
1,1,1],
pos = [0,3,0,0,
0,0,0,
0,1,2,
0,1,2];
/* Infinity doesn&#39;t make it through JSON */
ages[0] = -Infinity;
ages[ages.length-1] = Infinity;
for (i = 0; i &lt; steps; i++) {
if (births[i] !== null) { // NA in R becomes null
age = time - births[i];
for (j0 = 1; age &gt; ages[j0]; j0++);
if (ages[j0] == Infinity)
p[i] = 1;
else if (ages[j0] &gt; ages[j0-1])
p[i] = (ages[j0] - age)/(ages[j0] - ages[j0-1]);
else
p[i] = 0;
j[i] = j0;
}
}
// First, make sure color attributes vary in original
for (l = 0; l &lt; nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
varies = true;
if (typeof obj.vOffsets === &#34;undefined&#34;)
continue;
for (k = 0; k &lt; attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[k]];
if (ofs &lt; 0) {
switch(attribs[k]) {
case &#34;colors&#34;:
case &#34;alpha&#34;:
case &#34;red&#34;:
case &#34;green&#34;:
case &#34;blue&#34;:
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(objid);
}
for (l = 0; l &lt; nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
if (typeof obj.vOffsets === &#34;undefined&#34;)
continue;
aliases = obj.alias;
if (typeof aliases === &#34;undefined&#34;)
aliases = [];
propvals = obj.values;
stride = obj.vOffsets.stride;
for (k = 0; k &lt; attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[k]];
if (ofs &gt;= 0) {
dim = dims[k];
ofs = ofs + pos[k];
for (i = 0; i &lt; steps; i++) {
alias = aliases[i];
if (births[i] !== null) {
for (d=0; d &lt; dim; d++) {
propvals[i*stride + ofs + d] = p[i]*attrib[dim*(j[i]-1) + d] + (1-p[i])*attrib[dim*j[i] + d];
if (typeof alias !== &#34;undefined&#34;)
for (a=0; a &lt; alias.length; a++)
propvals[alias[a]*stride + ofs + d] = propvals[i*stride + ofs + d];
}
}
}
} else
this.alertOnce(&#34;\&#39;&#34;+attribs[k]+&#34;\&#39; property not found in object &#34;+objid);
}
}
obj.values = propvals;
if (typeof obj.buf !== &#34;undefined&#34;) {
gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
}
};
/**
* Bridge to old style control
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The bridge control data.
*/
rglwidgetClass.prototype.oldBridge = function(el, control) {
var attrname, global = window[control.prefix + &#34;rgl&#34;];
if (global)
for (attrname in global)
this[attrname] = global[attrname];
window[control.prefix + &#34;rgl&#34;] = this;
};
/**
* Set up a player control
* @param { Object } el - The player control element
* @param { Object } control - The player data.
*/
rglwidgetClass.prototype.Player = function(el, control) {
var
self = this,
components = [].concat(control.components),
buttonLabels = [].concat(control.buttonLabels),
Tick = function() { /* &#34;this&#34; will be a timer */
var i,
nominal = this.value,
slider = this.Slider,
labels = this.outputLabels,
output = this.Output,
step;
if (typeof slider !== &#34;undefined&#34; &amp;&amp; nominal != slider.value)
slider.value = nominal;
if (typeof output !== &#34;undefined&#34;) {
step = Math.round((nominal - output.sliderMin)/output.sliderStep);
if (labels !== null) {
output.innerHTML = labels[step];
} else {
step = step*output.sliderStep + output.sliderMin;
output.innerHTML = step.toPrecision(output.outputPrecision);
}
}
for (i=0; i &lt; this.actions.length; i++) {
this.actions[i].value = nominal;
}
self.applyControls(el, this.actions, false);
self.drawScene();
},
OnSliderInput = function() { /* &#34;this&#34; will be the slider */
this.rgltimer.value = Number(this.value);
this.rgltimer.Tick();
},
addSlider = function(min, max, step, value) {
var slider = document.createElement(&#34;input&#34;);
slider.type = &#34;range&#34;;
slider.min = min;
slider.max = max;
slider.step = step;
slider.value = value;
slider.oninput = OnSliderInput;
slider.sliderActions = control.actions;
slider.sliderScene = this;
slider.className = &#34;rgl-slider&#34;;
slider.id = el.id + &#34;-slider&#34;;
el.rgltimer.Slider = slider;
slider.rgltimer = el.rgltimer;
el.appendChild(slider);
},
addLabel = function(labels, min, step, precision) {
var output = document.createElement(&#34;output&#34;);
output.sliderMin = min;
output.sliderStep = step;
output.outputPrecision = precision;
output.className = &#34;rgl-label&#34;;
output.id = el.id + &#34;-label&#34;;
el.rgltimer.Output = output;
el.rgltimer.outputLabels = labels;
el.appendChild(output);
},
addButton = function(which, label, active) {
var button = document.createElement(&#34;input&#34;),
onclicks = {Reverse: function() { this.rgltimer.reverse();},
Play: function() { this.rgltimer.play();
this.value = this.rgltimer.enabled ? this.inactiveValue : this.activeValue; },
Slower: function() { this.rgltimer.slower(); },
Faster: function() { this.rgltimer.faster(); },
Reset: function() { this.rgltimer.reset(); },
Step: function() { this.rgltimer.step(); }
};
button.rgltimer = el.rgltimer;
button.type = &#34;button&#34;;
button.value = label;
button.activeValue = label;
button.inactiveValue = active;
if (which === &#34;Play&#34;)
button.rgltimer.PlayButton = button;
button.onclick = onclicks[which];
button.className = &#34;rgl-button&#34;;
button.id = el.id + &#34;-&#34; + which;
el.appendChild(button);
};
if (typeof control.reinit !== &#34;undefined&#34; &amp;&amp; control.reinit !== null) {
control.actions.reinit = control.reinit;
}
el.rgltimer = new rgltimerClass(Tick, control.start, control.interval, control.stop,
control.step, control.value, control.rate, control.loop, control.actions);
for (var i=0; i &lt; components.length; i++) {
switch(components[i]) {
case &#34;Slider&#34;: addSlider(control.start, control.stop,
control.step, control.value);
break;
case &#34;Label&#34;: addLabel(control.labels, control.start,
control.step, control.precision);
break;
default:
addButton(components[i], buttonLabels[i], control.pause);
}
}
el.rgltimer.Tick();
};
/**
* Apply all registered controls
* @param { Object } el - DOM element of the control
* @param { Object } x - List of actions to apply
* @param { boolean } [draw=true] - Whether to redraw after applying
*/
rglwidgetClass.prototype.applyControls = function(el, x, draw) {
var self = this, reinit = x.reinit, i, control, type;
for (i = 0; i &lt; x.length; i++) {
control = x[i];
type = control.type;
self[type](el, control);
}
if (typeof reinit !== &#34;undefined&#34; &amp;&amp; reinit !== null) {
reinit = [].concat(reinit);
for (i = 0; i &lt; reinit.length; i++)
self.getObj(reinit[i]).initialized = false;
}
if (typeof draw === &#34;undefined&#34; || draw)
self.drawScene();
};
/**
* Handler for scene change
* @param { Object } message - What sort of scene change to do?
*/
rglwidgetClass.prototype.sceneChangeHandler = function(message) {
var self = document.getElementById(message.elementId).rglinstance,
objs = message.objects, mat = message.material,
root = message.rootSubscene,
initSubs = message.initSubscenes,
redraw = message.redrawScene,
skipRedraw = message.skipRedraw,
deletes, subs, allsubs = [], i,j;
if (typeof message.delete !== &#34;undefined&#34;) {
deletes = [].concat(message.delete);
if (typeof message.delfromSubscenes !== &#34;undefined&#34;)
subs = [].concat(message.delfromSubscenes);
else
subs = [];
for (i = 0; i &lt; deletes.length; i++) {
for (j = 0; j &lt; subs.length; j++) {
self.delFromSubscene(deletes[i], subs[j]);
}
delete self.scene.objects[deletes[i]];
}
}
if (typeof objs !== &#34;undefined&#34;) {
Object.keys(objs).forEach(function(key){
key = parseInt(key, 10);
self.scene.objects[key] = objs[key];
self.initObj(key);
var obj = self.getObj(key),
subs = [].concat(obj.inSubscenes), k;
allsubs = allsubs.concat(subs);
for (k = 0; k &lt; subs.length; k++)
self.addToSubscene(key, subs[k]);
});
}
if (typeof mat !== &#34;undefined&#34;) {
self.scene.material = mat;
}
if (typeof root !== &#34;undefined&#34;) {
self.scene.rootSubscene = root;
}
if (typeof initSubs !== &#34;undefined&#34;)
allsubs = allsubs.concat(initSubs);
allsubs = self.unique(allsubs);
for (i = 0; i &lt; allsubs.length; i++) {
self.initSubscene(allsubs[i]);
}
if (typeof skipRedraw !== &#34;undefined&#34;) {
root = self.getObj(self.scene.rootSubscene);
root.par3d.skipRedraw = skipRedraw;
}
if (redraw)
self.drawScene();
};
/**
* Set mouse mode for a subscene
* @param { string } mode - name of mode
* @param { number } button - button number (1 to 3)
* @param { number } subscene - subscene id number
* @param { number } stayActive - if truthy, don&#39;t clear brush
*/
rglwidgetClass.prototype.setMouseMode = function(mode, button, subscene, stayActive) {
var sub = this.getObj(subscene),
which = [&#34;left&#34;, &#34;right&#34;, &#34;middle&#34;][button - 1];
if (!stayActive &amp;&amp; sub.par3d.mouseMode[which] === &#34;selecting&#34;)
this.clearBrush(null);
sub.par3d.mouseMode[which] = mode;
};
/**
* The class of an rgl timer object
* @class
*/
/**
* Construct an rgltimerClass object
* @constructor
* @param { function } Tick - action when timer fires
* @param { number } startTime - nominal start time in seconds
* @param { number } interval - seconds between updates
* @param { number } stopTime - nominal stop time in seconds
* @param { number } stepSize - nominal step size
* @param { number } value - current nominal time
* @param { number } rate - nominal units per second
* @param { string } loop - &#34;none&#34;, &#34;cycle&#34; or &#34;oscillate&#34;
* @param { Object } actions - list of actions
*/
rgltimerClass = function(Tick, startTime, interval, stopTime, stepSize, value, rate, loop, actions) {
this.enabled = false;
this.timerId = 0;
/** nominal start time in seconds */
this.startTime = startTime;
/** current nominal time */
this.value = value;
/** seconds between updates */
this.interval = interval;
/** nominal stop time */
this.stopTime = stopTime;
/** nominal step size */
this.stepSize = stepSize;
/** nominal units per second */
this.rate = rate;
/** &#34;none&#34;, &#34;cycle&#34;, or &#34;oscillate&#34; */
this.loop = loop;
/** real world start time */
this.realStart = undefined;
/** multiplier for fast-forward or reverse */
this.multiplier = 1;
this.actions = actions;
this.Tick = Tick;
};
/**
* Start playing timer object
*/
rgltimerClass.prototype.play = function() {
if (this.enabled) {
this.enabled = false;
window.clearInterval(this.timerId);
this.timerId = 0;
return;
}
var tick = function(self) {
var now = new Date();
self.value = self.multiplier*self.rate*(now - self.realStart)/1000 + self.startTime;
self.forceToRange();
if (typeof self.Tick !== &#34;undefined&#34;) {
self.Tick(self.value);
}
};
this.realStart = new Date() - 1000*(this.value - this.startTime)/this.rate/this.multiplier;
this.timerId = window.setInterval(tick, 1000*this.interval, this);
this.enabled = true;
};
/**
* Force value into legal range
*/
rgltimerClass.prototype.forceToRange = function() {
if (this.value &gt; this.stopTime + this.stepSize/2 || this.value &lt; this.startTime - this.stepSize/2) {
if (!this.loop) {
this.reset();
} else {
var cycle = this.stopTime - this.startTime + this.stepSize,
newval = (this.value - this.startTime) % cycle + this.startTime;
if (newval &lt; this.startTime) {
newval += cycle;
}
this.realStart += (this.value - newval)*1000/this.multiplier/this.rate;
this.value = newval;
}
}
};
/**
* Reset to start values
*/
rgltimerClass.prototype.reset = function() {
this.value = this.startTime;
this.newmultiplier(1);
if (typeof this.Tick !== &#34;undefined&#34;) {
this.Tick(this.value);
}
if (this.enabled)
this.play(); /* really pause... */
if (typeof this.PlayButton !== &#34;undefined&#34;)
this.PlayButton.value = &#34;Play&#34;;
};
/**
* Increase the multiplier to play faster
*/
rgltimerClass.prototype.faster = function() {
this.newmultiplier(Math.SQRT2*this.multiplier);
};
/**
* Decrease the multiplier to play slower
*/
rgltimerClass.prototype.slower = function() {
this.newmultiplier(this.multiplier/Math.SQRT2);
};
/**
* Change sign of multiplier to reverse direction
*/
rgltimerClass.prototype.reverse = function() {
this.newmultiplier(-this.multiplier);
};
/**
* Set multiplier for play speed
* @param { number } newmult - new value
*/
rgltimerClass.prototype.newmultiplier = function(newmult) {
if (newmult != this.multiplier) {
this.realStart += 1000*(this.value - this.startTime)/this.rate*(1/this.multiplier - 1/newmult);
this.multiplier = newmult;
}
};
/**
* Take one step
*/
rgltimerClass.prototype.step = function() {
this.value += this.rate*this.multiplier;
this.forceToRange();
if (typeof this.Tick !== &#34;undefined&#34;)
this.Tick(this.value);
};&lt;/script&gt;
&lt;div id=&#34;unnamed_chunk_31div&#34; class=&#34;rglWebGL&#34;&gt;&lt;/div&gt;
&lt;script type=&#34;text/javascript&#34;&gt;
var unnamed_chunk_31div = document.getElementById(&#34;unnamed_chunk_31div&#34;),
unnamed_chunk_31rgl = new rglwidgetClass();
unnamed_chunk_31div.width = 481;
unnamed_chunk_31div.height = 481;
unnamed_chunk_31rgl.initialize(unnamed_chunk_31div,
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unnamed_chunk_31rgl.prefix = &#34;unnamed_chunk_31&#34;;
&lt;/script&gt;
&lt;p id=&#34;unnamed_chunk_31debug&#34;&gt;
You must enable Javascript to view this page properly.&lt;/p&gt;
&lt;script&gt;unnamed_chunk_31rgl.start();&lt;/script&gt;
&lt;p&gt;You should be able to rotate (click and drag) and zoom (mouse wheel) this figure.&lt;/p&gt;
&lt;p&gt;Since this results in quite large html files when used with many neurons,
we will not use it further here. For now let&amp;rsquo;s show a plot in which we
both select a subset of neurons and colour them according to their glomerulus
of origin.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# 3d plot of neurons from olfactory glomeruli beginning with a D
# coloured by glomerulus
rval=plot3d(Cell07PNs, subset=grepl(&amp;quot;^D&amp;quot;, Glomerulus), col=Glomerulus,
lwd=2, WithNodes=FALSE)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-32-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# make a legend so that you know which colours match which glomerulus
plot.new()
with(attr(rval,&#39;df&#39;), legend(&#39;center&#39;, legend = unique(Glomerulus), fill=unique(col)))
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/plot3d-legend-1.png&#34; width=&#34;288&#34; /&gt;&lt;/p&gt;
&lt;h2 id=&#34;putting-it-all-together&#34;&gt;Putting it all together&lt;/h2&gt;
&lt;p&gt;To close this tutorial, let&amp;rsquo;s do some morphological analysis of the neurons in
this dataset. There are second order olfactory projection neurons
originating from 4 different glomeruli in the &lt;code&gt;Cell07PNs&lt;/code&gt; sample dataset, each
coming from a different animal. We can
ask whether their axon terminal arborisations in a brain area called the lateral
horn show any features that are distinctive for different classes. This would be
consistent with the hypothesis that information from different glomeruli
(i.e. olfactory channels) is handled in a stereotyped way in this brain area.&lt;/p&gt;
&lt;p&gt;Let&amp;rsquo;s start by cutting out the arbour within the lateral horn from all of the
neurons. We&amp;rsquo;ll use a very simple approach of cutting at X=250, although &lt;strong&gt;nat&lt;/strong&gt;
has more sophisticated ways to do this e.g. by using 3D spaces defined by a
surface mesh.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# note that we had to use OmitFailures=T due to a problem with the graph
# structure of one neuron
lha=nlapply(Cell07PNs, subset, X&amp;gt;250, OmitFailures = T)
# Let&#39;s plot what we have colouring by glomerulus
plot(lha, col=Glomerulus, WithNodes=F)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-33-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;Now we can get a basic statistical summary by axon arbour.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;lhstats=summary(lha, include.attached.dataframe = TRUE)
boxplot(lhstats$cable.length~lhstats$Glomerulus, log=&#39;y&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-34-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;boxplot(lhstats$branchpoints~lhstats$Glomerulus)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-neurons/index_files/figure-html/unnamed-chunk-34-2.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;
&lt;p&gt;We can also calculate the median position of the arbour for each neuron and add
that to the lhstats database&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# quick function to calculate centroid
arbour_centroid &amp;lt;- function(n) {
# extract location of all points in neuron object
xyzs=xyzmatrix(n)
# median in all 3 axes (=&amp;gt;2 columns)
apply(xyzs, 2, median)
}
# note that we have to transpose because sapply results in x,y,z rows
centroids=t(sapply(lha, arbour_centroid))
lhstats=cbind(lhstats, centroids)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Finally we can take these data and see how well we can predict the identity of
the neuron (i.e. its glomerulus) based on the statistics of the axon arbour in
the lateral horn. We use the linear discriminant analysis (provided by the
function &lt;code&gt;lda&lt;/code&gt; in recommended package &lt;code&gt;MASS&lt;/code&gt;). This also runs a leave one out
cross-validation to get a more robust initial estimate of prediction error.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;library(MASS)
lda.fit = lda(Glomerulus ~ cable.length+X+Y+Z+branchpoints, lhstats, CV = T)
table(lda.fit$class, lhstats$Glomerulus)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;##
## DA1 DL3 DP1m VA1d
## DA1 10 2 0 1
## DL3 0 7 0 0
## DP1m 0 0 8 0
## VA1d 1 0 0 10
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;The prediction accuracy of &lt;sup&gt;35&lt;/sup&gt;&amp;frasl;&lt;sub&gt;39&lt;/sub&gt; i.e. just under 90% is already very good compared
with a chance level of about 25% for these 4 classes.&lt;/p&gt;
&lt;h2 id=&#34;learning-more&#34;&gt;Learning More&lt;/h2&gt;
&lt;p&gt;We hope this tutorial will provide you with a good foundation for further use of
the &lt;strong&gt;nat&lt;/strong&gt; and related packages. Please visit the main
&lt;a href=&#34;https://natverse.github.io/nat/index.html&#34; target=&#34;_blank&#34;&gt;nat README&lt;/a&gt; for
suggestions of resources to learn more and solve problems. You may also
find that some time spent reading Hadley Wickham&amp;rsquo;s &lt;a href=&#34;http://adv-r.had.co.nz/&#34; target=&#34;_blank&#34;&gt;Advanced R&lt;/a&gt;
is a worthwhile investment. I recommend the first 7 chapters
(Introduction to OO field guide) as material that will be helpful for anyone who
intends to carry out a significant project using R.&lt;/p&gt;</description></item><item><title>NeuroGeometry - Analysing 3D morphology of neurons</title><link>https://natverse.github.io/news/2019/02/nat-1-8-13/</link><pubDate>Thu, 21 Feb 2019 00:00:00 +0000</pubDate><guid>https://natverse.github.io/news/2019/02/nat-1-8-13/</guid><description>
&lt;h2 id=&#34;introduction&#34;&gt;Introduction&lt;/h2&gt;
&lt;p&gt;One of the key distinguishing features of nat is the ability to analyse
neuronal morphology and connectivity from a geometric perspective.
In other words nat provides functions to analyse the placement of neurons within
the context of the brain and the organisation of local circuits.&lt;br /&gt;
This vignette will give a few examples, but this is only skimming the surface
of what is possible.&lt;/p&gt;
&lt;p&gt;If you see an analysis in a paper associated with the Jefferis lab but cannot
figure out how to use nat to achieve this, then feel free to contact the
&lt;a href=&#34;https://groups.google.com/d/forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat–user Google group&lt;/a&gt; to ask for help.&lt;/p&gt;
&lt;h2 id=&#34;vertex-information&#34;&gt;Vertex information&lt;/h2&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;library(nat)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## Loading required package: rgl
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## Registered S3 method overwritten by &#39;nat&#39;:
## method from
## as.mesh3d.ashape3d rgl
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;##
## Attaching package: &#39;nat&#39;
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## The following objects are masked from &#39;package:base&#39;:
##
## intersect, setdiff, union
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;One of the key tools for geometric work in nat is the &lt;code&gt;xyzmatrix&lt;/code&gt; function,
which extracts 3-D coordinate information from any object containing vertices.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;n=Cell07PNs[[1]]
xyz=xyzmatrix(n)
summary(xyz)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## X Y Z
## Min. :186.9 Min. : 90.36 Min. : 88.2
## 1st Qu.:225.6 1st Qu.: 97.56 1st Qu.:103.4
## Median :258.4 Median :102.70 Median :112.9
## Mean :249.4 Mean :104.03 Mean :120.9
## 3rd Qu.:277.7 3rd Qu.:109.04 3rd Qu.:139.0
## Max. :289.5 Max. :132.71 Max. :157.3
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(xyz[,c(&amp;quot;X&amp;quot;,&amp;quot;Y&amp;quot;)], type=&#39;p&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-1-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;p&gt;This also works for neuronlists, so we can extract all of the points in a
collection of neurons:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;xyz=xyzmatrix(Cell07PNs)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;We could ask for all the points close to a specific X coordinate&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;close_to_x250=abs(xyz[,&#39;X&#39;]-250)&amp;lt;10
table(close_to_x250)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## close_to_x250
## FALSE TRUE
## 20479 1728
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;We can also select points interactively by using the &lt;code&gt;rgl::select3d&lt;/code&gt; function.&lt;/p&gt;
&lt;h2 id=&#34;worked-example-plane-cutting-a-tract&#34;&gt;Worked example - plane cutting a tract&lt;/h2&gt;
&lt;p&gt;As a worked example let&amp;rsquo;s try to find the plane cutting a tract defined by the
axons of some example neurons:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs, WithNodes=F)
dist=10
abline(v=250, col=&#39;red&#39;)
abline(v=c(250-dist, 250+dist), col=&#39;red&#39;, lty=&#39;dotted&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-4-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;p&gt;We could ask for all the points close to a specific X coordinate&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;close_to_x250=abs(xyz[,&#39;X&#39;]-250)&amp;lt;10
table(close_to_x250)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## close_to_x250
## FALSE TRUE
## 20479 1728
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Let&amp;rsquo;s find the centroid of those selected points:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;centroid=colMeans(xyz[close_to_x250,])
centroid
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## X Y Z
## 251.16788 94.76735 141.11495
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plot(Cell07PNs, WithNodes=F)
points(matrix(centroid[1:2],ncol=2), pch=20)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-6-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;h3 id=&#34;pca-to-find-tract-vector&#34;&gt;PCA to find tract vector&lt;/h3&gt;
&lt;p&gt;Now let&amp;rsquo;s do a principal components analysis on those points&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;pc=prcomp(xyz[close_to_x250,])
pc1=pc$rotation[,&#39;PC1&#39;]
plot(Cell07PNs, WithNodes=F)
points(matrix(centroid[1:2],ncol=2), pch=20)
res=rbind(centroid-pc1*10, centroid, centroid+pc1*10)
lines(res[,1:2])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-7-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;p&gt;OK, perhaps it would be better if we only used the spine of the neurons&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# There is a problem with one neuron with a loop, hence OmitFailures
spines=nlapply(Cell07PNs, spine, UseStartPoint=T, OmitFailures = T)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## Warning in get.shortest.paths(ng, from = from, to = to, mode = &amp;quot;all&amp;quot;): At
## structural_properties.c:4597 :Couldn&#39;t reach some vertices
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;xyz=xyzmatrix(spines)
close_to_x250=abs(xyz[,&#39;X&#39;]-250)&amp;lt;10
table(close_to_x250)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## close_to_x250
## FALSE TRUE
## 5137 876
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;pc=prcomp(xyz[close_to_x250,])
pc1=pc$rotation[,&#39;PC1&#39;]
plot(spines, WithNodes=F)
points(matrix(centroid[1:2],ncol=2), pch=20)
res=rbind(centroid-pc1*10, centroid, centroid+pc1*10)
# nb 1:2 =&amp;gt; just the xy coords
lines(res[,1:2])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-9-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;h3 id=&#34;tract-vector-for-each-neuron&#34;&gt;Tract vector for each neuron&lt;/h3&gt;
&lt;p&gt;Alternatively, we could find the vector of the first PC for each neuron.
Let&amp;rsquo;s write a function to do that and then apply it to the spine of each neuron.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# returns 6 vector
# first 3 values are centroid
# second three values first principal component
tract_vector &amp;lt;- function(n, xval=250, thresh=10) {
p=xyzmatrix(n)
near=abs(p[,&#39;X&#39;]-xval)&amp;lt;thresh
pc=prcomp(p[near,])
c(colMeans(p[near,]), pc$rotation[,&#39;PC1&#39;])
}
tvs=sapply(spines, tract_vector)
mean_cent=rowMeans(tvs[1:3,])
mean_vec=rowMeans(tvs[4:6,])
# nb *10 to make the vector longer (10 µm) and more visible
res2=rbind(mean_cent-mean_vec*10, mean_cent, mean_cent+mean_vec*10)
plot(spines, col=&#39;grey&#39;, WithNodes=F)
lines(res2[,1:2], lwd=3)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-10-1.png&#34; width=&#34;576&#34; /&gt;&lt;/p&gt;
&lt;h3 id=&#34;lines-crossing-a-plane&#34;&gt;Lines crossing a plane&lt;/h3&gt;
&lt;p&gt;We can look at the plane we have defined in a 3D context as follows:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;plc=plane_coefficients(mean_cent, mean_vec)
plot3d(Cell07PNs[c(1,30)], col=&#39;grey&#39;, WithNodes = F)
planes3d(plc[,1:3], d=plc[,&#39;d&#39;])
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-12-1.png&#34; width=&#34;672&#34; /&gt;&lt;/p&gt;
&lt;p&gt;We can also make a small square plane centred on the chosen point&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;library(rgl)
clear3d()
make_centred_plane &amp;lt;- function(point, normal, scale = 1) {
# find the two orthogonal vectors to this one
uv = Morpho::tangentPlane(normal)
uv = sapply(uv, &amp;quot;*&amp;quot;, scale, simplify = F)
qmesh3d(
cbind(
point + uv$z,
point + uv$y,
point - uv$z,
point - uv$y
),
homogeneous = F,
indices = 1:4
)
}
plane=make_centred_plane(mean_cent, mean_vec, scale=15)
plot3d(spines, col=&#39;grey&#39;)
shade3d(plane, col=&#39;red&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-13-1.png&#34; width=&#34;672&#34; /&gt;&lt;/p&gt;
&lt;p&gt;Finally, we can find the positions at which each neuron intersects the plane.
Note that when there are multiple intersections, we only choose the closest
point to the centroid that we calculated when defining the plane.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;intersections=t(sapply(Cell07PNs, intersect_plane, plc, closestpoint=mean_cent))
# center those intersection points
intersections.cent=scale(intersections, center = T, scale = F)
d=sqrt(rowSums(intersections.cent^2))
mean(d)
&lt;/code&gt;&lt;/pre&gt;
&lt;pre&gt;&lt;code&gt;## [1] 3.118692
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;Then we can plot those positions on the plane&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;spheres3d(intersections, col=&#39;red&#39;, rad=.5)
shade3d(plane, col=&#39;black&#39;)
plot3d(spines, col=&#39;grey&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;script&gt;/*
* Copyright (C) 2009 Apple Inc. All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS&#39;&#39; AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* Copyright (2016) Duncan Murdoch - fixed CanvasMatrix4.ortho,
* cleaned up.
*/
/*
CanvasMatrix4 class
This class implements a 4x4 matrix. It has functions which
duplicate the functionality of the OpenGL matrix stack and
glut functions.
IDL:
[
Constructor(in CanvasMatrix4 matrix), // copy passed matrix into new CanvasMatrix4
Constructor(in sequence&lt;float&gt; array) // create new CanvasMatrix4 with 16 floats (row major)
Constructor() // create new CanvasMatrix4 with identity matrix
]
interface CanvasMatrix4 {
attribute float m11;
attribute float m12;
attribute float m13;
attribute float m14;
attribute float m21;
attribute float m22;
attribute float m23;
attribute float m24;
attribute float m31;
attribute float m32;
attribute float m33;
attribute float m34;
attribute float m41;
attribute float m42;
attribute float m43;
attribute float m44;
void load(in CanvasMatrix4 matrix); // copy the values from the passed matrix
void load(in sequence&lt;float&gt; array); // copy 16 floats into the matrix
sequence&lt;float&gt; getAsArray(); // return the matrix as an array of 16 floats
WebGLFloatArray getAsCanvasFloatArray(); // return the matrix as a WebGLFloatArray with 16 values
void makeIdentity(); // replace the matrix with identity
void transpose(); // replace the matrix with its transpose
void invert(); // replace the matrix with its inverse
void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
void scale(in float x, in float y, in float z); // multiply the matrix by passed scale values on the right
void rotate(in float angle, // multiply the matrix by passed rotation values on the right
in float x, in float y, in float z); // (angle is in degrees)
void multRight(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
void multLeft(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the left
void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
in float bottom, in float top,
in float near, in float far);
void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
in float bottom, in float top,
in float near, in float far);
void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
in float zNear, in float zFar);
void lookat(in float eyex, in float eyey, in float eyez, // multiply the matrix by the passed lookat
in float ctrx, in float ctry, in float ctrz, // values on the right
in float upx, in float upy, in float upz);
}
*/
CanvasMatrix4 = function(m)
{
if (typeof m == &#39;object&#39;) {
if (&#34;length&#34; in m &amp;&amp; m.length &gt;= 16) {
this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
return;
}
else if (m instanceof CanvasMatrix4) {
this.load(m);
return;
}
}
this.makeIdentity();
};
CanvasMatrix4.prototype.load = function()
{
if (arguments.length == 1 &amp;&amp; typeof arguments[0] == &#39;object&#39;) {
var matrix = arguments[0];
if (&#34;length&#34; in matrix &amp;&amp; matrix.length == 16) {
this.m11 = matrix[0];
this.m12 = matrix[1];
this.m13 = matrix[2];
this.m14 = matrix[3];
this.m21 = matrix[4];
this.m22 = matrix[5];
this.m23 = matrix[6];
this.m24 = matrix[7];
this.m31 = matrix[8];
this.m32 = matrix[9];
this.m33 = matrix[10];
this.m34 = matrix[11];
this.m41 = matrix[12];
this.m42 = matrix[13];
this.m43 = matrix[14];
this.m44 = matrix[15];
return;
}
if (arguments[0] instanceof CanvasMatrix4) {
this.m11 = matrix.m11;
this.m12 = matrix.m12;
this.m13 = matrix.m13;
this.m14 = matrix.m14;
this.m21 = matrix.m21;
this.m22 = matrix.m22;
this.m23 = matrix.m23;
this.m24 = matrix.m24;
this.m31 = matrix.m31;
this.m32 = matrix.m32;
this.m33 = matrix.m33;
this.m34 = matrix.m34;
this.m41 = matrix.m41;
this.m42 = matrix.m42;
this.m43 = matrix.m43;
this.m44 = matrix.m44;
return;
}
}
this.makeIdentity();
};
CanvasMatrix4.prototype.getAsArray = function()
{
return [
this.m11, this.m12, this.m13, this.m14,
this.m21, this.m22, this.m23, this.m24,
this.m31, this.m32, this.m33, this.m34,
this.m41, this.m42, this.m43, this.m44
];
};
CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
{
return new WebGLFloatArray(this.getAsArray());
};
CanvasMatrix4.prototype.makeIdentity = function()
{
this.m11 = 1;
this.m12 = 0;
this.m13 = 0;
this.m14 = 0;
this.m21 = 0;
this.m22 = 1;
this.m23 = 0;
this.m24 = 0;
this.m31 = 0;
this.m32 = 0;
this.m33 = 1;
this.m34 = 0;
this.m41 = 0;
this.m42 = 0;
this.m43 = 0;
this.m44 = 1;
};
CanvasMatrix4.prototype.transpose = function()
{
var tmp = this.m12;
this.m12 = this.m21;
this.m21 = tmp;
tmp = this.m13;
this.m13 = this.m31;
this.m31 = tmp;
tmp = this.m14;
this.m14 = this.m41;
this.m41 = tmp;
tmp = this.m23;
this.m23 = this.m32;
this.m32 = tmp;
tmp = this.m24;
this.m24 = this.m42;
this.m42 = tmp;
tmp = this.m34;
this.m34 = this.m43;
this.m43 = tmp;
};
CanvasMatrix4.prototype.invert = function()
{
// Calculate the 4x4 determinant
// If the determinant is zero,
// then the inverse matrix is not unique.
var det = this._determinant4x4();
if (Math.abs(det) &lt; 1e-8)
return null;
this._makeAdjoint();
// Scale the adjoint matrix to get the inverse
this.m11 /= det;
this.m12 /= det;
this.m13 /= det;
this.m14 /= det;
this.m21 /= det;
this.m22 /= det;
this.m23 /= det;
this.m24 /= det;
this.m31 /= det;
this.m32 /= det;
this.m33 /= det;
this.m34 /= det;
this.m41 /= det;
this.m42 /= det;
this.m43 /= det;
this.m44 /= det;
};
CanvasMatrix4.prototype.translate = function(x,y,z)
{
if (x === undefined)
x = 0;
if (y === undefined)
y = 0;
if (z === undefined)
z = 0;
var matrix = new CanvasMatrix4();
matrix.m41 = x;
matrix.m42 = y;
matrix.m43 = z;
this.multRight(matrix);
};
CanvasMatrix4.prototype.scale = function(x,y,z)
{
if (x === undefined)
x = 1;
if (z === undefined) {
if (y === undefined) {
y = x;
z = x;
}
else
z = 1;
}
else if (y === undefined)
y = x;
var matrix = new CanvasMatrix4();
matrix.m11 = x;
matrix.m22 = y;
matrix.m33 = z;
this.multRight(matrix);
};
CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
{
// angles are in degrees. Switch to radians
angle = angle / 180 * Math.PI;
angle /= 2;
var sinA = Math.sin(angle);
var cosA = Math.cos(angle);
var sinA2 = sinA * sinA;
// normalize
var length = Math.sqrt(x * x + y * y + z * z);
if (length === 0) {
// bad vector, just use something reasonable
x = 0;
y = 0;
z = 1;
} else if (length != 1) {
x /= length;
y /= length;
z /= length;
}
var mat = new CanvasMatrix4();
// optimize case where axis is along major axis
if (x == 1 &amp;&amp; y === 0 &amp;&amp; z === 0) {
mat.m11 = 1;
mat.m12 = 0;
mat.m13 = 0;
mat.m21 = 0;
mat.m22 = 1 - 2 * sinA2;
mat.m23 = 2 * sinA * cosA;
mat.m31 = 0;
mat.m32 = -2 * sinA * cosA;
mat.m33 = 1 - 2 * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else if (x === 0 &amp;&amp; y == 1 &amp;&amp; z === 0) {
mat.m11 = 1 - 2 * sinA2;
mat.m12 = 0;
mat.m13 = -2 * sinA * cosA;
mat.m21 = 0;
mat.m22 = 1;
mat.m23 = 0;
mat.m31 = 2 * sinA * cosA;
mat.m32 = 0;
mat.m33 = 1 - 2 * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else if (x === 0 &amp;&amp; y === 0 &amp;&amp; z == 1) {
mat.m11 = 1 - 2 * sinA2;
mat.m12 = 2 * sinA * cosA;
mat.m13 = 0;
mat.m21 = -2 * sinA * cosA;
mat.m22 = 1 - 2 * sinA2;
mat.m23 = 0;
mat.m31 = 0;
mat.m32 = 0;
mat.m33 = 1;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
} else {
var x2 = x*x;
var y2 = y*y;
var z2 = z*z;
mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
mat.m14 = mat.m24 = mat.m34 = 0;
mat.m41 = mat.m42 = mat.m43 = 0;
mat.m44 = 1;
}
this.multRight(mat);
};
CanvasMatrix4.prototype.multRight = function(mat)
{
var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21 +
this.m13 * mat.m31 + this.m14 * mat.m41);
var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22 +
this.m13 * mat.m32 + this.m14 * mat.m42);
var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23 +
this.m13 * mat.m33 + this.m14 * mat.m43);
var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24 +
this.m13 * mat.m34 + this.m14 * mat.m44);
var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21 +
this.m23 * mat.m31 + this.m24 * mat.m41);
var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22 +
this.m23 * mat.m32 + this.m24 * mat.m42);
var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23 +
this.m23 * mat.m33 + this.m24 * mat.m43);
var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24 +
this.m23 * mat.m34 + this.m24 * mat.m44);
var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21 +
this.m33 * mat.m31 + this.m34 * mat.m41);
var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22 +
this.m33 * mat.m32 + this.m34 * mat.m42);
var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23 +
this.m33 * mat.m33 + this.m34 * mat.m43);
var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24 +
this.m33 * mat.m34 + this.m34 * mat.m44);
var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21 +
this.m43 * mat.m31 + this.m44 * mat.m41);
var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22 +
this.m43 * mat.m32 + this.m44 * mat.m42);
var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23 +
this.m43 * mat.m33 + this.m44 * mat.m43);
var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24 +
this.m43 * mat.m34 + this.m44 * mat.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.multLeft = function(mat)
{
var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21 +
mat.m13 * this.m31 + mat.m14 * this.m41);
var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22 +
mat.m13 * this.m32 + mat.m14 * this.m42);
var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23 +
mat.m13 * this.m33 + mat.m14 * this.m43);
var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24 +
mat.m13 * this.m34 + mat.m14 * this.m44);
var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21 +
mat.m23 * this.m31 + mat.m24 * this.m41);
var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22 +
mat.m23 * this.m32 + mat.m24 * this.m42);
var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23 +
mat.m23 * this.m33 + mat.m24 * this.m43);
var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24 +
mat.m23 * this.m34 + mat.m24 * this.m44);
var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21 +
mat.m33 * this.m31 + mat.m34 * this.m41);
var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22 +
mat.m33 * this.m32 + mat.m34 * this.m42);
var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23 +
mat.m33 * this.m33 + mat.m34 * this.m43);
var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24 +
mat.m33 * this.m34 + mat.m34 * this.m44);
var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21 +
mat.m43 * this.m31 + mat.m44 * this.m41);
var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22 +
mat.m43 * this.m32 + mat.m44 * this.m42);
var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23 +
mat.m43 * this.m33 + mat.m44 * this.m43);
var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24 +
mat.m43 * this.m34 + mat.m44 * this.m44);
this.m11 = m11;
this.m12 = m12;
this.m13 = m13;
this.m14 = m14;
this.m21 = m21;
this.m22 = m22;
this.m23 = m23;
this.m24 = m24;
this.m31 = m31;
this.m32 = m32;
this.m33 = m33;
this.m34 = m34;
this.m41 = m41;
this.m42 = m42;
this.m43 = m43;
this.m44 = m44;
};
CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
{
var tx = (left + right) / (left - right);
var ty = (top + bottom) / (bottom - top);
var tz = (far + near) / (near - far);
var matrix = new CanvasMatrix4();
matrix.m11 = 2 / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = 0;
matrix.m32 = 0;
matrix.m33 = -2 / (far - near);
matrix.m34 = 0;
matrix.m41 = tx;
matrix.m42 = ty;
matrix.m43 = tz;
matrix.m44 = 1;
this.multRight(matrix);
};
CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
{
var matrix = new CanvasMatrix4();
var A = (right + left) / (right - left);
var B = (top + bottom) / (top - bottom);
var C = -(far + near) / (far - near);
var D = -(2 * far * near) / (far - near);
matrix.m11 = (2 * near) / (right - left);
matrix.m12 = 0;
matrix.m13 = 0;
matrix.m14 = 0;
matrix.m21 = 0;
matrix.m22 = 2 * near / (top - bottom);
matrix.m23 = 0;
matrix.m24 = 0;
matrix.m31 = A;
matrix.m32 = B;
matrix.m33 = C;
matrix.m34 = -1;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = D;
matrix.m44 = 0;
this.multRight(matrix);
};
CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
{
var top = Math.tan(fovy * Math.PI / 360) * zNear;
var bottom = -top;
var left = aspect * bottom;
var right = aspect * top;
this.frustum(left, right, bottom, top, zNear, zFar);
};
CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
{
var matrix = new CanvasMatrix4();
// Make rotation matrix
// Z vector
var zx = eyex - centerx;
var zy = eyey - centery;
var zz = eyez - centerz;
var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
if (mag) {
zx /= mag;
zy /= mag;
zz /= mag;
}
// Y vector
var yx = upx;
var yy = upy;
var yz = upz;
// X vector = Y cross Z
xx = yy * zz - yz * zy;
xy = -yx * zz + yz * zx;
xz = yx * zy - yy * zx;
// Recompute Y = Z cross X
yx = zy * xz - zz * xy;
yy = -zx * xz + zz * xx;
yx = zx * xy - zy * xx;
// cross product gives area of parallelogram, which is &lt; 1.0 for
// non-perpendicular unit-length vectors; so normalize x, y here
mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
if (mag) {
xx /= mag;
xy /= mag;
xz /= mag;
}
mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
if (mag) {
yx /= mag;
yy /= mag;
yz /= mag;
}
matrix.m11 = xx;
matrix.m12 = xy;
matrix.m13 = xz;
matrix.m14 = 0;
matrix.m21 = yx;
matrix.m22 = yy;
matrix.m23 = yz;
matrix.m24 = 0;
matrix.m31 = zx;
matrix.m32 = zy;
matrix.m33 = zz;
matrix.m34 = 0;
matrix.m41 = 0;
matrix.m42 = 0;
matrix.m43 = 0;
matrix.m44 = 1;
matrix.translate(-eyex, -eyey, -eyez);
this.multRight(matrix);
};
// Support functions
CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
{
return a * d - b * c;
};
CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
{
return a1 * this._determinant2x2(b2, b3, c2, c3) -
b1 * this._determinant2x2(a2, a3, c2, c3) +
c1 * this._determinant2x2(a2, a3, b2, b3);
};
CanvasMatrix4.prototype._determinant4x4 = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
};
CanvasMatrix4.prototype._makeAdjoint = function()
{
var a1 = this.m11;
var b1 = this.m12;
var c1 = this.m13;
var d1 = this.m14;
var a2 = this.m21;
var b2 = this.m22;
var c2 = this.m23;
var d2 = this.m24;
var a3 = this.m31;
var b3 = this.m32;
var c3 = this.m33;
var d3 = this.m34;
var a4 = this.m41;
var b4 = this.m42;
var c4 = this.m43;
var d4 = this.m44;
// Row column labeling reversed since we transpose rows &amp; columns
this.m11 = this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
this.m21 = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
this.m31 = this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
this.m41 = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
this.m12 = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
this.m22 = this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
this.m32 = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
this.m42 = this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
this.m13 = this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
this.m23 = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
this.m33 = this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
this.m43 = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
this.m14 = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
this.m24 = this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
this.m34 = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
this.m44 = this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
};&lt;/script&gt;
&lt;script&gt;// To generate the help pages for this library, use
// jsdoc --destination ../../../doc/rglwidgetClass --template ~/node_modules/jsdoc-baseline rglClass.src.js
// To validate, use
// setwd(&#34;.../inst/htmlwidgets/lib/rglClass&#34;)
// hints &lt;- js::jshint(readLines(&#34;rglClass.src.js&#34;))
// hints[, c(&#34;line&#34;, &#34;reason&#34;)]
/**
* The class of an rgl widget
* @class
*/
rglwidgetClass = function() {
this.canvas = null;
this.userMatrix = new CanvasMatrix4();
this.types = [];
this.prMatrix = new CanvasMatrix4();
this.mvMatrix = new CanvasMatrix4();
this.vp = null;
this.prmvMatrix = null;
this.origs = null;
this.gl = null;
this.scene = null;
this.select = {state: &#34;inactive&#34;, subscene: null, region: {p1: {x:0, y:0}, p2: {x:0, y:0}}};
this.drawing = false;
};
/**
* Multiply matrix by vector
* @returns {number[]}
* @param M {number[][]} Left operand
* @param v {number[]} Right operand
*/
rglwidgetClass.prototype.multMV = function(M, v) {
return [ M.m11 * v[0] + M.m12 * v[1] + M.m13 * v[2] + M.m14 * v[3],
M.m21 * v[0] + M.m22 * v[1] + M.m23 * v[2] + M.m24 * v[3],
M.m31 * v[0] + M.m32 * v[1] + M.m33 * v[2] + M.m34 * v[3],
M.m41 * v[0] + M.m42 * v[1] + M.m43 * v[2] + M.m44 * v[3]
];
};
/**
* Multiply row vector by Matrix
* @returns {number[]}
* @param v {number[]} left operand
* @param M {number[][]} right operand
*/
rglwidgetClass.prototype.multVM = function(v, M) {
return [ M.m11 * v[0] + M.m21 * v[1] + M.m31 * v[2] + M.m41 * v[3],
M.m12 * v[0] + M.m22 * v[1] + M.m32 * v[2] + M.m42 * v[3],
M.m13 * v[0] + M.m23 * v[1] + M.m33 * v[2] + M.m43 * v[3],
M.m14 * v[0] + M.m24 * v[1] + M.m34 * v[2] + M.m44 * v[3]
];
};
/**
* Euclidean length of a vector
* @returns {number}
* @param v {number[]}
*/
rglwidgetClass.prototype.vlen = function(v) {
return Math.sqrt(this.dotprod(v, v));
};
/**
* Dot product of two vectors
* @instance rglwidgetClass
* @returns {number}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.dotprod = function(a, b) {
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
};
/**
* Cross product of two vectors
* @returns {number[]}
* @param a {number[]}
* @param b {number[]}
*/
rglwidgetClass.prototype.xprod = function(a, b) {
return [a[1]*b[2] - a[2]*b[1],
a[2]*b[0] - a[0]*b[2],
a[0]*b[1] - a[1]*b[0]];
};
/**
* Bind vectors or matrices by columns
* @returns {number[][]}
* @param a {number[]|number[][]}
* @param b {number[]|number[][]}
*/
rglwidgetClass.prototype.cbind = function(a, b) {
if (b.length &lt; a.length)
b = this.repeatToLen(b, a.length);
else if (a.length &lt; b.length)
a = this.repeatToLen(a, b.length);
return a.map(function(currentValue, index, array) {
return currentValue.concat(b[index]);
});
};
/**
* Swap elements
* @returns {any[]}
* @param a {any[]}
* @param i {number} Element to swap
* @param j {number} Other element to swap
*/
rglwidgetClass.prototype.swap = function(a, i, j) {
var temp = a[i];
a[i] = a[j];
a[j] = temp;
};
/**
* Flatten a matrix into a vector
* @returns {any[]}
* @param a {any[][]}
*/
rglwidgetClass.prototype.flatten = function(arr, result) {
var value;
if (typeof result === &#34;undefined&#34;) result = [];
for (var i = 0, length = arr.length; i &lt; length; i++) {
value = arr[i];
if (Array.isArray(value)) {
this.flatten(value, result);
} else {
result.push(value);
}
}
return result;
};
/**
* set element of 1d or 2d array as if it was flattened.
* Column major, zero based!
* @returns {any[]|any[][]}
* @param {any[]|any[][]} a - array
* @param {number} i - element
* @param {any} value
*/
rglwidgetClass.prototype.setElement = function(a, i, value) {
if (Array.isArray(a[0])) {
var dim = a.length,
col = Math.floor(i/dim),
row = i % dim;
a[row][col] = value;
} else {
a[i] = value;
}
};
/**
* Transpose an array
* @returns {any[][]}
* @param {any[][]} a
*/
rglwidgetClass.prototype.transpose = function(a) {
var newArray = [],
n = a.length,
m = a[0].length,
i;
for(i = 0; i &lt; m; i++){
newArray.push([]);
}
for(i = 0; i &lt; n; i++){
for(var j = 0; j &lt; m; j++){
newArray[j].push(a[i][j]);
}
}
return newArray;
};
/**
* Calculate sum of squares of a numeric vector
* @returns {number}
* @param {number[]} x
*/
rglwidgetClass.prototype.sumsq = function(x) {
var result = 0, i;
for (i=0; i &lt; x.length; i++)
result += x[i]*x[i];
return result;
};
/**
* Convert a matrix to a CanvasMatrix4
* @returns {CanvasMatrix4}
* @param {number[][]|number[]} mat
*/
rglwidgetClass.prototype.toCanvasMatrix4 = function(mat) {
if (mat instanceof CanvasMatrix4)
return mat;
var result = new CanvasMatrix4();
mat = this.flatten(this.transpose(mat));
result.load(mat);
return result;
};
/**
* Convert an R-style numeric colour string to an rgb vector
* @returns {number[]}
* @param {string} s
*/
rglwidgetClass.prototype.stringToRgb = function(s) {
s = s.replace(&#34;#&#34;, &#34;&#34;);
var bigint = parseInt(s, 16);
return [((bigint &gt;&gt; 16) &amp; 255)/255,
((bigint &gt;&gt; 8) &amp; 255)/255,
(bigint &amp; 255)/255];
};
/**
* Take a component-by-component product of two 3 vectors
* @returns {number[]}
* @param {number[]} x
* @param {number[]} y
*/
rglwidgetClass.prototype.componentProduct = function(x, y) {
if (typeof y === &#34;undefined&#34;) {
this.alertOnce(&#34;Bad arg to componentProduct&#34;);
}
var result = new Float32Array(3), i;
for (i = 0; i&lt;3; i++)
result[i] = x[i]*y[i];
return result;
};
/**
* Get next higher power of two
* @returns { number }
* @param { number } value - input value
*/
rglwidgetClass.prototype.getPowerOfTwo = function(value) {
var pow = 1;
while(pow&lt;value) {
pow *= 2;
}
return pow;
};
/**
* Unique entries
* @returns { any[] }
* @param { any[] } arr - An array
*/
rglwidgetClass.prototype.unique = function(arr) {
arr = [].concat(arr);
return arr.filter(function(value, index, self) {
return self.indexOf(value) === index;
});
};
/**
* Shallow compare of arrays
* @returns { boolean }
* @param { any[] } a - An array
* @param { any[] } b - Another array
*/
rglwidgetClass.prototype.equalArrays = function(a, b) {
return a === b || (a &amp;&amp; b &amp;&amp;
a.length === b.length &amp;&amp;
a.every(function(v, i) {return v === b[i];}));
};
/**
* Repeat an array to a desired length
* @returns {any[]}
* @param {any | any[]} arr The input array
* @param {number} len The desired output length
*/
rglwidgetClass.prototype.repeatToLen = function(arr, len) {
arr = [].concat(arr);
while (arr.length &lt; len/2)
arr = arr.concat(arr);
return arr.concat(arr.slice(0, len - arr.length));
};
/**
* Give a single alert message, not to be repeated.
* @param {string} msg The message to give.
*/
rglwidgetClass.prototype.alertOnce = function(msg) {
if (typeof this.alerted !== &#34;undefined&#34;)
return;
this.alerted = true;
alert(msg);
};
rglwidgetClass.prototype.f_is_lit = 1;
rglwidgetClass.prototype.f_is_smooth = 2;
rglwidgetClass.prototype.f_has_texture = 4;
rglwidgetClass.prototype.f_depth_sort = 8;
rglwidgetClass.prototype.f_fixed_quads = 16;
rglwidgetClass.prototype.f_is_transparent = 32;
rglwidgetClass.prototype.f_is_lines = 64;
rglwidgetClass.prototype.f_sprites_3d = 128;
rglwidgetClass.prototype.f_sprite_3d = 256;
rglwidgetClass.prototype.f_is_subscene = 512;
rglwidgetClass.prototype.f_is_clipplanes = 1024;
rglwidgetClass.prototype.f_fixed_size = 2048;
rglwidgetClass.prototype.f_is_points = 4096;
rglwidgetClass.prototype.f_is_twosided = 8192;
rglwidgetClass.prototype.f_fat_lines = 16384;
rglwidgetClass.prototype.f_is_brush = 32768;
/**
* Which list does a particular id come from?
* @returns { string }
* @param {number} id The id to look up.
*/
rglwidgetClass.prototype.whichList = function(id) {
var obj = this.getObj(id),
flags = obj.flags;
if (obj.type === &#34;light&#34;)
return &#34;lights&#34;;
if (flags &amp; this.f_is_subscene)
return &#34;subscenes&#34;;
if (flags &amp; this.f_is_clipplanes)
return &#34;clipplanes&#34;;
if (flags &amp; this.f_is_transparent)
return &#34;transparent&#34;;
return &#34;opaque&#34;;
};
/**
* Get an object by id number.
* @returns { Object }
* @param {number} id
*/
rglwidgetClass.prototype.getObj = function(id) {
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;getObj id is &#34;+typeof id);
}
return this.scene.objects[id];
};
/**
* Get ids of a particular type from a subscene or the whole scene
* @returns { number[] }
* @param {string} type What type of object?
* @param {number} subscene Which subscene? If not given, find in the whole scene
*/
rglwidgetClass.prototype.getIdsByType = function(type, subscene) {
var
result = [], i, self = this;
if (typeof subscene === &#34;undefined&#34;) {
Object.keys(this.scene.objects).forEach(
function(key) {
key = parseInt(key, 10);
if (self.getObj(key).type === type)
result.push(key);
});
} else {
ids = this.getObj(subscene).objects;
for (i=0; i &lt; ids.length; i++) {
if (this.getObj(ids[i]).type === type) {
result.push(ids[i]);
}
}
}
return result;
};
/**
* Get a particular material property for an id
* @returns { any }
* @param {number} id Which object?
* @param {string} property Which material property?
*/
rglwidgetClass.prototype.getMaterial = function(id, property) {
var obj = this.getObj(id), mat;
if (typeof obj.material === &#34;undefined&#34;)
console.error(&#34;material undefined&#34;);
mat = obj.material[property];
if (typeof mat === &#34;undefined&#34;)
mat = this.scene.material[property];
return mat;
};
/**
* Is a particular id in a subscene?
* @returns { boolean }
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.inSubscene = function(id, subscene) {
return this.getObj(subscene).objects.indexOf(id) &gt; -1;
};
/**
* Add an id to a subscene.
* @param {number} id Which id?
* @param {number} subscene Which subscene id?
*/
rglwidgetClass.prototype.addToSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
ids = [id],
obj = this.getObj(id), i;
if (typeof obj != &#34;undefined&#34; &amp;&amp; typeof (obj.newIds) !== &#34;undefined&#34;) {
ids = ids.concat(obj.newIds);
}
thesub.objects = [].concat(thesub.objects);
for (i = 0; i &lt; ids.length; i++) {
id = ids[i];
if (thesub.objects.indexOf(id) == -1) {
thelist = this.whichList(id);
thesub.objects.push(id);
thesub[thelist].push(id);
}
}
};
/**
* Delete an id from a subscene
* @param { number } id - the id to add
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.delFromSubscene = function(id, subscene) {
var thelist,
thesub = this.getObj(subscene),
obj = this.getObj(id),
ids = [id], i;
if (typeof obj !== &#34;undefined&#34; &amp;&amp; typeof (obj.newIds) !== &#34;undefined&#34;)
ids = ids.concat(obj.newIds);
thesub.objects = [].concat(thesub.objects); // It might be a scalar
for (j=0; j&lt;ids.length;j++) {
id = ids[j];
i = thesub.objects.indexOf(id);
if (i &gt; -1) {
thesub.objects.splice(i, 1);
thelist = this.whichList(id);
i = thesub[thelist].indexOf(id);
thesub[thelist].splice(i, 1);
}
}
};
/**
* Set the ids in a subscene
* @param { number[] } ids - the ids to set
* @param { number } subsceneid - the id of the subscene
*/
rglwidgetClass.prototype.setSubsceneEntries = function(ids, subsceneid) {
var sub = this.getObj(subsceneid);
sub.objects = ids;
this.initSubscene(subsceneid);
};
/**
* Get the ids in a subscene
* @returns {number[]}
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getSubsceneEntries = function(subscene) {
return this.getObj(subscene).objects;
};
/**
* Get the ids of the subscenes within a subscene
* @returns { number[] }
* @param { number } subscene - the id of the subscene
*/
rglwidgetClass.prototype.getChildSubscenes = function(subscene) {
return this.getObj(subscene).subscenes;
};
/**
* Start drawing
* @returns { boolean } Previous state
*/
rglwidgetClass.prototype.startDrawing = function() {
var value = this.drawing;
this.drawing = true;
return value;
};
/**
* Stop drawing and check for context loss
* @param { boolean } saved - Previous state
*/
rglwidgetClass.prototype.stopDrawing = function(saved) {
this.drawing = saved;
if (!saved &amp;&amp; this.gl &amp;&amp; this.gl.isContextLost())
this.restartCanvas();
};
/**
* Generate the vertex shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getVertexShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userVertexShader,
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
nclipplanes = this.countClipplanes(),
fixed_size = flags &amp; this.f_fixed_size,
is_points = flags &amp; this.f_is_points,
is_twosided = flags &amp; this.f_is_twosided,
fat_lines = flags &amp; this.f_fat_lines,
is_brush = flags &amp; this.f_is_brush,
result;
if (type === &#34;clipplanes&#34; || sprites_3d) return;
if (typeof userShader !== &#34;undefined&#34;) return userShader;
result = &#34; /* ****** &#34;+type+&#34; object &#34;+id+&#34; vertex shader ****** */\n&#34;+
&#34; attribute vec3 aPos;\n&#34;+
&#34; attribute vec4 aCol;\n&#34;+
&#34; uniform mat4 mvMatrix;\n&#34;+
&#34; uniform mat4 prMatrix;\n&#34;+
&#34; varying vec4 vCol;\n&#34;+
&#34; varying vec4 vPosition;\n&#34;;
if ((is_lit &amp;&amp; !fixed_quads &amp;&amp; !is_brush) || sprite_3d)
result = result + &#34; attribute vec3 aNorm;\n&#34;+
&#34; uniform mat4 normMatrix;\n&#34;+
&#34; varying vec3 vNormal;\n&#34;;
if (has_texture || type === &#34;text&#34;)
result = result + &#34; attribute vec2 aTexcoord;\n&#34;+
&#34; varying vec2 vTexcoord;\n&#34;;
if (fixed_size)
result = result + &#34; uniform vec2 textScale;\n&#34;;
if (fixed_quads)
result = result + &#34; attribute vec2 aOfs;\n&#34;;
else if (sprite_3d)
result = result + &#34; uniform vec3 uOrig;\n&#34;+
&#34; uniform float uSize;\n&#34;+
&#34; uniform mat4 usermat;\n&#34;;
if (is_twosided)
result = result + &#34; attribute vec3 aPos1;\n&#34;+
&#34; attribute vec3 aPos2;\n&#34;+
&#34; varying float normz;\n&#34;;
if (fat_lines) {
result = result + &#34; attribute vec3 aNext;\n&#34;+
&#34; attribute vec2 aPoint;\n&#34;+
&#34; varying vec2 vPoint;\n&#34;+
&#34; varying float vLength;\n&#34;+
&#34; uniform float uAspect;\n&#34;+
&#34; uniform float uLwd;\n&#34;;
}
result = result + &#34; void main(void) {\n&#34;;
if ((nclipplanes || (!fixed_quads &amp;&amp; !sprite_3d)) &amp;&amp; !is_brush)
result = result + &#34; vPosition = mvMatrix * vec4(aPos, 1.);\n&#34;;
if (!fixed_quads &amp;&amp; !sprite_3d &amp;&amp; !is_brush)
result = result + &#34; gl_Position = prMatrix * vPosition;\n&#34;;
if (is_points) {
var size = this.getMaterial(id, &#34;size&#34;);
result = result + &#34; gl_PointSize = &#34;+size.toFixed(1)+&#34;;\n&#34;;
}
result = result + &#34; vCol = aCol;\n&#34;;
if (is_lit &amp;&amp; !fixed_quads &amp;&amp; !sprite_3d &amp;&amp; !is_brush)
result = result + &#34; vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n&#34;;
if (has_texture || type == &#34;text&#34;)
result = result + &#34; vTexcoord = aTexcoord;\n&#34;;
if (fixed_size)
result = result + &#34; vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n&#34;+
&#34; pos = pos/pos.w;\n&#34;+
&#34; gl_Position = pos + vec4(aOfs*textScale, 0.,0.);\n&#34;;
if (type == &#34;sprites&#34; &amp;&amp; !fixed_size)
result = result + &#34; vec4 pos = mvMatrix * vec4(aPos, 1.);\n&#34;+
&#34; pos = pos/pos.w + vec4(aOfs, 0., 0.);\n&#34;+
&#34; gl_Position = prMatrix*pos;\n&#34;;
if (sprite_3d)
result = result + &#34; vNormal = normalize((normMatrix * vec4(aNorm, 1.)).xyz);\n&#34;+
&#34; vec4 pos = mvMatrix * vec4(uOrig, 1.);\n&#34;+
&#34; vPosition = pos/pos.w + vec4(uSize*(vec4(aPos, 1.)*usermat).xyz,0.);\n&#34;+
&#34; gl_Position = prMatrix * vPosition;\n&#34;;
if (is_twosided)
result = result + &#34; vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n&#34;+
&#34; pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n&#34;+
&#34; vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n&#34;+
&#34; pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n&#34;+
&#34; normz = pos1.x*pos2.y - pos1.y*pos2.x;\n&#34;;
if (fat_lines)
/* This code was inspired by Matt Deslauriers&#39; code in https://mattdesl.svbtle.com/drawing-lines-is-hard */
result = result + &#34; vec2 aspectVec = vec2(uAspect, 1.0);\n&#34;+
&#34; mat4 projViewModel = prMatrix * mvMatrix;\n&#34;+
&#34; vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n&#34;+
&#34; currentProjected = currentProjected/currentProjected.w;\n&#34;+
&#34; vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n&#34;+
&#34; vec2 currentScreen = currentProjected.xy * aspectVec;\n&#34;+
&#34; vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n&#34;+
&#34; float len = uLwd;\n&#34;+
&#34; vec2 dir = vec2(1.0, 0.0);\n&#34;+
&#34; vPoint = aPoint;\n&#34;+
&#34; vLength = length(nextScreen - currentScreen)/2.0;\n&#34;+
&#34; vLength = vLength/(vLength + len);\n&#34;+
&#34; if (vLength &gt; 0.0) {\n&#34;+
&#34; dir = normalize(nextScreen - currentScreen);\n&#34;+
&#34; }\n&#34;+
&#34; vec2 normal = vec2(-dir.y, dir.x);\n&#34;+
&#34; dir.x /= uAspect;\n&#34;+
&#34; normal.x /= uAspect;\n&#34;+
&#34; vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n&#34;+
&#34; gl_Position = currentProjected + offset;\n&#34;;
if (is_brush)
result = result + &#34; gl_Position = vec4(aPos, 1.);\n&#34;;
result = result + &#34; }\n&#34;;
// console.log(result);
return result;
};
/**
* Generate the fragment shader for an object
* @returns {string}
* @param { number } id - Id of object
*/
rglwidgetClass.prototype.getFragmentShader = function(id) {
var obj = this.getObj(id),
userShader = obj.userFragmentShader,
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
sprites_3d = flags &amp; this.f_sprites_3d,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
fat_lines = flags &amp; this.f_fat_lines,
is_transparent = flags &amp; this.f_is_transparent,
nclipplanes = this.countClipplanes(), i,
texture_format, nlights,
result;
if (type === &#34;clipplanes&#34; || sprites_3d) return;
if (typeof userShader !== &#34;undefined&#34;) return userShader;
if (has_texture)
texture_format = this.getMaterial(id, &#34;textype&#34;);
result = &#34;/* ****** &#34;+type+&#34; object &#34;+id+&#34; fragment shader ****** */\n&#34;+
&#34;#ifdef GL_ES\n&#34;+
&#34;#ifdef GL_FRAGMENT_PRECISION_HIGH\n&#34;+
&#34; precision highp float;\n&#34;+
&#34;#else\n&#34;+
&#34; precision mediump float;\n&#34;+
&#34;#endif\n&#34;+
&#34;#endif\n&#34;+
&#34; varying vec4 vCol; // carries alpha\n&#34;+
&#34; varying vec4 vPosition;\n&#34;;
if (has_texture || type === &#34;text&#34;)
result = result + &#34; varying vec2 vTexcoord;\n&#34;+
&#34; uniform sampler2D uSampler;\n&#34;;
if (is_lit &amp;&amp; !fixed_quads)
result = result + &#34; varying vec3 vNormal;\n&#34;;
for (i = 0; i &lt; nclipplanes; i++)
result = result + &#34; uniform vec4 vClipplane&#34;+i+&#34;;\n&#34;;
if (is_lit) {
nlights = this.countLights();
if (nlights)
result = result + &#34; uniform mat4 mvMatrix;\n&#34;;
else
is_lit = false;
}
if (is_lit) {
result = result + &#34; uniform vec3 emission;\n&#34;+
&#34; uniform float shininess;\n&#34;;
for (i=0; i &lt; nlights; i++) {
result = result + &#34; uniform vec3 ambient&#34; + i + &#34;;\n&#34;+
&#34; uniform vec3 specular&#34; + i +&#34;; // light*material\n&#34;+
&#34; uniform vec3 diffuse&#34; + i + &#34;;\n&#34;+
&#34; uniform vec3 lightDir&#34; + i + &#34;;\n&#34;+
&#34; uniform bool viewpoint&#34; + i + &#34;;\n&#34;+
&#34; uniform bool finite&#34; + i + &#34;;\n&#34;;
}
}
if (is_twosided)
result = result + &#34; uniform bool front;\n&#34;+
&#34; varying float normz;\n&#34;;
if (fat_lines)
result = result + &#34; varying vec2 vPoint;\n&#34;+
&#34; varying float vLength;\n&#34;;
result = result + &#34; void main(void) {\n&#34;;
if (fat_lines) {
result = result + &#34; vec2 point = vPoint;\n&#34;+
&#34; bool neg = point.y &lt; 0.0;\n&#34;+
&#34; point.y = neg ? &#34;+
&#34; (point.y + vLength)/(1.0 - vLength) :\n&#34;+
&#34; -(point.y - vLength)/(1.0 - vLength);\n&#34;;
if (is_transparent &amp;&amp; type == &#34;linestrip&#34;)
result = result+&#34; if (neg &amp;&amp; length(point) &lt;= 1.0) discard;\n&#34;;
result = result + &#34; point.y = min(point.y, 0.0);\n&#34;+
&#34; if (length(point) &gt; 1.0) discard;\n&#34;;
}
for (i=0; i &lt; nclipplanes;i++)
result = result + &#34; if (dot(vPosition, vClipplane&#34;+i+&#34;) &lt; 0.0) discard;\n&#34;;
if (fixed_quads) {
result = result + &#34; vec3 n = vec3(0., 0., 1.);\n&#34;;
} else if (is_lit) {
result = result + &#34; vec3 n = normalize(vNormal);\n&#34;;
}
if (is_twosided) {
result = result + &#34; if ((normz &lt;= 0.) != front) discard;\n&#34;;
}
if (is_lit) {
result = result + &#34; vec3 eye = normalize(-vPosition.xyz);\n&#34;+
&#34; vec3 lightdir;\n&#34;+
&#34; vec4 colDiff;\n&#34;+
&#34; vec3 halfVec;\n&#34;+
&#34; vec4 lighteffect = vec4(emission, 0.);\n&#34;+
&#34; vec3 col;\n&#34;+
&#34; float nDotL;\n&#34;;
if (!fixed_quads) {
result = result + &#34; n = -faceforward(n, n, eye);\n&#34;;
}
for (i=0; i &lt; nlights; i++) {
result = result + &#34; colDiff = vec4(vCol.rgb * diffuse&#34; + i + &#34;, vCol.a);\n&#34;+
&#34; lightdir = lightDir&#34; + i + &#34;;\n&#34;+
&#34; if (!viewpoint&#34; + i +&#34;)\n&#34;+
&#34; lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n&#34;+
&#34; if (!finite&#34; + i + &#34;) {\n&#34;+
&#34; halfVec = normalize(lightdir + eye);\n&#34;+
&#34; } else {\n&#34;+
&#34; lightdir = normalize(lightdir - vPosition.xyz);\n&#34;+
&#34; halfVec = normalize(lightdir + eye);\n&#34;+
&#34; }\n&#34;+
&#34; col = ambient&#34; + i + &#34;;\n&#34;+
&#34; nDotL = dot(n, lightdir);\n&#34;+
&#34; col = col + max(nDotL, 0.) * colDiff.rgb;\n&#34;+
&#34; col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular&#34; + i + &#34;;\n&#34;+
&#34; lighteffect = lighteffect + vec4(col, colDiff.a);\n&#34;;
}
} else {
result = result + &#34; vec4 colDiff = vCol;\n&#34;+
&#34; vec4 lighteffect = colDiff;\n&#34;;
}
if (type === &#34;text&#34;)
result = result + &#34; vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n&#34;;
if (has_texture) {
result = result + {
rgb: &#34; vec4 textureColor = lighteffect*vec4(texture2D(uSampler, vTexcoord).rgb, 1.);\n&#34;,
rgba: &#34; vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n&#34;,
alpha: &#34; vec4 textureColor = texture2D(uSampler, vTexcoord);\n&#34;+
&#34; float luminance = dot(vec3(1.,1.,1.), textureColor.rgb)/3.;\n&#34;+
&#34; textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n&#34;,
luminance: &#34; vec4 textureColor = vec4(lighteffect.rgb*dot(texture2D(uSampler, vTexcoord).rgb, vec3(1.,1.,1.))/3., lighteffect.a);\n&#34;,
&#34;luminance.alpha&#34;:&#34; vec4 textureColor = texture2D(uSampler, vTexcoord);\n&#34;+
&#34; float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n&#34;+
&#34; textureColor = vec4(lighteffect.rgb*luminance, lighteffect.a*textureColor.a);\n&#34;
}[texture_format]+
&#34; gl_FragColor = textureColor;\n&#34;;
} else if (type === &#34;text&#34;) {
result = result + &#34; if (textureColor.a &lt; 0.1)\n&#34;+
&#34; discard;\n&#34;+
&#34; else\n&#34;+
&#34; gl_FragColor = textureColor;\n&#34;;
} else
result = result + &#34; gl_FragColor = lighteffect;\n&#34;;
//if (fat_lines)
// result = result + &#34; gl_FragColor = vec4(0.0, abs(point.x), abs(point.y), 1.0);&#34;
result = result + &#34; }\n&#34;;
// console.log(result);
return result;
};
/**
* Call gl functions to create and compile shader
* @returns {Object}
* @param { number } shaderType - gl code for shader type
* @param { string } code - code for the shader
*/
rglwidgetClass.prototype.getShader = function(shaderType, code) {
var gl = this.gl, shader;
shader = gl.createShader(shaderType);
gl.shaderSource(shader, code);
gl.compileShader(shader);
if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS) &amp;&amp; !gl.isContextLost())
alert(gl.getShaderInfoLog(shader));
return shader;
};
/**
* Handle a texture after its image has been loaded
* @param { Object } texture - the gl texture object
* @param { Object } textureCanvas - the canvas holding the image
*/
rglwidgetClass.prototype.handleLoadedTexture = function(texture, textureCanvas) {
var gl = this.gl || this.initGL();
gl.pixelStorei(gl.UNPACK_FLIP_Y_WEBGL, true);
gl.bindTexture(gl.TEXTURE_2D, texture);
gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, textureCanvas);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR);
gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR_MIPMAP_NEAREST);
gl.generateMipmap(gl.TEXTURE_2D);
gl.bindTexture(gl.TEXTURE_2D, null);
};
/**
* Get maximum dimension of texture in current browser.
* @returns {number}
*/
rglwidgetClass.prototype.getMaxTexSize = function() {
var gl = this.gl || this.initGL();
return Math.min(4096, gl.getParameter(gl.MAX_TEXTURE_SIZE));
};
/**
* Load an image to a texture
* @param { string } uri - The image location
* @param { Object } texture - the gl texture object
*/
rglwidgetClass.prototype.loadImageToTexture = function(uri, texture) {
var canvas = this.textureCanvas,
ctx = canvas.getContext(&#34;2d&#34;),
image = new Image(),
self = this;
image.onload = function() {
var w = image.width,
h = image.height,
canvasX = self.getPowerOfTwo(w),
canvasY = self.getPowerOfTwo(h),
gl = self.gl || self.initGL(),
maxTexSize = self.getMaxTexSize();
while (canvasX &gt; 1 &amp;&amp; canvasY &gt; 1 &amp;&amp; (canvasX &gt; maxTexSize || canvasY &gt; maxTexSize)) {
canvasX /= 2;
canvasY /= 2;
}
canvas.width = canvasX;
canvas.height = canvasY;
ctx.imageSmoothingEnabled = true;
ctx.drawImage(image, 0, 0, canvasX, canvasY);
self.handleLoadedTexture(texture, canvas);
self.drawScene();
};
image.src = uri;
};
/**
* Draw text to the texture canvas
* @returns { Object } object with text measurements
* @param { string } text - the text
* @param { number } cex - expansion
* @param { string } family - font family
* @param { number } font - font number
*/
rglwidgetClass.prototype.drawTextToCanvas = function(text, cex, family, font) {
var canvasX, canvasY,
textY,
scaling = 20,
textColour = &#34;white&#34;,
backgroundColour = &#34;rgba(0,0,0,0)&#34;,
canvas = this.textureCanvas,
ctx = canvas.getContext(&#34;2d&#34;),
i, textHeight = 0, textHeights = [], width, widths = [],
offsetx, offsety = 0, line, lines = [], offsetsx = [],
offsetsy = [], lineoffsetsy = [], fontStrings = [],
maxTexSize = this.getMaxTexSize(),
getFontString = function(i) {
textHeights[i] = scaling*cex[i];
var fontString = textHeights[i] + &#34;px&#34;,
family0 = family[i],
font0 = font[i];
if (family0 === &#34;sans&#34;)
family0 = &#34;sans-serif&#34;;
else if (family0 === &#34;mono&#34;)
family0 = &#34;monospace&#34;;
fontString = fontString + &#34; &#34; + family0;
if (font0 === 2 || font0 === 4)
fontString = &#34;bold &#34; + fontString;
if (font0 === 3 || font0 === 4)
fontString = &#34;italic &#34; + fontString;
return fontString;
};
cex = this.repeatToLen(cex, text.length);
family = this.repeatToLen(family, text.length);
font = this.repeatToLen(font, text.length);
canvasX = 1;
line = -1;
offsetx = maxTexSize;
for (i = 0; i &lt; text.length; i++) {
ctx.font = fontStrings[i] = getFontString(i);
width = widths[i] = ctx.measureText(text[i]).width;
if (offsetx + width &gt; maxTexSize) {
line += 1;
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
if (offsety &gt; maxTexSize)
console.error(&#34;Too many strings for texture.&#34;);
textHeight = 0;
offsetx = 0;
}
textHeight = Math.max(textHeight, textHeights[i]);
offsetsx[i] = offsetx;
offsetx += width;
canvasX = Math.max(canvasX, offsetx);
lines[i] = line;
}
offsety = lineoffsetsy[line] = offsety + 2*textHeight;
for (i = 0; i &lt; text.length; i++) {
offsetsy[i] = lineoffsetsy[lines[i]];
}
canvasX = this.getPowerOfTwo(canvasX);
canvasY = this.getPowerOfTwo(offsety);
canvas.width = canvasX;
canvas.height = canvasY;
ctx.fillStyle = backgroundColour;
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.textBaseline = &#34;alphabetic&#34;;
for(i = 0; i &lt; text.length; i++) {
ctx.font = fontStrings[i];
ctx.fillStyle = textColour;
ctx.textAlign = &#34;left&#34;;
ctx.fillText(text[i], offsetsx[i], offsetsy[i]);
}
return {canvasX:canvasX, canvasY:canvasY,
widths:widths, textHeights:textHeights,
offsetsx:offsetsx, offsetsy:offsetsy};
};
/**
* Set the gl viewport and scissor test
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setViewport = function(id) {
var gl = this.gl || this.initGL(),
vp = this.getObj(id).par3d.viewport,
x = vp.x*this.canvas.width,
y = vp.y*this.canvas.height,
width = vp.width*this.canvas.width,
height = vp.height*this.canvas.height;
this.vp = {x:x, y:y, width:width, height:height};
gl.viewport(x, y, width, height);
gl.scissor(x, y, width, height);
gl.enable(gl.SCISSOR_TEST);
};
/**
* Set the projection matrix for a subscene
* @param { number } id - id of subscene
*/
rglwidgetClass.prototype.setprMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.projection;
if (embedding === &#34;replace&#34;)
this.prMatrix.makeIdentity();
else
this.setprMatrix(subscene.parent);
if (embedding === &#34;inherit&#34;)
return;
// This is based on the Frustum::enclose code from geom.cpp
var bbox = subscene.par3d.bbox,
scale = subscene.par3d.scale,
ranges = [(bbox[1]-bbox[0])*scale[0]/2,
(bbox[3]-bbox[2])*scale[1]/2,
(bbox[5]-bbox[4])*scale[2]/2],
radius = Math.sqrt(this.sumsq(ranges))*1.1; // A bit bigger to handle labels
if (radius &lt;= 0) radius = 1;
var observer = subscene.par3d.observer,
distance = observer[2],
FOV = subscene.par3d.FOV, ortho = FOV === 0,
t = ortho ? 1 : Math.tan(FOV*Math.PI/360),
near = distance - radius,
far = distance + radius,
hlen,
aspect = this.vp.width/this.vp.height,
z = subscene.par3d.zoom,
userProjection = subscene.par3d.userProjection;
if (far &lt; 0.0)
far = 1.0;
if (near &lt; far/100.0)
near = far/100.0;
hlen = t*near;
if (ortho) {
if (aspect &gt; 1)
this.prMatrix.ortho(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.ortho(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
} else {
if (aspect &gt; 1)
this.prMatrix.frustum(-hlen*aspect*z, hlen*aspect*z,
-hlen*z, hlen*z, near, far);
else
this.prMatrix.frustum(-hlen*z, hlen*z,
-hlen*z/aspect, hlen*z/aspect,
near, far);
}
this.prMatrix.multRight(userProjection);
};
/**
* Set the model-view matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmvMatrix = function(id) {
var observer = this.getObj(id).par3d.observer;
this.mvMatrix.makeIdentity();
this.setmodelMatrix(id);
this.mvMatrix.translate(-observer[0], -observer[1], -observer[2]);
};
/**
* Set the model matrix for a subscene
* @param { number } id - id of the subscene
*/
rglwidgetClass.prototype.setmodelMatrix = function(id) {
var subscene = this.getObj(id),
embedding = subscene.embeddings.model;
if (embedding !== &#34;inherit&#34;) {
var scale = subscene.par3d.scale,
bbox = subscene.par3d.bbox,
center = [(bbox[0]+bbox[1])/2,
(bbox[2]+bbox[3])/2,
(bbox[4]+bbox[5])/2];
this.mvMatrix.translate(-center[0], -center[1], -center[2]);
this.mvMatrix.scale(scale[0], scale[1], scale[2]);
this.mvMatrix.multRight( subscene.par3d.userMatrix );
}
if (embedding !== &#34;replace&#34;)
this.setmodelMatrix(subscene.parent);
};
/**
* Set the normals matrix for a subscene
* @param { number } subsceneid - id of the subscene
*/
rglwidgetClass.prototype.setnormMatrix = function(subsceneid) {
var self = this,
recurse = function(id) {
var sub = self.getObj(id),
embedding = sub.embeddings.model;
if (embedding !== &#34;inherit&#34;) {
var scale = sub.par3d.scale;
self.normMatrix.scale(1/scale[0], 1/scale[1], 1/scale[2]);
self.normMatrix.multRight(sub.par3d.userMatrix);
}
if (embedding !== &#34;replace&#34;)
recurse(sub.parent);
};
self.normMatrix.makeIdentity();
recurse(subsceneid);
};
/**
* Set the combined projection-model-view matrix
*/
rglwidgetClass.prototype.setprmvMatrix = function() {
this.prmvMatrix = new CanvasMatrix4( this.mvMatrix );
this.prmvMatrix.multRight( this.prMatrix );
};
/**
* Count clipping planes in a scene
* @returns {number}
*/
rglwidgetClass.prototype.countClipplanes = function() {
return this.countObjs(&#34;clipplanes&#34;);
};
/**
* Count lights in a scene
* @returns { number }
*/
rglwidgetClass.prototype.countLights = function() {
return this.countObjs(&#34;light&#34;);
};
/**
* Count objects of specific type in a scene
* @returns { number }
* @param { string } type - Type of object to count
*/
rglwidgetClass.prototype.countObjs = function(type) {
var self = this,
bound = 0;
Object.keys(this.scene.objects).forEach(
function(key) {
if (self.getObj(parseInt(key, 10)).type === type)
bound = bound + 1;
});
return bound;
};
/**
* Initialize a subscene
* @param { number } id - id of subscene.
*/
rglwidgetClass.prototype.initSubscene = function(id) {
var sub = this.getObj(id),
i, obj;
if (sub.type !== &#34;subscene&#34;)
return;
sub.par3d.userMatrix = this.toCanvasMatrix4(sub.par3d.userMatrix);
sub.par3d.userProjection = this.toCanvasMatrix4(sub.par3d.userProjection);
sub.par3d.userProjection.transpose();
sub.par3d.listeners = [].concat(sub.par3d.listeners);
sub.backgroundId = undefined;
sub.subscenes = [];
sub.clipplanes = [];
sub.transparent = [];
sub.opaque = [];
sub.lights = [];
for (i=0; i &lt; sub.objects.length; i++) {
obj = this.getObj(sub.objects[i]);
if (typeof obj === &#34;undefined&#34;) {
sub.objects.splice(i, 1);
i--;
} else if (obj.type === &#34;background&#34;)
sub.backgroundId = obj.id;
else
sub[this.whichList(obj.id)].push(obj.id);
}
};
/**
* Copy object
* @param { number } id - id of object to copy
* @param { string } reuse - Document id of scene to reuse
*/
rglwidgetClass.prototype.copyObj = function(id, reuse) {
var obj = this.getObj(id),
prev = document.getElementById(reuse);
if (prev !== null) {
prev = prev.rglinstance;
var
prevobj = prev.getObj(id),
fields = [&#34;flags&#34;, &#34;type&#34;,
&#34;colors&#34;, &#34;vertices&#34;, &#34;centers&#34;,
&#34;normals&#34;, &#34;offsets&#34;,
&#34;texts&#34;, &#34;cex&#34;, &#34;family&#34;, &#34;font&#34;, &#34;adj&#34;,
&#34;material&#34;,
&#34;radii&#34;,
&#34;texcoords&#34;,
&#34;userMatrix&#34;, &#34;ids&#34;,
&#34;dim&#34;,
&#34;par3d&#34;, &#34;userMatrix&#34;,
&#34;viewpoint&#34;, &#34;finite&#34;,
&#34;pos&#34;],
i;
for (i = 0; i &lt; fields.length; i++) {
if (typeof prevobj[fields[i]] !== &#34;undefined&#34;)
obj[fields[i]] = prevobj[fields[i]];
}
} else
console.warn(&#34;copyObj failed&#34;);
};
/**
* Update the triangles used to display a plane
* @param { number } id - id of the plane
* @param { Object } bbox - bounding box in which to display the plane
*/
rglwidgetClass.prototype.planeUpdateTriangles = function(id, bbox) {
var perms = [[0,0,1], [1,2,2], [2,1,0]],
x, xrow, elem, A, d, nhits, i, j, k, u, v, w, intersect, which, v0, v2, vx, reverse,
face1 = [], face2 = [], normals = [],
obj = this.getObj(id),
nPlanes = obj.normals.length;
obj.bbox = bbox;
obj.vertices = [];
obj.initialized = false;
for (elem = 0; elem &lt; nPlanes; elem++) {
// Vertex Av = normal.getRecycled(elem);
x = [];
A = obj.normals[elem];
d = obj.offsets[elem][0];
nhits = 0;
for (i=0; i&lt;3; i++)
for (j=0; j&lt;2; j++)
for (k=0; k&lt;2; k++) {
u = perms[0][i];
v = perms[1][i];
w = perms[2][i];
if (A[w] !== 0.0) {
intersect = -(d + A[u]*bbox[j+2*u] + A[v]*bbox[k+2*v])/A[w];
if (bbox[2*w] &lt; intersect &amp;&amp; intersect &lt; bbox[1+2*w]) {
xrow = [];
xrow[u] = bbox[j+2*u];
xrow[v] = bbox[k+2*v];
xrow[w] = intersect;
x.push(xrow);
face1[nhits] = j + 2*u;
face2[nhits] = k + 2*v;
nhits++;
}
}
}
if (nhits &gt; 3) {
/* Re-order the intersections so the triangles work */
for (i=0; i&lt;nhits-2; i++) {
which = 0; /* initialize to suppress warning */
for (j=i+1; j&lt;nhits; j++) {
if (face1[i] == face1[j] || face1[i] == face2[j] ||
face2[i] == face1[j] || face2[i] == face2[j] ) {
which = j;
break;
}
}
if (which &gt; i+1) {
this.swap(x, i+1, which);
this.swap(face1, i+1, which);
this.swap(face2, i+1, which);
}
}
}
if (nhits &gt;= 3) {
/* Put in order so that the normal points out the FRONT of the faces */
v0 = [x[0][0] - x[1][0] , x[0][1] - x[1][1], x[0][2] - x[1][2]];
v2 = [x[2][0] - x[1][0] , x[2][1] - x[1][1], x[2][2] - x[1][2]];
/* cross-product */
vx = this.xprod(v0, v2);
reverse = this.dotprod(vx, A) &gt; 0;
for (i=0; i&lt;nhits-2; i++) {
obj.vertices.push(x[0]);
normals.push(A);
for (j=1; j&lt;3; j++) {
obj.vertices.push(x[i + (reverse ? 3-j : j)]);
normals.push(A);
}
}
}
}
obj.pnormals = normals;
};
rglwidgetClass.prototype.getAdj = function (pos, offset, text) {
switch(pos) {
case 1: return [0.5, 1 + offset];
case 2: return [1 + offset/text.length, 0.5];
case 3: return [0.5, -offset];
case 4: return [-offset/text.length, 0.5];
}
}
/**
* Initialize object for display
* @param { number } id - id of object to initialize
*/
rglwidgetClass.prototype.initObj = function(id) {
var obj = this.getObj(id),
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
is_lines = flags &amp; this.f_is_lines,
fat_lines = flags &amp; this.f_fat_lines,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
is_transparent = obj.is_transparent,
depth_sort = flags &amp; this.f_depth_sort,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
fixed_size = flags &amp; this.f_fixed_size,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
is_brush = flags &amp; this.f_is_brush,
gl = this.gl || this.initGL(),
polygon_offset,
texinfo, drawtype, nclipplanes, f, nrows, oldrows,
i,j,v,v1,v2, mat, uri, matobj, pass, passes, pmode,
dim, nx, nz, attr;
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;initObj id is &#34;+typeof id);
}
obj.initialized = true;
if (type === &#34;bboxdeco&#34; || type === &#34;subscene&#34;)
return;
if (type === &#34;light&#34;) {
obj.ambient = new Float32Array(obj.colors[0].slice(0,3));
obj.diffuse = new Float32Array(obj.colors[1].slice(0,3));
obj.specular = new Float32Array(obj.colors[2].slice(0,3));
obj.lightDir = new Float32Array(obj.vertices[0]);
return;
}
if (type === &#34;clipplanes&#34;) {
obj.vClipplane = this.flatten(this.cbind(obj.normals, obj.offsets));
return;
}
if (type === &#34;background&#34; &amp;&amp; typeof obj.ids !== &#34;undefined&#34;) {
obj.quad = this.flatten([].concat(obj.ids));
return;
}
polygon_offset = this.getMaterial(id, &#34;polygon_offset&#34;);
if (polygon_offset[0] != 0 || polygon_offset[1] != 0)
obj.polygon_offset = polygon_offset;
if (is_transparent) {
depth_sort = [&#34;triangles&#34;, &#34;quads&#34;, &#34;surface&#34;,
&#34;spheres&#34;, &#34;sprites&#34;, &#34;text&#34;].indexOf(type) &gt;= 0;
}
if (is_brush)
this.initSelection(id);
if (typeof obj.vertices === &#34;undefined&#34;)
obj.vertices = [];
v = obj.vertices;
obj.vertexCount = v.length;
if (!obj.vertexCount) return;
if (is_twosided) {
if (typeof obj.userAttributes === &#34;undefined&#34;)
obj.userAttributes = {};
v1 = Array(v.length);
v2 = Array(v.length);
if (obj.type == &#34;triangles&#34; || obj.type == &#34;quads&#34;) {
if (obj.type == &#34;triangles&#34;)
nrow = 3;
else
nrow = 4;
for (i=0; i&lt;Math.floor(v.length/nrow); i++)
for (j=0; j&lt;nrow; j++) {
v1[nrow*i + j] = v[nrow*i + ((j+1) % nrow)];
v2[nrow*i + j] = v[nrow*i + ((j+2) % nrow)];
}
} else if (obj.type == &#34;surface&#34;) {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
for (j=0; j&lt;nx; j++) {
for (i=0; i&lt;nz; i++) {
if (i+1 &lt; nz &amp;&amp; j+1 &lt; nx) {
v2[j + nx*i] = v[j + nx*(i+1)];
v1[j + nx*i] = v[j+1 + nx*(i+1)];
} else if (i+1 &lt; nz) {
v2[j + nx*i] = v[j-1 + nx*i];
v1[j + nx*i] = v[j + nx*(i+1)];
} else {
v2[j + nx*i] = v[j + nx*(i-1)];
v1[j + nx*i] = v[j-1 + nx*(i-1)];
}
}
}
}
obj.userAttributes.aPos1 = v1;
obj.userAttributes.aPos2 = v2;
}
if (!sprites_3d) {
if (gl.isContextLost()) return;
obj.prog = gl.createProgram();
gl.attachShader(obj.prog, this.getShader( gl.VERTEX_SHADER,
this.getVertexShader(id) ));
gl.attachShader(obj.prog, this.getShader( gl.FRAGMENT_SHADER,
this.getFragmentShader(id) ));
// Force aPos to location 0, aCol to location 1
gl.bindAttribLocation(obj.prog, 0, &#34;aPos&#34;);
gl.bindAttribLocation(obj.prog, 1, &#34;aCol&#34;);
gl.linkProgram(obj.prog);
var linked = gl.getProgramParameter(obj.prog, gl.LINK_STATUS);
if (!linked) {
// An error occurred while linking
var lastError = gl.getProgramInfoLog(obj.prog);
console.warn(&#34;Error in program linking:&#34; + lastError);
gl.deleteProgram(obj.prog);
return;
}
}
if (type === &#34;text&#34;) {
texinfo = this.drawTextToCanvas(obj.texts,
this.flatten(obj.cex),
this.flatten(obj.family),
this.flatten(obj.family));
}
if (fixed_quads &amp;&amp; !sprites_3d) {
obj.ofsLoc = gl.getAttribLocation(obj.prog, &#34;aOfs&#34;);
}
if (sprite_3d) {
obj.origLoc = gl.getUniformLocation(obj.prog, &#34;uOrig&#34;);
obj.sizeLoc = gl.getUniformLocation(obj.prog, &#34;uSize&#34;);
obj.usermatLoc = gl.getUniformLocation(obj.prog, &#34;usermat&#34;);
}
if (has_texture || type == &#34;text&#34;) {
if (!obj.texture)
obj.texture = gl.createTexture();
obj.texLoc = gl.getAttribLocation(obj.prog, &#34;aTexcoord&#34;);
obj.sampler = gl.getUniformLocation(obj.prog, &#34;uSampler&#34;);
}
if (has_texture) {
mat = obj.material;
if (typeof mat.uri !== &#34;undefined&#34;)
uri = mat.uri;
else if (typeof mat.uriElementId === &#34;undefined&#34;) {
matobj = this.getObj(mat.uriId);
if (typeof matobj !== &#34;undefined&#34;) {
uri = matobj.material.uri;
} else {
uri = &#34;&#34;;
}
} else
uri = document.getElementById(mat.uriElementId).rglinstance.getObj(mat.uriId).material.uri;
this.loadImageToTexture(uri, obj.texture);
}
if (type === &#34;text&#34;) {
this.handleLoadedTexture(obj.texture, this.textureCanvas);
}
var stride = 3, nc, cofs, nofs, radofs, oofs, tofs, vnew, fnew,
nextofs = -1, pointofs = -1, alias, colors, key, selection, filter, adj, pos, offset;
obj.alias = undefined;
colors = obj.colors;
j = this.scene.crosstalk.id.indexOf(id);
if (j &gt;= 0) {
key = this.scene.crosstalk.key[j];
options = this.scene.crosstalk.options[j];
colors = colors.slice(0);
for (i = 0; i &lt; v.length; i++)
colors[i] = obj.colors[i % obj.colors.length].slice(0);
if ( (selection = this.scene.crosstalk.selection) &amp;&amp;
(selection.length || !options.selectedIgnoreNone) )
for (i = 0; i &lt; v.length; i++) {
if (!selection.includes(key[i])) {
if (options.deselectedColor)
colors[i] = options.deselectedColor.slice(0);
colors[i][3] = colors[i][3]*options.deselectedFade; /* default: mostly transparent if not selected */
} else if (options.selectedColor)
colors[i] = options.selectedColor.slice(0);
}
if ( (filter = this.scene.crosstalk.filter) )
for (i = 0; i &lt; v.length; i++)
if (!filter.includes(key[i])) {
if (options.filteredColor)
colors[i] = options.filteredColor.slice(0);
colors[i][3] = colors[i][3]*options.filteredFade; /* default: completely hidden if filtered */
}
}
nc = obj.colorCount = colors.length;
if (nc &gt; 1) {
cofs = stride;
stride = stride + 4;
v = this.cbind(v, colors);
} else {
cofs = -1;
obj.onecolor = this.flatten(colors);
}
if (typeof obj.normals !== &#34;undefined&#34;) {
nofs = stride;
stride = stride + 3;
v = this.cbind(v, typeof obj.pnormals !== &#34;undefined&#34; ? obj.pnormals : obj.normals);
} else
nofs = -1;
if (typeof obj.radii !== &#34;undefined&#34;) {
radofs = stride;
stride = stride + 1;
// FIXME: always concat the radii?
if (obj.radii.length === v.length) {
v = this.cbind(v, obj.radii);
} else if (obj.radii.length === 1) {
v = v.map(function(row, i, arr) { return row.concat(obj.radii[0]);});
}
} else
radofs = -1;
// Add default indices
f = Array(v.length);
for (i = 0; i &lt; v.length; i++)
f[i] = i;
obj.f = [f,f];
if (type == &#34;sprites&#34; &amp;&amp; !sprites_3d) {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
fnew = new Array(4*v.length);
alias = new Array(v.length);
var rescale = fixed_size ? 72 : 1,
size = obj.radii, s = rescale*size[0]/2;
last = v.length;
f = obj.f[0];
for (i=0; i &lt; v.length; i++) {
if (size.length &gt; 1)
s = rescale*size[i]/2;
vnew[i] = v[i].concat([0,0,-s,-s]);
fnew[4*i] = f[i];
vnew[last]= v[i].concat([1,0, s,-s]);
fnew[4*i+1] = last++;
vnew[last]= v[i].concat([1,1, s, s]);
fnew[4*i+2] = last++;
vnew[last]= v[i].concat([0,1,-s, s]);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (type === &#34;text&#34;) {
tofs = stride;
stride += 2;
oofs = stride;
stride += 2;
vnew = new Array(4*v.length);
f = obj.f[0];
fnew = new Array(4*f.length);
alias = new Array(v.length);
last = v.length;
adj = this.flatten(obj.adj);
if (typeof obj.pos !== &#34;undefined&#34;) {
pos = this.flatten(obj.pos);
offset = adj[0];
}
for (i=0; i &lt; v.length; i++) {
if (typeof pos !== &#34;undefined&#34;)
adj = this.getAdj(pos[i % pos.length], offset, obj.texts[i]);
vnew[i] = v[i].concat([0,-0.5]).concat(adj);
fnew[4*i] = f[i];
vnew[last] = v[i].concat([1,-0.5]).concat(adj);
fnew[4*i+1] = last++;
vnew[last] = v[i].concat([1, 1.5]).concat(adj);
fnew[4*i+2] = last++;
vnew[last] = v[i].concat([0, 1.5]).concat(adj);
fnew[4*i+3] = last++;
alias[i] = [last-3, last-2, last-1];
for (j=0; j &lt; 4; j++) {
v1 = vnew[fnew[4*i+j]];
v1[tofs+2] = 2*(v1[tofs]-v1[tofs+2])*texinfo.widths[i];
v1[tofs+3] = 2*(v1[tofs+1]-v1[tofs+3])*texinfo.textHeights[i];
v1[tofs] = (texinfo.offsetsx[i] + v1[tofs]*texinfo.widths[i])/texinfo.canvasX;
v1[tofs+1] = 1.0-(texinfo.offsetsy[i] -
v1[tofs+1]*texinfo.textHeights[i])/texinfo.canvasY;
vnew[fnew[4*i+j]] = v1;
}
}
v = vnew;
obj.vertexCount = v.length;
obj.f = [fnew, fnew];
} else if (typeof obj.texcoords !== &#34;undefined&#34;) {
tofs = stride;
stride += 2;
oofs = -1;
v = this.cbind(v, obj.texcoords);
} else {
tofs = -1;
oofs = -1;
}
obj.alias = alias;
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
obj.userAttribOffsets = {};
obj.userAttribLocations = {};
obj.userAttribSizes = {};
for (attr in obj.userAttributes) {
obj.userAttribLocations[attr] = gl.getAttribLocation(obj.prog, attr);
if (obj.userAttribLocations[attr] &gt;= 0) { // Attribute may not have been used
obj.userAttribOffsets[attr] = stride;
v = this.cbind(v, obj.userAttributes[attr]);
stride = v[0].length;
obj.userAttribSizes[attr] = stride - obj.userAttribOffsets[attr];
}
}
}
if (typeof obj.userUniforms !== &#34;undefined&#34;) {
obj.userUniformLocations = {};
for (attr in obj.userUniforms)
obj.userUniformLocations[attr] = gl.getUniformLocation(obj.prog, attr);
}
if (sprites_3d) {
obj.userMatrix = new CanvasMatrix4(obj.userMatrix);
obj.objects = this.flatten([].concat(obj.ids));
is_lit = false;
for (i=0; i &lt; obj.objects.length; i++)
this.initObj(obj.objects[i]);
}
if (is_lit &amp;&amp; !fixed_quads) {
obj.normLoc = gl.getAttribLocation(obj.prog, &#34;aNorm&#34;);
}
nclipplanes = this.countClipplanes();
if (nclipplanes &amp;&amp; !sprites_3d) {
obj.clipLoc = [];
for (i=0; i &lt; nclipplanes; i++)
obj.clipLoc[i] = gl.getUniformLocation(obj.prog,&#34;vClipplane&#34; + i);
}
if (is_lit) {
obj.emissionLoc = gl.getUniformLocation(obj.prog, &#34;emission&#34;);
obj.emission = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;emission&#34;)));
obj.shininessLoc = gl.getUniformLocation(obj.prog, &#34;shininess&#34;);
obj.shininess = this.getMaterial(id, &#34;shininess&#34;);
obj.nlights = this.countLights();
obj.ambientLoc = [];
obj.ambient = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;ambient&#34;)));
obj.specularLoc = [];
obj.specular = new Float32Array(this.stringToRgb(this.getMaterial(id, &#34;specular&#34;)));
obj.diffuseLoc = [];
obj.lightDirLoc = [];
obj.viewpointLoc = [];
obj.finiteLoc = [];
for (i=0; i &lt; obj.nlights; i++) {
obj.ambientLoc[i] = gl.getUniformLocation(obj.prog, &#34;ambient&#34; + i);
obj.specularLoc[i] = gl.getUniformLocation(obj.prog, &#34;specular&#34; + i);
obj.diffuseLoc[i] = gl.getUniformLocation(obj.prog, &#34;diffuse&#34; + i);
obj.lightDirLoc[i] = gl.getUniformLocation(obj.prog, &#34;lightDir&#34; + i);
obj.viewpointLoc[i] = gl.getUniformLocation(obj.prog, &#34;viewpoint&#34; + i);
obj.finiteLoc[i] = gl.getUniformLocation(obj.prog, &#34;finite&#34; + i);
}
}
obj.passes = is_twosided + 1;
obj.pmode = new Array(obj.passes);
for (pass = 0; pass &lt; obj.passes; pass++) {
if (type === &#34;triangles&#34; || type === &#34;quads&#34; || type === &#34;surface&#34;)
pmode = this.getMaterial(id, (pass === 0) ? &#34;front&#34; : &#34;back&#34;);
else pmode = &#34;filled&#34;;
obj.pmode[pass] = pmode;
}
obj.f.length = obj.passes;
for (pass = 0; pass &lt; obj.passes; pass++) {
f = fnew = obj.f[pass];
pmode = obj.pmode[pass];
if (pmode === &#34;culled&#34;)
f = [];
else if (pmode === &#34;points&#34;) {
// stay with default
} else if ((type === &#34;quads&#34; || type === &#34;text&#34; ||
type === &#34;sprites&#34;) &amp;&amp; !sprites_3d) {
nrows = Math.floor(obj.vertexCount/4);
if (pmode === &#34;filled&#34;) {
fnew = Array(6*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[6*i] = f[4*i];
fnew[6*i+1] = f[4*i + 1];
fnew[6*i+2] = f[4*i + 2];
fnew[6*i+3] = f[4*i];
fnew[6*i+4] = f[4*i + 2];
fnew[6*i+5] = f[4*i + 3];
}
} else {
fnew = Array(8*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[8*i] = f[4*i];
fnew[8*i+1] = f[4*i + 1];
fnew[8*i+2] = f[4*i + 1];
fnew[8*i+3] = f[4*i + 2];
fnew[8*i+4] = f[4*i + 2];
fnew[8*i+5] = f[4*i + 3];
fnew[8*i+6] = f[4*i + 3];
fnew[8*i+7] = f[4*i];
}
}
} else if (type === &#34;triangles&#34;) {
nrows = Math.floor(obj.vertexCount/3);
if (pmode === &#34;filled&#34;) {
fnew = Array(3*nrows);
for (i=0; i &lt; fnew.length; i++) {
fnew[i] = f[i];
}
} else if (pmode === &#34;lines&#34;) {
fnew = Array(6*nrows);
for (i=0; i &lt; nrows; i++) {
fnew[6*i] = f[3*i];
fnew[6*i + 1] = f[3*i + 1];
fnew[6*i + 2] = f[3*i + 1];
fnew[6*i + 3] = f[3*i + 2];
fnew[6*i + 4] = f[3*i + 2];
fnew[6*i + 5] = f[3*i];
}
}
} else if (type === &#34;spheres&#34;) {
// default
} else if (type === &#34;surface&#34;) {
dim = obj.dim[0];
nx = dim[0];
nz = dim[1];
if (pmode === &#34;filled&#34;) {
fnew = [];
for (j=0; j&lt;nx-1; j++) {
for (i=0; i&lt;nz-1; i++) {
fnew.push(f[j + nx*i],
f[j + nx*(i+1)],
f[j + 1 + nx*(i+1)],
f[j + nx*i],
f[j + 1 + nx*(i+1)],
f[j + 1 + nx*i]);
}
}
} else if (pmode === &#34;lines&#34;) {
fnew = [];
for (j=0; j&lt;nx; j++) {
for (i=0; i&lt;nz; i++) {
if (i+1 &lt; nz)
fnew.push(f[j + nx*i],
f[j + nx*(i+1)]);
if (j+1 &lt; nx)
fnew.push(f[j + nx*i],
f[j+1 + nx*i]);
}
}
}
}
obj.f[pass] = fnew;
if (depth_sort) {
drawtype = &#34;DYNAMIC_DRAW&#34;;
} else {
drawtype = &#34;STATIC_DRAW&#34;;
}
}
if (fat_lines) {
alias = undefined;
obj.nextLoc = gl.getAttribLocation(obj.prog, &#34;aNext&#34;);
obj.pointLoc = gl.getAttribLocation(obj.prog, &#34;aPoint&#34;);
obj.aspectLoc = gl.getUniformLocation(obj.prog, &#34;uAspect&#34;);
obj.lwdLoc = gl.getUniformLocation(obj.prog, &#34;uLwd&#34;);
// Expand vertices to turn each segment into a pair of triangles
for (pass = 0; pass &lt; obj.passes; pass++) {
f = obj.f[pass];
oldrows = f.length;
if (obj.pmode[pass] === &#34;lines&#34;)
break;
}
if (type === &#34;linestrip&#34;)
nrows = 4*(oldrows - 1);
else
nrows = 2*oldrows;
vnew = new Array(nrows);
fnew = new Array(1.5*nrows);
var fnext = new Array(nrows),
fpt = new Array(nrows),
pt, start, gap = type === &#34;linestrip&#34; ? 3 : 1;
// We&#39;re going to turn each pair of vertices into 4 new ones, with the &#34;next&#34; and &#34;pt&#34; attributes
// added.
// We do this by copying the originals in the first pass, adding the new attributes, then in a
// second pass add new vertices at the end.
for (i = 0; i &lt; v.length; i++) {
vnew[i] = v[i].concat([0,0,0,0,0]);
}
nextofs = stride;
pointofs = stride + 3;
stride = stride + 5;
// Now add the extras
last = v.length - 1;
ind = 0;
alias = new Array(f.length);
for (i = 0; i &lt; f.length; i++)
alias[i] = [];
for (i = 0; i &lt; f.length - 1; i++) {
if (type !== &#34;linestrip&#34; &amp;&amp; i % 2 == 1)
continue;
k = ++last;
vnew[k] = vnew[f[i]].slice();
for (j=0; j&lt;3; j++)
vnew[k][nextofs + j] = vnew[f[i+1]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = -1;
fnew[ind] = k;
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+1] = last;
alias[f[i]].push(last-1, last);
last++;
k = last;
vnew[k] = vnew[f[i+1]].slice();
for (j=0; j&lt;3; j++)
vnew[k][nextofs + j] = vnew[f[i]][j];
vnew[k][pointofs] = -1;
vnew[k][pointofs+1] = 1;
fnew[ind+2] = k;
fnew[ind+3] = fnew[ind+1];
last++;
vnew[last] = vnew[k].slice();
vnew[last][pointofs] = 1;
fnew[ind+4] = last;
fnew[ind+5] = fnew[ind+2];
ind += 6;
alias[f[i+1]].push(last-1, last);
}
vnew.length = last+1;
v = vnew;
obj.vertexCount = v.length;
if (typeof alias !== &#34;undefined&#34; &amp;&amp; typeof obj.alias !== &#34;undefined&#34;) { // Already have aliases from previous section?
var oldalias = obj.alias, newalias = Array(obj.alias.length);
for (i = 0; i &lt; newalias.length; i++) {
newalias[i] = oldalias[i].slice();
for (j = 0; j &lt; oldalias[i].length; j++)
Array.prototype.push.apply(newalias[i], alias[oldalias[j]]); // pushes each element
}
obj.alias = newalias;
} else
obj.alias = alias;
for (pass = 0; pass &lt; obj.passes; pass++)
if (type === &#34;lines&#34; || type === &#34;linestrip&#34; || obj.pmode[pass] == &#34;lines&#34;) {
obj.f[pass] = fnew;
}
if (depth_sort)
drawtype = &#34;DYNAMIC_DRAW&#34;;
else
drawtype = &#34;STATIC_DRAW&#34;;
}
for (pass = 0; pass &lt; obj.passes; pass++) {
if (obj.vertexCount &gt; 65535) {
if (this.index_uint) {
obj.f[pass] = new Uint32Array(obj.f[pass]);
obj.index_uint = true;
} else
this.alertOnce(&#34;Object has &#34;+obj.vertexCount+&#34; vertices, not supported in this browser.&#34;);
} else {
obj.f[pass] = new Uint16Array(obj.f[pass]);
obj.index_uint = false;
}
}
if (stride !== v[0].length) {
this.alertOnce(&#34;problem in stride calculation&#34;);
}
obj.vOffsets = {vofs:0, cofs:cofs, nofs:nofs, radofs:radofs, oofs:oofs, tofs:tofs,
nextofs:nextofs, pointofs:pointofs, stride:stride};
obj.values = new Float32Array(this.flatten(v));
if (type !== &#34;spheres&#34; &amp;&amp; !sprites_3d) {
obj.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW); //
obj.ibuf = Array(obj.passes);
obj.ibuf[0] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[0]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[0], gl[drawtype]);
if (is_twosided) {
obj.ibuf[1] = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[1]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[1], gl[drawtype]);
}
}
if (!sprites_3d) {
obj.mvMatLoc = gl.getUniformLocation(obj.prog, &#34;mvMatrix&#34;);
obj.prMatLoc = gl.getUniformLocation(obj.prog, &#34;prMatrix&#34;);
}
if (fixed_size) {
obj.textScaleLoc = gl.getUniformLocation(obj.prog, &#34;textScale&#34;);
}
if (is_lit &amp;&amp; !sprites_3d) {
obj.normMatLoc = gl.getUniformLocation(obj.prog, &#34;normMatrix&#34;);
}
if (is_twosided) {
obj.frontLoc = gl.getUniformLocation(obj.prog, &#34;front&#34;);
}
};
/**
* Set gl depth test based on object&#39;s material
* @param { number } id - object to use
*/
rglwidgetClass.prototype.setDepthTest = function(id) {
var gl = this.gl || this.initGL(),
tests = {never: gl.NEVER,
less: gl.LESS,
equal: gl.EQUAL,
lequal:gl.LEQUAL,
greater: gl.GREATER,
notequal: gl.NOTEQUAL,
gequal: gl.GEQUAL,
always: gl.ALWAYS},
test = tests[this.getMaterial(id, &#34;depth_test&#34;)];
gl.depthFunc(test);
};
rglwidgetClass.prototype.mode4type = {points : &#34;POINTS&#34;,
linestrip : &#34;LINE_STRIP&#34;,
abclines : &#34;LINES&#34;,
lines : &#34;LINES&#34;,
sprites : &#34;TRIANGLES&#34;,
planes : &#34;TRIANGLES&#34;,
text : &#34;TRIANGLES&#34;,
quads : &#34;TRIANGLES&#34;,
surface : &#34;TRIANGLES&#34;,
triangles : &#34;TRIANGLES&#34;};
/**
* Sort objects from back to front
* @returns { number[] }
* @param { Object } obj - object to sort
*/
rglwidgetClass.prototype.depthSort = function(obj) {
var n = obj.centers.length,
depths = new Float32Array(n),
result = new Array(n),
compare = function(i,j) { return depths[j] - depths[i]; },
z, w;
for(i=0; i&lt;n; i++) {
z = this.prmvMatrix.m13*obj.centers[i][0] +
this.prmvMatrix.m23*obj.centers[i][1] +
this.prmvMatrix.m33*obj.centers[i][2] +
this.prmvMatrix.m43;
w = this.prmvMatrix.m14*obj.centers[i][0] +
this.prmvMatrix.m24*obj.centers[i][1] +
this.prmvMatrix.m34*obj.centers[i][2] +
this.prmvMatrix.m44;
depths[i] = z/w;
result[i] = i;
}
result.sort(compare);
return result;
};
rglwidgetClass.prototype.disableArrays = function(obj, enabled) {
var gl = this.gl || this.initGL(),
objLocs = [&#34;normLoc&#34;, &#34;texLoc&#34;, &#34;ofsLoc&#34;, &#34;pointLoc&#34;, &#34;nextLoc&#34;],
thisLocs = [&#34;posLoc&#34;, &#34;colLoc&#34;], i, attr;
for (i = 0; i &lt; objLocs.length; i++)
if (enabled[objLocs[i]]) gl.disableVertexAttribArray(obj[objLocs[i]]);
for (i = 0; i &lt; thisLocs.length; i++)
if (enabled[thisLocs[i]]) gl.disableVertexAttribArray(this[objLocs[i]]);
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
for (attr in obj.userAttribSizes) { // Not all attributes may have been used
gl.disableVertexAttribArray( obj.userAttribLocations[attr] );
}
}
}
/**
* Draw an object in a subscene
* @param { number } id - object to draw
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawObj = function(id, subsceneid) {
var obj = this.getObj(id),
subscene = this.getObj(subsceneid),
flags = obj.flags,
type = obj.type,
is_lit = flags &amp; this.f_is_lit,
has_texture = flags &amp; this.f_has_texture,
fixed_quads = flags &amp; this.f_fixed_quads,
is_transparent = flags &amp; this.f_is_transparent,
depth_sort = flags &amp; this.f_depth_sort,
sprites_3d = flags &amp; this.f_sprites_3d,
sprite_3d = flags &amp; this.f_sprite_3d,
is_lines = flags &amp; this.f_is_lines,
fat_lines = flags &amp; this.f_fat_lines,
is_points = flags &amp; this.f_is_points,
fixed_size = flags &amp; this.f_fixed_size,
is_twosided = (flags &amp; this.f_is_twosided) &gt; 0,
gl = this.gl || this.initGL(),
mat,
sphereMV, baseofs, ofs, sscale, i, count, light,
pass, mode, pmode, attr,
enabled = {};
if (typeof id !== &#34;number&#34;) {
this.alertOnce(&#34;drawObj id is &#34;+typeof id);
}
if (type === &#34;planes&#34;) {
if (obj.bbox !== subscene.par3d.bbox || !obj.initialized) {
this.planeUpdateTriangles(id, subscene.par3d.bbox);
}
}
if (!obj.initialized)
this.initObj(id);
if (type === &#34;clipplanes&#34;) {
count = obj.offsets.length;
var IMVClip = [];
for (i=0; i &lt; count; i++) {
IMVClip[i] = this.multMV(this.invMatrix, obj.vClipplane.slice(4*i, 4*(i+1)));
}
obj.IMVClip = IMVClip;
return;
}
if (type === &#34;light&#34; || type === &#34;bboxdeco&#34; || !obj.vertexCount)
return;
if (!is_transparent &amp;&amp;
obj.someHidden) {
is_transparent = true;
depth_sort = [&#34;triangles&#34;, &#34;quads&#34;, &#34;surface&#34;,
&#34;spheres&#34;, &#34;sprites&#34;, &#34;text&#34;].indexOf(type) &gt;= 0;
}
this.setDepthTest(id);
if (sprites_3d) {
var norigs = obj.vertices.length,
savenorm = new CanvasMatrix4(this.normMatrix);
this.origs = obj.vertices;
this.usermat = new Float32Array(obj.userMatrix.getAsArray());
this.radii = obj.radii;
this.normMatrix = subscene.spriteNormmat;
for (this.iOrig=0; this.iOrig &lt; norigs; this.iOrig++) {
for (i=0; i &lt; obj.objects.length; i++) {
this.drawObj(obj.objects[i], subsceneid);
}
}
this.normMatrix = savenorm;
return;
} else {
gl.useProgram(obj.prog);
}
if (typeof obj.polygon_offset !== &#34;undefined&#34;) {
gl.polygonOffset(obj.polygon_offset[0],
obj.polygon_offset[1]);
gl.enable(gl.POLYGON_OFFSET_FILL);
}
if (sprite_3d) {
gl.uniform3fv(obj.origLoc, new Float32Array(this.origs[this.iOrig]));
if (this.radii.length &gt; 1) {
gl.uniform1f(obj.sizeLoc, this.radii[this.iOrig][0]);
} else {
gl.uniform1f(obj.sizeLoc, this.radii[0][0]);
}
gl.uniformMatrix4fv(obj.usermatLoc, false, this.usermat);
}
if (type === &#34;spheres&#34;) {
gl.bindBuffer(gl.ARRAY_BUFFER, this.sphere.buf);
} else {
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
}
gl.uniformMatrix4fv( obj.prMatLoc, false, new Float32Array(this.prMatrix.getAsArray()) );
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(this.mvMatrix.getAsArray()) );
var clipcheck = 0,
clipplaneids = subscene.clipplanes,
clip, j;
for (i=0; i &lt; clipplaneids.length; i++) {
clip = this.getObj(clipplaneids[i]);
for (j=0; j &lt; clip.offsets.length; j++) {
gl.uniform4fv(obj.clipLoc[clipcheck + j], clip.IMVClip[j]);
}
clipcheck += clip.offsets.length;
}
if (typeof obj.clipLoc !== &#34;undefined&#34;)
for (i=clipcheck; i &lt; obj.clipLoc.length; i++)
gl.uniform4f(obj.clipLoc[i], 0,0,0,0);
if (is_lit) {
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(this.normMatrix.getAsArray()) );
gl.uniform3fv( obj.emissionLoc, obj.emission);
gl.uniform1f( obj.shininessLoc, obj.shininess);
for (i=0; i &lt; subscene.lights.length; i++) {
light = this.getObj(subscene.lights[i]);
if (!light.initialized) this.initObj(subscene.lights[i]);
gl.uniform3fv( obj.ambientLoc[i], this.componentProduct(light.ambient, obj.ambient));
gl.uniform3fv( obj.specularLoc[i], this.componentProduct(light.specular, obj.specular));
gl.uniform3fv( obj.diffuseLoc[i], light.diffuse);
gl.uniform3fv( obj.lightDirLoc[i], light.lightDir);
gl.uniform1i( obj.viewpointLoc[i], light.viewpoint);
gl.uniform1i( obj.finiteLoc[i], light.finite);
}
for (i=subscene.lights.length; i &lt; obj.nlights; i++) {
gl.uniform3f( obj.ambientLoc[i], 0,0,0);
gl.uniform3f( obj.specularLoc[i], 0,0,0);
gl.uniform3f( obj.diffuseLoc[i], 0,0,0);
}
}
if (fixed_size) {
gl.uniform2f( obj.textScaleLoc, 0.75/this.vp.width, 0.75/this.vp.height);
}
gl.enableVertexAttribArray( this.posLoc );
enabled.posLoc = true;
var nc = obj.colorCount;
count = obj.vertexCount;
if (type === &#34;spheres&#34;) {
subscene = this.getObj(subsceneid);
var scale = subscene.par3d.scale,
scount = count, indices;
gl.vertexAttribPointer(this.posLoc, 3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 0);
gl.enableVertexAttribArray(obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 0);
gl.disableVertexAttribArray( this.colLoc );
var sphereNorm = new CanvasMatrix4();
sphereNorm.scale(scale[0], scale[1], scale[2]);
sphereNorm.multRight(this.normMatrix);
gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(sphereNorm.getAsArray()) );
if (nc == 1) {
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
}
if (has_texture) {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*this.sphere.vOffsets.stride,
4*this.sphere.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (depth_sort)
indices = this.depthSort(obj);
for (i = 0; i &lt; scount; i++) {
sphereMV = new CanvasMatrix4();
if (depth_sort) {
baseofs = indices[i]*obj.vOffsets.stride;
} else {
baseofs = i*obj.vOffsets.stride;
}
ofs = baseofs + obj.vOffsets.radofs;
sscale = obj.values[ofs];
sphereMV.scale(sscale/scale[0], sscale/scale[1], sscale/scale[2]);
sphereMV.translate(obj.values[baseofs],
obj.values[baseofs+1],
obj.values[baseofs+2]);
sphereMV.multRight(this.mvMatrix);
gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(sphereMV.getAsArray()) );
if (nc &gt; 1) {
ofs = baseofs + obj.vOffsets.cofs;
gl.vertexAttrib4f( this.colLoc, obj.values[ofs],
obj.values[ofs+1],
obj.values[ofs+2],
obj.values[ofs+3] );
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, this.sphere.ibuf);
gl.drawElements(gl.TRIANGLES, this.sphere.sphereCount, gl.UNSIGNED_SHORT, 0);
}
this.disableArrays(obj, enabled);
if (typeof obj.polygon_offset !== &#34;undefined&#34;)
gl.disable(gl.POLYGON_OFFSET_FILL);
return;
} else {
if (obj.colorCount === 1) {
gl.disableVertexAttribArray( this.colLoc );
gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
} else {
gl.enableVertexAttribArray( this.colLoc );
enabled.colLoc = true;
gl.vertexAttribPointer(this.colLoc, 4, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.cofs);
}
}
if (is_lit &amp;&amp; obj.vOffsets.nofs &gt; 0) {
gl.enableVertexAttribArray( obj.normLoc );
enabled.normLoc = true;
gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nofs);
}
if (has_texture || type === &#34;text&#34;) {
gl.enableVertexAttribArray( obj.texLoc );
enabled.texLoc = true;
gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.tofs);
gl.activeTexture(gl.TEXTURE0);
gl.bindTexture(gl.TEXTURE_2D, obj.texture);
gl.uniform1i( obj.sampler, 0);
}
if (fixed_quads) {
gl.enableVertexAttribArray( obj.ofsLoc );
enabled.ofsLoc = true;
gl.vertexAttribPointer(obj.ofsLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.oofs);
}
if (typeof obj.userAttributes !== &#34;undefined&#34;) {
for (attr in obj.userAttribSizes) { // Not all attributes may have been used
gl.enableVertexAttribArray( obj.userAttribLocations[attr] );
gl.vertexAttribPointer( obj.userAttribLocations[attr], obj.userAttribSizes[attr],
gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.userAttribOffsets[attr]);
}
}
if (typeof obj.userUniforms !== &#34;undefined&#34;) {
for (attr in obj.userUniformLocations) {
var loc = obj.userUniformLocations[attr];
if (loc !== null) {
var uniform = obj.userUniforms[attr];
if (typeof uniform.length === &#34;undefined&#34;)
gl.uniform1f(loc, uniform);
else if (typeof uniform[0].length === &#34;undefined&#34;) {
uniform = new Float32Array(uniform);
switch(uniform.length) {
case 2: gl.uniform2fv(loc, uniform); break;
case 3: gl.uniform3fv(loc, uniform); break;
case 4: gl.uniform4fv(loc, uniform); break;
default: console.warn(&#34;bad uniform length&#34;);
}
} else if (uniform.length == 4 &amp;&amp; uniform[0].length == 4)
gl.uniformMatrix4fv(loc, false, new Float32Array(uniform.getAsArray()));
else
console.warn(&#34;unsupported uniform matrix&#34;);
}
}
}
for (pass = 0; pass &lt; obj.passes; pass++) {
pmode = obj.pmode[pass];
if (pmode === &#34;culled&#34;)
continue;
mode = fat_lines &amp;&amp; (is_lines || pmode == &#34;lines&#34;) ? &#34;TRIANGLES&#34; : this.mode4type[type];
if (depth_sort &amp;&amp; pmode == &#34;filled&#34;) {// Don&#39;t try depthsorting on wireframe or points
var faces = this.depthSort(obj),
nfaces = faces.length,
frowsize = Math.floor(obj.f[pass].length/nfaces);
if (type !== &#34;spheres&#34;) {
var f = obj.index_uint ? new Uint32Array(obj.f[pass].length) : new Uint16Array(obj.f[pass].length);
for (i=0; i&lt;nfaces; i++) {
for (j=0; j&lt;frowsize; j++) {
f[frowsize*i + j] = obj.f[pass][frowsize*faces[i] + j];
}
}
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, f, gl.DYNAMIC_DRAW);
}
}
if (is_twosided)
gl.uniform1i(obj.frontLoc, pass !== 0);
if (type !== &#34;spheres&#34;)
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
if (type === &#34;sprites&#34; || type === &#34;text&#34; || type === &#34;quads&#34;) {
count = count * 6/4;
} else if (type === &#34;surface&#34;) {
count = obj.f[pass].length;
}
count = obj.f[pass].length;
if (!is_lines &amp;&amp; pmode === &#34;lines&#34; &amp;&amp; !fat_lines) {
mode = &#34;LINES&#34;;
} else if (pmode === &#34;points&#34;) {
mode = &#34;POINTS&#34;;
}
if ((is_lines || pmode === &#34;lines&#34;) &amp;&amp; fat_lines) {
gl.enableVertexAttribArray(obj.pointLoc);
enabled.pointLoc = true;
gl.vertexAttribPointer(obj.pointLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.pointofs);
gl.enableVertexAttribArray(obj.nextLoc );
enabled.nextLoc = true;
gl.vertexAttribPointer(obj.nextLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nextofs);
gl.uniform1f(obj.aspectLoc, this.vp.width/this.vp.height);
gl.uniform1f(obj.lwdLoc, this.getMaterial(id, &#34;lwd&#34;)/this.vp.height);
}
gl.vertexAttribPointer(this.posLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.vofs);
gl.drawElements(gl[mode], count, obj.index_uint ? gl.UNSIGNED_INT : gl.UNSIGNED_SHORT, 0);
this.disableArrays(obj, enabled);
}
if (typeof obj.polygon_offset !== &#34;undefined&#34;)
gl.disable(gl.POLYGON_OFFSET_FILL);
};
/**
* Draw the background for a subscene
* @param { number } id - id of background object
* @param { number } subsceneid - id of subscene
*/
rglwidgetClass.prototype.drawBackground = function(id, subsceneid) {
var gl = this.gl || this.initGL(),
obj = this.getObj(id),
bg, i;
if (!obj.initialized)
this.initObj(id);
if (obj.colors.length) {
bg = obj.colors[0];
gl.clearColor(bg[0], bg[1], bg[2], bg[3]);
gl.depthMask(true);
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
}
if (typeof obj.quad !== &#34;undefined&#34;) {
this.prMatrix.makeIdentity();
this.mvMatrix.makeIdentity();
gl.disable(gl.BLEND);
gl.disable(gl.DEPTH_TEST);
gl.depthMask(false);
for (i=0; i &lt; obj.quad.length; i++)
this.drawObj(obj.quad[i], subsceneid);
}
};
/**
* Draw a subscene
* @param { number } subsceneid - id of subscene
* @param { boolean } opaquePass - is this the opaque drawing pass?
*/
rglwidgetClass.prototype.drawSubscene = function(subsceneid, opaquePass) {
var gl = this.gl || this.initGL(),
sub = this.getObj(subsceneid),
objects = this.scene.objects,
subids = sub.objects,
subscene_has_faces = false,
subscene_needs_sorting = false,
flags, i, obj;
if (sub.par3d.skipRedraw)
return;
for (i=0; i &lt; subids.length; i++) {
obj = objects[subids[i]];
flags = obj.flags;
if (typeof flags !== &#34;undefined&#34;) {
subscene_has_faces |= (flags &amp; this.f_is_lit)
&amp; !(flags &amp; this.f_fixed_quads);
obj.is_transparent = (flags &amp; this.f_is_transparent) || obj.someHidden;
subscene_needs_sorting |= (flags &amp; this.f_depth_sort) || obj.is_transparent;
}
}
this.setViewport(subsceneid);
if (typeof sub.backgroundId !== &#34;undefined&#34; &amp;&amp; opaquePass)
this.drawBackground(sub.backgroundId, subsceneid);
if (subids.length) {
this.setprMatrix(subsceneid);
this.setmvMatrix(subsceneid);
if (subscene_has_faces) {
this.setnormMatrix(subsceneid);
if ((sub.flags &amp; this.f_sprites_3d) &amp;&amp;
typeof sub.spriteNormmat === &#34;undefined&#34;) {
sub.spriteNormmat = new CanvasMatrix4(this.normMatrix);
}
}
if (subscene_needs_sorting)
this.setprmvMatrix();
var clipids = sub.clipplanes;
if (typeof clipids === &#34;undefined&#34;) {
console.warn(&#34;bad clipids&#34;);
}
if (clipids.length &gt; 0) {
this.invMatrix = new CanvasMatrix4(this.mvMatrix);
this.invMatrix.invert();
for (i = 0; i &lt; clipids.length; i++)
this.drawObj(clipids[i], subsceneid);
}
subids = sub.opaque.concat(sub.transparent);
if (opaquePass) {
gl.enable(gl.DEPTH_TEST);
gl.depthMask(true);
gl.disable(gl.BLEND);
for (i = 0; i &lt; subids.length; i++) {
if (!this.getObj(subids[i]).is_transparent)
this.drawObj(subids[i], subsceneid);
}
} else {
gl.depthMask(false);
gl.blendFuncSeparate(gl.SRC_ALPHA, gl.ONE_MINUS_SRC_ALPHA,
gl.ONE, gl.ONE);
gl.enable(gl.BLEND);
for (i = 0; i &lt; subids.length; i++) {
if (this.getObj(subids[i]).is_transparent)
this.drawObj(subids[i], subsceneid);
}
}
subids = sub.subscenes;
for (i = 0; i &lt; subids.length; i++) {
this.drawSubscene(subids[i], opaquePass);
}
}
};
/**
* Respond to brush change
*/
rglwidgetClass.prototype.selectionChanged = function() {
var i, j, k, id, subid = this.select.subscene, subscene,
objids, obj,
p1 = this.select.region.p1, p2 = this.select.region.p2,
filter, selection = [], handle, keys, xmin, x, xmax, ymin, y, ymax, z, v,
someHidden;
if (!subid)
return;
subscene = this.getObj(subid);
objids = subscene.objects;
filter = this.scene.crosstalk.filter;
this.setmvMatrix(subid);
this.setprMatrix(subid);
this.setprmvMatrix();
xmin = Math.min(p1.x, p2.x);
xmax = Math.max(p1.x, p2.x);
ymin = Math.min(p1.y, p2.y);
ymax = Math.max(p1.y, p2.y);
for (i = 0; i &lt; objids.length; i++) {
id = objids[i];
j = this.scene.crosstalk.id.indexOf(id);
if (j &gt;= 0) {
keys = this.scene.crosstalk.key[j];
obj = this.getObj(id);
someHidden = false;
for (k = 0; k &lt; keys.length; k++) {
if (filter &amp;&amp; filter.indexOf(keys[k]) &lt; 0) {
someHidden = true;
continue;
}
v = [].concat(obj.vertices[k]).concat(1.0);
v = this.multVM(v, this.prmvMatrix);
x = v[0]/v[3];
y = v[1]/v[3];
z = v[2]/v[3];
if (xmin &lt;= x &amp;&amp; x &lt;= xmax &amp;&amp; ymin &lt;= y &amp;&amp; y &lt;= ymax &amp;&amp; -1.0 &lt;= z &amp;&amp; z &lt;= 1.0) {
selection.push(keys[k]);
} else
someHidden = true;
}
obj.someHidden = someHidden &amp;&amp; (filter || selection.length);
obj.initialized = false;
/* Who should we notify? Only shared data in the current subscene, or everyone? */
if (!this.equalArrays(selection, this.scene.crosstalk.selection)) {
handle = this.scene.crosstalk.sel_handle[j];
handle.set(selection, {rglSubsceneId: this.select.subscene});
}
}
}
};
/**
* Respond to selection or filter change from crosstalk
* @param { Object } event - crosstalk event
* @param { boolean } filter - filter or selection?
*/
rglwidgetClass.prototype.selection = function(event, filter) {
var i, j, ids, obj, keys, crosstalk = this.scene.crosstalk,
selection, someHidden;
// Record the message and find out if this event makes some objects have mixed values:
crosstalk = this.scene.crosstalk;
if (filter) {
filter = crosstalk.filter = event.value;
selection = crosstalk.selection;
} else {
selection = crosstalk.selection = event.value;
filter = crosstalk.filter;
}
ids = crosstalk.id;
for (i = 0; i &lt; ids.length ; i++) {
obj = this.getObj(ids[i]);
obj.initialized = false;
keys = crosstalk.key[i];
someHidden = false;
for (j = 0; j &lt; keys.length &amp;&amp; !someHidden; j++) {
if ((filter &amp;&amp; filter.indexOf(keys[j]) &lt; 0) ||
(selection.length &amp;&amp; selection.indexOf(keys[j]) &lt; 0))
someHidden = true;
}
obj.someHidden = someHidden;
}
this.drawScene();
};
/**
* Clear the selection brush
* @param { number } except - Subscene that should ignore this request
*/
rglwidgetClass.prototype.clearBrush = function(except) {
if (this.select.subscene != except) {
this.select.state = &#34;inactive&#34;;
this.delFromSubscene(this.scene.brushId, this.select.subscene);
}
this.drawScene();
};
/**
* Compute mouse coordinates relative to current canvas
* @returns { Object }
* @param { Object } event - event object from mouse click
*/
rglwidgetClass.prototype.relMouseCoords = function(event) {
var totalOffsetX = 0,
totalOffsetY = 0,
currentElement = this.canvas;
do {
totalOffsetX += currentElement.offsetLeft;
totalOffsetY += currentElement.offsetTop;
currentElement = currentElement.offsetParent;
}
while(currentElement);
var canvasX = event.pageX - totalOffsetX,
canvasY = event.pageY - totalOffsetY;
return {x:canvasX, y:canvasY};
};
/**
* Set mouse handlers for the scene
*/
rglwidgetClass.prototype.setMouseHandlers = function() {
var self = this, activeSubscene, handler,
handlers = {}, drag = 0;
handlers.rotBase = 0;
this.screenToVector = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
radius = Math.max(width, height)/2.0,
cx = width/2.0,
cy = height/2.0,
px = (x-cx)/radius,
py = (y-cy)/radius,
plen = Math.sqrt(px*px+py*py);
if (plen &gt; 1.e-6) {
px = px/plen;
py = py/plen;
}
var angle = (Math.SQRT2 - plen)/Math.SQRT2*Math.PI/2,
z = Math.sin(angle),
zlen = Math.sqrt(1.0 - z*z);
px = px * zlen;
py = py * zlen;
return [px, py, z];
};
handlers.trackballdown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
handlers.rotBase = this.screenToVector(x, y);
this.saveMat = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.trackballmove = function(x,y) {
var rotCurrent = this.screenToVector(x,y),
rotBase = handlers.rotBase,
dot = rotBase[0]*rotCurrent[0] +
rotBase[1]*rotCurrent[1] +
rotBase[2]*rotCurrent[2],
angle = Math.acos( dot/this.vlen(rotBase)/this.vlen(rotCurrent) )*180.0/Math.PI,
axis = this.xprod(rotBase, rotCurrent),
objects = this.scene.objects,
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
l = activeModel.par3d.listeners,
i;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(angle, axis[0], axis[1], axis[2]);
}
this.drawScene();
};
handlers.trackballend = 0;
this.clamp = function(x, lo, hi) {
return Math.max(lo, Math.min(x, hi));
};
this.screenToPolar = function(x,y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
r = Math.min(width, height)/2,
dx = this.clamp(x - width/2, -r, r),
dy = this.clamp(y - height/2, -r, r);
return [Math.asin(dx/r), Math.asin(-dy/r)];
};
handlers.polardown = function(x,y) {
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
handlers.dragBase = this.screenToPolar(x, y);
this.saveMat = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
activeSub.camBase = [-Math.atan2(activeSub.saveMat.m13, activeSub.saveMat.m11),
Math.atan2(activeSub.saveMat.m32, activeSub.saveMat.m22)];
}
};
handlers.polarmove = function(x,y) {
var dragCurrent = this.screenToPolar(x,y),
activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
objects = this.scene.objects,
l = activeModel.par3d.listeners,
i, changepos = [];
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
for (j=0; j&lt;2; j++)
changepos[j] = -(dragCurrent[j] - handlers.dragBase[j]);
activeSub.par3d.userMatrix.makeIdentity();
activeSub.par3d.userMatrix.rotate(changepos[0]*180/Math.PI, 0,-1,0);
activeSub.par3d.userMatrix.multRight(objects[l[i]].saveMat);
activeSub.par3d.userMatrix.rotate(changepos[1]*180/Math.PI, -1,0,0);
}
this.drawScene();
};
handlers.polarend = 0;
handlers.axisdown = function(x,y) {
handlers.rotBase = this.screenToVector(x, this.canvas.height/2);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
}
};
handlers.axismove = function(x,y) {
var rotCurrent = this.screenToVector(x, this.canvas.height/2),
rotBase = handlers.rotBase,
angle = (rotCurrent[0] - rotBase[0])*180/Math.PI,
rotMat = new CanvasMatrix4();
rotMat.rotate(angle, handlers.axis[0], handlers.axis[1], handlers.axis[2]);
var activeSub = this.getObj(activeSubscene),
activeModel = this.getObj(this.useid(activeSub.id, &#34;model&#34;)),
i, l = activeModel.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.userMatrix.load(activeSub.saveMat);
activeSub.par3d.userMatrix.multLeft(rotMat);
}
this.drawScene();
};
handlers.axisend = 0;
handlers.y0zoom = 0;
handlers.zoom0 = 0;
handlers.zoomdown = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
handlers.y0zoom = y;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.zoom0 = Math.log(activeSub.par3d.zoom);
}
};
handlers.zoommove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.zoom = Math.exp(activeSub.zoom0 + (y-handlers.y0zoom)/this.canvas.height);
}
this.drawScene();
};
handlers.zoomend = 0;
handlers.y0fov = 0;
handlers.fovdown = function(x, y) {
handlers.y0fov = y;
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.fov0 = activeSub.par3d.FOV;
}
};
handlers.fovmove = function(x, y) {
var activeSub = this.getObj(activeSubscene),
activeProjection = this.getObj(this.useid(activeSub.id, &#34;projection&#34;)),
i, l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = this.getObj(l[i]);
activeSub.par3d.FOV = Math.max(1, Math.min(179, activeSub.fov0 +
180*(y-handlers.y0fov)/this.canvas.height));
}
this.drawScene();
};
handlers.fovend = 0;
handlers.selectingdown = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height,
p = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
this.select.region = {p1: p, p2: p};
if (this.select.subscene &amp;&amp; this.select.subscene != activeSubscene)
this.delFromSubscene(this.scene.brushId, this.select.subscene);
this.select.subscene = activeSubscene;
this.addToSubscene(this.scene.brushId, activeSubscene);
this.select.state = &#34;changing&#34;;
if (typeof this.scene.brushId !== &#34;undefined&#34;)
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingmove = function(x, y) {
var viewport = this.getObj(activeSubscene).par3d.viewport,
width = viewport.width*this.canvas.width,
height = viewport.height*this.canvas.height;
if (this.select.state === &#34;inactive&#34;)
return;
this.select.region.p2 = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
if (typeof this.scene.brushId !== &#34;undefined&#34;)
this.getObj(this.scene.brushId).initialized = false;
this.drawScene();
};
handlers.selectingend = 0;
this.canvas.onmousedown = function ( ev ){
if (!ev.which) // Use w3c defns in preference to MS
switch (ev.button) {
case 0: ev.which = 1; break;
case 1:
case 4: ev.which = 2; break;
case 2: ev.which = 3;
}
drag = [&#34;left&#34;, &#34;middle&#34;, &#34;right&#34;][ev.which-1];
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height-coords.y;
activeSubscene = self.whichSubscene(coords);
var sub = self.getObj(activeSubscene), f;
handler = sub.par3d.mouseMode[drag];
switch (handler) {
case &#34;xAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [1.0, 0.0, 0.0];
break;
case &#34;yAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [0.0, 1.0, 0.0];
break;
case &#34;zAxis&#34;:
handler = &#34;axis&#34;;
handlers.axis = [0.0, 0.0, 1.0];
break;
}
f = handlers[handler + &#34;down&#34;];
if (f) {
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
ev.preventDefault();
} else
console.warn(&#34;Mouse handler &#39;&#34; + handler + &#34;&#39; is not implemented.&#34;);
};
this.canvas.onmouseup = function ( ev ){
if ( drag === 0 ) return;
var f = handlers[handler + &#34;end&#34;];
if (f) {
f.call(self);
ev.preventDefault();
}
drag = 0;
};
this.canvas.onmouseout = this.canvas.onmouseup;
this.canvas.onmousemove = function ( ev ) {
if ( drag === 0 ) return;
var f = handlers[handler + &#34;move&#34;];
if (f) {
var coords = self.relMouseCoords(ev);
coords.y = self.canvas.height - coords.y;
coords = self.translateCoords(activeSubscene, coords);
f.call(self, coords.x, coords.y);
}
};
handlers.wheelHandler = function(ev) {
var del = 1.02, i;
if (ev.shiftKey) del = 1.002;
var ds = ((ev.detail || ev.wheelDelta) &gt; 0) ? del : (1 / del);
if (typeof activeSubscene === &#34;undefined&#34;)
activeSubscene = self.scene.rootSubscene;
var activeSub = self.getObj(activeSubscene),
activeProjection = self.getObj(self.useid(activeSub.id, &#34;projection&#34;)),
l = activeProjection.par3d.listeners;
for (i = 0; i &lt; l.length; i++) {
activeSub = self.getObj(l[i]);
activeSub.par3d.zoom *= ds;
}
self.drawScene();
ev.preventDefault();
};
this.canvas.addEventListener(&#34;DOMMouseScroll&#34;, handlers.wheelHandler, false);
this.canvas.addEventListener(&#34;mousewheel&#34;, handlers.wheelHandler, false);
};
/**
* Find a particular subscene by inheritance
* @returns { number } id of subscene to use
* @param { number } subsceneid - child subscene
* @param { string } type - type of inheritance: &#34;projection&#34; or &#34;model&#34;
*/
rglwidgetClass.prototype.useid = function(subsceneid, type) {
var sub = this.getObj(subsceneid);
if (sub.embeddings[type] === &#34;inherit&#34;)
return(this.useid(sub.parent, type));
else
return subsceneid;
};
/**
* Check whether point is in viewport of subscene
* @returns {boolean}
* @param { Object } coords - screen coordinates of point
* @param { number } subsceneid - subscene to check
*/
rglwidgetClass.prototype.inViewport = function(coords, subsceneid) {
var viewport = this.getObj(subsceneid).par3d.viewport,
x0 = coords.x - viewport.x*this.canvas.width,
y0 = coords.y - viewport.y*this.canvas.height;
return 0 &lt;= x0 &amp;&amp; x0 &lt;= viewport.width*this.canvas.width &amp;&amp;
0 &lt;= y0 &amp;&amp; y0 &lt;= viewport.height*this.canvas.height;
};
/**
* Find which subscene contains a point
* @returns { number } subscene id
* @param { Object } coords - coordinates of point
*/
rglwidgetClass.prototype.whichSubscene = function(coords) {
var self = this,
recurse = function(subsceneid) {
var subscenes = self.getChildSubscenes(subsceneid), i, id;
for (i=0; i &lt; subscenes.length; i++) {
id = recurse(subscenes[i]);
if (typeof(id) !== &#34;undefined&#34;)
return(id);
}
if (self.inViewport(coords, subsceneid))
return(subsceneid);
else
return undefined;
},
rootid = this.scene.rootSubscene,
result = recurse(rootid);
if (typeof(result) === &#34;undefined&#34;)
result = rootid;
return result;
};
/**
* Translate from window coordinates to viewport coordinates
* @returns { Object } translated coordinates
* @param { number } subsceneid - which subscene to use?
* @param { Object } coords - point to translate
*/
rglwidgetClass.prototype.translateCoords = function(subsceneid, coords) {
var viewport = this.getObj(subsceneid).par3d.viewport;
return {x: coords.x - viewport.x*this.canvas.width,
y: coords.y - viewport.y*this.canvas.height};
};
/**
* Initialize the sphere object
*/
rglwidgetClass.prototype.initSphere = function() {
var verts = this.scene.sphereVerts,
reuse = verts.reuse, result;
if (typeof reuse !== &#34;undefined&#34;) {
var prev = document.getElementById(reuse).rglinstance.sphere;
result = {values: prev.values, vOffsets: prev.vOffsets, it: prev.it};
} else
result = {values: new Float32Array(this.flatten(this.cbind(this.transpose(verts.vb),
this.transpose(verts.texcoords)))),
it: new Uint16Array(this.flatten(this.transpose(verts.it))),
vOffsets: {vofs:0, cofs:-1, nofs:-1, radofs:-1, oofs:-1,
tofs:3, nextofs:-1, pointofs:-1, stride:5}};
result.sphereCount = result.it.length;
this.sphere = result;
};
/**
* Set the vertices in the selection box object
*/
rglwidgetClass.prototype.initSelection = function(id) {
if (typeof this.select.region === &#34;undefined&#34;)
return;
var obj = this.getObj(id),
width = this.canvas.width,
height = this.canvas.height,
p1 = this.select.region.p1,
p2 = this.select.region.p2;
obj.vertices = [[p1.x, p1.y, 0.0],
[p2.x, p1.y, 0.0],
[p2.x, p2.y, 0.0],
[p1.x, p2.y, 0.0],
[p1.x, p1.y, 0.0]];
};
/**
* Do the gl part of initializing the sphere
*/
rglwidgetClass.prototype.initSphereGL = function() {
var gl = this.gl || this.initGL(), sphere = this.sphere;
if (gl.isContextLost()) return;
sphere.buf = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, sphere.buf);
gl.bufferData(gl.ARRAY_BUFFER, sphere.values, gl.STATIC_DRAW);
sphere.ibuf = gl.createBuffer();
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, sphere.ibuf);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, sphere.it, gl.STATIC_DRAW);
return;
};
/**
* Initialize the DOM object
* @param { Object } el - the DOM object
* @param { Object } x - the scene data sent by JSON from R
*/
rglwidgetClass.prototype.initialize = function(el, x) {
this.textureCanvas = document.createElement(&#34;canvas&#34;);
this.textureCanvas.style.display = &#34;block&#34;;
this.scene = x;
this.normMatrix = new CanvasMatrix4();
this.saveMat = {};
this.distance = null;
this.posLoc = 0;
this.colLoc = 1;
if (el) {
el.rglinstance = this;
this.el = el;
this.webGLoptions = el.rglinstance.scene.webGLoptions;
this.initCanvas();
}
if (typeof Shiny !== &#34;undefined&#34;) {
var self = this;
Shiny.addCustomMessageHandler(&#34;shinyGetPar3d&#34;,
function(message) {
var i, param,
subscene = self.getObj(message.subscene),
parameters = [].concat(message.parameters),
result = {tag: message.tag, subscene: message.subscene};
if (typeof subscene !== &#34;undefined&#34;) {
for (i = 0; i &lt; parameters.length; i++) {
param = parameters[i];
result[param] = subscene.par3d[param];
};
} else {
console.log(&#34;subscene &#34;+message.subscene+&#34; undefined.&#34;)
}
Shiny.setInputValue(&#34;par3d:shinyPar3d&#34;, result, {priority: &#34;event&#34;});
});
Shiny.addCustomMessageHandler(&#34;shinySetPar3d&#34;,
function(message) {
var param = message.parameter,
subscene = self.getObj(message.subscene);
if (typeof subscene !== &#34;undefined&#34;) {
subscene.par3d[param] = message.value;
subscene.initialized = false;
self.drawScene();
} else {
console.log(&#34;subscene &#34;+message.subscene+&#34; undefined.&#34;)
}
})
}
};
/**
* Restart the WebGL canvas
*/
rglwidgetClass.prototype.restartCanvas = function() {
var newcanvas = document.createElement(&#34;canvas&#34;),
self = this;
newcanvas.width = this.el.width;
newcanvas.height = this.el.height;
newcanvas.addEventListener(&#34;webglcontextrestored&#34;,
this.onContextRestored, false);
newcanvas.addEventListener(&#34;webglcontextlost&#34;,
this.onContextLost, false);
while (this.el.firstChild) {
this.el.removeChild(this.el.firstChild);
}
this.el.appendChild(newcanvas);
this.canvas = newcanvas;
this.setMouseHandlers();
if (this.gl)
Object.keys(this.scene.objects).forEach(function(key){
self.getObj(parseInt(key, 10)).texture = undefined;
});
this.gl = null;
};
/**
* Initialize the WebGL canvas
*/
rglwidgetClass.prototype.initCanvas = function() {
this.restartCanvas();
var objs = this.scene.objects,
self = this;
Object.keys(objs).forEach(function(key){
var id = parseInt(key, 10),
obj = self.getObj(id);
if (typeof obj.reuse !== &#34;undefined&#34;)
self.copyObj(id, obj.reuse);
});
Object.keys(objs).forEach(function(key){
self.initSubscene(parseInt(key, 10));
});
this.setMouseHandlers();
this.initSphere();
this.onContextRestored = function(event) {
self.initGL();
self.drawScene();
};
this.onContextLost = function(event) {
if (!self.drawing)
this.gl = null;
event.preventDefault();
};
this.initGL0();
this.lazyLoadScene = function() {
if (typeof self.slide === &#34;undefined&#34;)
self.slide = self.getSlide();
if (self.isInBrowserViewport()) {
if (!self.gl || self.gl.isContextLost())
self.initGL();
self.drawScene();
}
};
window.addEventListener(&#34;DOMContentLoaded&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;load&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;resize&#34;, this.lazyLoadScene, false);
window.addEventListener(&#34;scroll&#34;, this.lazyLoadScene, false);
this.slide = this.getSlide();
if (this.slide) {
if (typeof this.slide.rgl === &#34;undefined&#34;)
this.slide.rgl = [this];
else
this.slide.rgl.push(this);
if (this.scene.context.rmarkdown)
if (this.scene.context.rmarkdown === &#34;ioslides_presentation&#34;) {
this.slide.setAttribute(&#34;slideenter&#34;, &#34;this.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window);})&#34;);
} else if (this.scene.context.rmarkdown === &#34;slidy_presentation&#34;) {
// This method would also work in ioslides, but it gets triggered
// something like 5 times per slide for every slide change, so
// you&#39;d need a quicker function than lazyLoadScene.
var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver,
observer = new MutationObserver(function(mutations) {
mutations.forEach(function(mutation) {
self.slide.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window); });});});
observer.observe(this.slide, { attributes: true, attributeFilter:[&#34;class&#34;] });
}
}
};
/**
* Start the writeWebGL scene. This is only used by writeWebGL; rglwidget has
no debug element and does the drawing in rglwidget.js.
*/
rglwidgetClass.prototype.start = function() {
if (typeof this.prefix !== &#34;undefined&#34;) {
this.debugelement = document.getElementById(this.prefix + &#34;debug&#34;);
this.debug(&#34;&#34;);
}
this.drag = 0;
this.drawScene();
};
/**
* Display a debug message
* @param { string } msg - The message to display
* @param { Object } [img] - Image to insert before message
*/
rglwidgetClass.prototype.debug = function(msg, img) {
if (typeof this.debugelement !== &#34;undefined&#34; &amp;&amp; this.debugelement !== null) {
this.debugelement.innerHTML = msg;
if (typeof img !== &#34;undefined&#34;) {
this.debugelement.insertBefore(img, this.debugelement.firstChild);
}
} else if (msg !== &#34;&#34;)
alert(msg);
};
/**
* Get the snapshot image of this scene
* @returns { Object } The img DOM element
*/
rglwidgetClass.prototype.getSnapshot = function() {
var img;
if (typeof this.scene.snapshot !== &#34;undefined&#34;) {
img = document.createElement(&#34;img&#34;);
img.src = this.scene.snapshot;
img.alt = &#34;Snapshot&#34;;
}
return img;
};
/**
* Initial test for WebGL
*/
rglwidgetClass.prototype.initGL0 = function() {
if (!window.WebGLRenderingContext){
alert(&#34;Your browser does not support WebGL. See http://get.webgl.org&#34;);
return;
}
};
/**
* If we are in an ioslides or slidy presentation, get the
* DOM element of the current slide
* @returns { Object }
*/
rglwidgetClass.prototype.getSlide = function() {
var result = this.el, done = false;
while (result &amp;&amp; !done &amp;&amp; this.scene.context.rmarkdown) {
switch(this.scene.context.rmarkdown) {
case &#34;ioslides_presentation&#34;:
if (result.tagName === &#34;SLIDE&#34;) return result;
break;
case &#34;slidy_presentation&#34;:
if (result.tagName === &#34;DIV&#34; &amp;&amp; result.classList.contains(&#34;slide&#34;))
return result;
break;
default: return null;
}
result = result.parentElement;
}
return null;
};
/**
* Is this scene visible in the browser?
* @returns { boolean }
*/
rglwidgetClass.prototype.isInBrowserViewport = function() {
var rect = this.canvas.getBoundingClientRect(),
windHeight = (window.innerHeight || document.documentElement.clientHeight),
windWidth = (window.innerWidth || document.documentElement.clientWidth);
if (this.scene.context &amp;&amp; this.scene.context.rmarkdown !== null) {
if (this.slide)
return (this.scene.context.rmarkdown === &#34;ioslides_presentation&#34; &amp;&amp;
this.slide.classList.contains(&#34;current&#34;)) ||
(this.scene.context.rmarkdown === &#34;slidy_presentation&#34; &amp;&amp;
!this.slide.classList.contains(&#34;hidden&#34;));
}
return (
rect.top &gt;= -windHeight &amp;&amp;
rect.left &gt;= -windWidth &amp;&amp;
rect.bottom &lt;= 2*windHeight &amp;&amp;
rect.right &lt;= 2*windWidth);
};
/**
* Initialize WebGL
* @returns { Object } the WebGL context
*/
rglwidgetClass.prototype.initGL = function() {
var self = this;
if (this.gl) {
if (!this.drawing &amp;&amp; this.gl.isContextLost())
this.restartCanvas();
else
return this.gl;
}
// if (!this.isInBrowserViewport()) return; Return what??? At this point we know this.gl is null.
this.canvas.addEventListener(&#34;webglcontextrestored&#34;,
this.onContextRestored, false);
this.canvas.addEventListener(&#34;webglcontextlost&#34;,
this.onContextLost, false);
this.gl = this.canvas.getContext(&#34;webgl&#34;, this.webGLoptions) ||
this.canvas.getContext(&#34;experimental-webgl&#34;, this.webGLoptions);
this.index_uint = this.gl.getExtension(&#34;OES_element_index_uint&#34;);
var save = this.startDrawing();
this.initSphereGL();
Object.keys(this.scene.objects).forEach(function(key){
self.initObj(parseInt(key, 10));
});
this.stopDrawing(save);
return this.gl;
};
/**
* Resize the display to match element
* @param { Object } el - DOM element to match
*/
rglwidgetClass.prototype.resize = function(el) {
this.canvas.width = el.width;
this.canvas.height = el.height;
};
/**
* Draw the whole scene
*/
rglwidgetClass.prototype.drawScene = function() {
var gl = this.gl || this.initGL(),
wasDrawing = this.startDrawing();
if (!wasDrawing) {
if (this.select.state !== &#34;inactive&#34;)
this.selectionChanged();
gl.enable(gl.DEPTH_TEST);
gl.depthFunc(gl.LEQUAL);
gl.clearDepth(1.0);
gl.clearColor(1,1,1,1);
gl.depthMask(true); // Must be true before clearing depth buffer
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
this.drawSubscene(this.scene.rootSubscene, true);
this.drawSubscene(this.scene.rootSubscene, false);
}
this.stopDrawing(wasDrawing);
};
/**
* Change the displayed subset
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The subset control data.
*/
rglwidgetClass.prototype.subsetSetter = function(el, control) {
if (typeof control.subscenes === &#34;undefined&#34; ||
control.subscenes === null)
control.subscenes = this.scene.rootSubscene;
var value = Math.round(control.value),
subscenes = [].concat(control.subscenes),
fullset = [].concat(control.fullset),
i, j, entries, subsceneid,
adds = [], deletes = [],
ismissing = function(x) {
return fullset.indexOf(x) &lt; 0;
},
tointeger = function(x) {
return parseInt(x, 10);
};
if (isNaN(value))
value = control.value = 0;
if (control.accumulate)
for (i=0; i &lt;= value; i++)
adds = adds.concat(control.subsets[i]);
else
adds = adds.concat(control.subsets[value]);
deletes = fullset.filter(function(x) { return adds.indexOf(x) &lt; 0; });
for (i = 0; i &lt; subscenes.length; i++) {
subsceneid = subscenes[i];
if (typeof this.getObj(subsceneid) === &#34;undefined&#34;)
this.alertOnce(&#34;typeof object is undefined&#34;);
for (j = 0; j &lt; adds.length; j++)
this.addToSubscene(adds[j], subsceneid);
for (j = 0; j &lt; deletes.length; j++)
this.delFromSubscene(deletes[j], subsceneid);
}
};
/**
* Change the requested property
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The property setter control data.
*/
rglwidgetClass.prototype.propertySetter = function(el, control) {
var value = control.value,
values = [].concat(control.values),
svals = [].concat(control.param),
direct = values[0] === null,
entries = [].concat(control.entries),
ncol = entries.length,
nrow = values.length/ncol,
properties = this.repeatToLen(control.properties, ncol),
objids = this.repeatToLen(control.objids, ncol),
property, objid = objids[0],
obj = this.getObj(objid),
propvals, i, v1, v2, p, entry, gl, needsBinding,
newprop, newid,
getPropvals = function() {
if (property === &#34;userMatrix&#34;)
return obj.par3d.userMatrix.getAsArray();
else if (property === &#34;scale&#34; || property === &#34;FOV&#34; || property === &#34;zoom&#34;)
return [].concat(obj.par3d[property]);
else
return [].concat(obj[property]);
};
putPropvals = function(newvals) {
if (newvals.length == 1)
newvals = newvals[0];
if (property === &#34;userMatrix&#34;)
obj.par3d.userMatrix.load(newvals);
else if (property === &#34;scale&#34; || property === &#34;FOV&#34; || property === &#34;zoom&#34;)
obj.par3d[property] = newvals;
else
obj[property] = newvals;
};
if (direct &amp;&amp; typeof value === &#34;undefined&#34;)
return;
if (control.interp) {
values = values.slice(0, ncol).concat(values).
concat(values.slice(ncol*(nrow-1), ncol*nrow));
svals = [-Infinity].concat(svals).concat(Infinity);
for (i = 1; i &lt; svals.length; i++) {
if (value &lt;= svals[i]) {
if (svals[i] === Infinity)
p = 1;
else
p = (svals[i] - value)/(svals[i] - svals[i-1]);
break;
}
}
} else if (!direct) {
value = Math.round(value);
}
for (j=0; j&lt;entries.length; j++) {
entry = entries[j];
newprop = properties[j];
newid = objids[j];
if (newprop !== property || newid != objid) {
if (typeof property !== &#34;undefined&#34;)
putPropvals(propvals);
property = newprop;
objid = newid;
obj = this.getObj(objid);
propvals = getPropvals();
}
if (control.interp) {
v1 = values[ncol*(i-1) + j];
v2 = values[ncol*i + j];
this.setElement(propvals, entry, p*v1 + (1-p)*v2);
} else if (!direct) {
this.setElement(propvals, entry, values[ncol*value + j]);
} else {
this.setElement(propvals, entry, value[j]);
}
}
putPropvals(propvals);
needsBinding = [];
for (j=0; j &lt; entries.length; j++) {
if (properties[j] === &#34;values&#34; &amp;&amp;
needsBinding.indexOf(objids[j]) === -1) {
needsBinding.push(objids[j]);
}
}
for (j=0; j &lt; needsBinding.length; j++) {
gl = this.gl || this.initGL();
obj = this.getObj(needsBinding[j]);
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertices
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The vertext setter control data.
*/
rglwidgetClass.prototype.vertexSetter = function(el, control) {
var svals = [].concat(control.param),
j, k, p, a, propvals, stride, ofs, obj, entry,
attrib,
ofss = {x:&#34;vofs&#34;, y:&#34;vofs&#34;, z:&#34;vofs&#34;,
red:&#34;cofs&#34;, green:&#34;cofs&#34;, blue:&#34;cofs&#34;,
alpha:&#34;cofs&#34;, radii:&#34;radofs&#34;,
nx:&#34;nofs&#34;, ny:&#34;nofs&#34;, nz:&#34;nofs&#34;,
ox:&#34;oofs&#34;, oy:&#34;oofs&#34;, oz:&#34;oofs&#34;,
ts:&#34;tofs&#34;, tt:&#34;tofs&#34;},
pos = {x:0, y:1, z:2,
red:0, green:1, blue:2,
alpha:3,radii:0,
nx:0, ny:1, nz:2,
ox:0, oy:1, oz:2,
ts:0, tt:1},
values = control.values,
direct = values === null,
ncol,
interp = control.interp,
vertices = [].concat(control.vertices),
attributes = [].concat(control.attributes),
value = control.value, newval, aliases, alias;
ncol = Math.max(vertices.length, attributes.length);
if (!ncol)
return;
vertices = this.repeatToLen(vertices, ncol);
attributes = this.repeatToLen(attributes, ncol);
if (direct)
interp = false;
/* JSON doesn&#39;t pass Infinity */
svals[0] = -Infinity;
svals[svals.length - 1] = Infinity;
for (j = 1; j &lt; svals.length; j++) {
if (value &lt;= svals[j]) {
if (interp) {
if (svals[j] === Infinity)
p = 1;
else
p = (svals[j] - value)/(svals[j] - svals[j-1]);
} else {
if (svals[j] - value &gt; value - svals[j-1])
j = j - 1;
}
break;
}
}
obj = this.getObj(control.objid);
// First, make sure color attributes vary in original
if (typeof obj.vOffsets !== &#34;undefined&#34;) {
varies = true;
for (k = 0; k &lt; ncol; k++) {
attrib = attributes[k];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[attrib]];
if (ofs &lt; 0) {
switch(attrib) {
case &#34;alpha&#34;:
case &#34;red&#34;:
case &#34;green&#34;:
case &#34;blue&#34;:
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(control.objid);
}
propvals = obj.values;
aliases = obj.alias;
if (typeof aliases === &#34;undefined&#34;)
aliases = [];
for (k=0; k&lt;ncol; k++) {
if (direct) {
newval = value;
} else if (interp) {
newval = p*values[j-1][k] + (1-p)*values[j][k];
} else {
newval = values[j][k];
}
attrib = attributes[k];
vertex = vertices[k];
alias = aliases[vertex];
if (obj.type === &#34;planes&#34; || obj.type === &#34;clipplanes&#34;) {
ofs = [&#34;nx&#34;, &#34;ny&#34;, &#34;nz&#34;, &#34;offset&#34;].indexOf(attrib);
if (ofs &gt;= 0) {
if (ofs &lt; 3) {
if (obj.normals[vertex][ofs] != newval) { // Assume no aliases here...
obj.normals[vertex][ofs] = newval;
obj.initialized = false;
}
} else {
if (obj.offsets[vertex][0] != newval) {
obj.offsets[vertex][0] = newval;
obj.initialized = false;
}
}
continue;
}
}
// Not a plane setting...
ofs = obj.vOffsets[ofss[attrib]];
if (ofs &lt; 0)
this.alertOnce(&#34;Attribute &#39;&#34;+attrib+&#34;&#39; not found in object &#34;+control.objid);
else {
stride = obj.vOffsets.stride;
ofs = ofs + pos[attrib];
entry = vertex*stride + ofs;
propvals[entry] = newval;
if (typeof alias !== &#34;undefined&#34;)
for (a = 0; a &lt; alias.length; a++)
propvals[alias[a]*stride + ofs] = newval;
}
}
if (typeof obj.buf !== &#34;undefined&#34;) {
var gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, propvals, gl.STATIC_DRAW);
}
};
/**
* Change the requested vertex properties by age
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The age setter control data.
*/
rglwidgetClass.prototype.ageSetter = function(el, control) {
var objids = [].concat(control.objids),
nobjs = objids.length,
time = control.value,
births = [].concat(control.births),
ages = [].concat(control.ages),
steps = births.length,
j = Array(steps),
p = Array(steps),
i, k, age, j0, propvals, stride, ofs, objid, obj,
attrib, dim, varies, alias, aliases, a, d,
attribs = [&#34;colors&#34;, &#34;alpha&#34;, &#34;radii&#34;, &#34;vertices&#34;,
&#34;normals&#34;, &#34;origins&#34;, &#34;texcoords&#34;,
&#34;x&#34;, &#34;y&#34;, &#34;z&#34;,
&#34;red&#34;, &#34;green&#34;, &#34;blue&#34;],
ofss = [&#34;cofs&#34;, &#34;cofs&#34;, &#34;radofs&#34;, &#34;vofs&#34;,
&#34;nofs&#34;, &#34;oofs&#34;, &#34;tofs&#34;,
&#34;vofs&#34;, &#34;vofs&#34;, &#34;vofs&#34;,
&#34;cofs&#34;, &#34;cofs&#34;, &#34;cofs&#34;],
dims = [3,1,1,3,
3,2,2,
1,1,1,
1,1,1],
pos = [0,3,0,0,
0,0,0,
0,1,2,
0,1,2];
/* Infinity doesn&#39;t make it through JSON */
ages[0] = -Infinity;
ages[ages.length-1] = Infinity;
for (i = 0; i &lt; steps; i++) {
if (births[i] !== null) { // NA in R becomes null
age = time - births[i];
for (j0 = 1; age &gt; ages[j0]; j0++);
if (ages[j0] == Infinity)
p[i] = 1;
else if (ages[j0] &gt; ages[j0-1])
p[i] = (ages[j0] - age)/(ages[j0] - ages[j0-1]);
else
p[i] = 0;
j[i] = j0;
}
}
// First, make sure color attributes vary in original
for (l = 0; l &lt; nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
varies = true;
if (typeof obj.vOffsets === &#34;undefined&#34;)
continue;
for (k = 0; k &lt; attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[k]];
if (ofs &lt; 0) {
switch(attribs[k]) {
case &#34;colors&#34;:
case &#34;alpha&#34;:
case &#34;red&#34;:
case &#34;green&#34;:
case &#34;blue&#34;:
obj.colors = [obj.colors[0], obj.colors[0]];
break;
}
varies = false;
}
}
}
if (!varies)
this.initObj(objid);
}
for (l = 0; l &lt; nobjs; l++) {
objid = objids[l];
obj = this.getObj(objid);
if (typeof obj.vOffsets === &#34;undefined&#34;)
continue;
aliases = obj.alias;
if (typeof aliases === &#34;undefined&#34;)
aliases = [];
propvals = obj.values;
stride = obj.vOffsets.stride;
for (k = 0; k &lt; attribs.length; k++) {
attrib = control[attribs[k]];
if (typeof attrib !== &#34;undefined&#34;) {
ofs = obj.vOffsets[ofss[k]];
if (ofs &gt;= 0) {
dim = dims[k];
ofs = ofs + pos[k];
for (i = 0; i &lt; steps; i++) {
alias = aliases[i];
if (births[i] !== null) {
for (d=0; d &lt; dim; d++) {
propvals[i*stride + ofs + d] = p[i]*attrib[dim*(j[i]-1) + d] + (1-p[i])*attrib[dim*j[i] + d];
if (typeof alias !== &#34;undefined&#34;)
for (a=0; a &lt; alias.length; a++)
propvals[alias[a]*stride + ofs + d] = propvals[i*stride + ofs + d];
}
}
}
} else
this.alertOnce(&#34;\&#39;&#34;+attribs[k]+&#34;\&#39; property not found in object &#34;+objid);
}
}
obj.values = propvals;
if (typeof obj.buf !== &#34;undefined&#34;) {
gl = this.gl || this.initGL();
gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
}
}
};
/**
* Bridge to old style control
* @param { Object } el - Element of the control; not used.
* @param { Object } control - The bridge control data.
*/
rglwidgetClass.prototype.oldBridge = function(el, control) {
var attrname, global = window[control.prefix + &#34;rgl&#34;];
if (global)
for (attrname in global)
this[attrname] = global[attrname];
window[control.prefix + &#34;rgl&#34;] = this;
};
/**
* Set up a player control
* @param { Object } el - The player control element
* @param { Object } control - The player data.
*/
rglwidgetClass.prototype.Player = function(el, control) {
var
self = this,
components = [].concat(control.components),
buttonLabels = [].concat(control.buttonLabels),
Tick = function() { /* &#34;this&#34; will be a timer */
var i,
nominal = this.value,
slider = this.Slider,
labels = this.outputLabels,
output = this.Output,
step;
if (typeof slider !== &#34;undefined&#34; &amp;&amp; nominal != slider.value)
slider.value = nominal;
if (typeof output !== &#34;undefined&#34;) {
step = Math.round((nominal - output.sliderMin)/output.sliderStep);
if (labels !== null) {
output.innerHTML = labels[step];
} else {
step = step*output.sliderStep + output.sliderMin;
output.innerHTML = step.toPrecision(output.outputPrecision);
}
}
for (i=0; i &lt; this.actions.length; i++) {
this.actions[i].value = nominal;
}
self.applyControls(el, this.actions, false);
self.drawScene();
},
OnSliderInput = function() { /* &#34;this&#34; will be the slider */
this.rgltimer.value = Number(this.value);
this.rgltimer.Tick();
},
addSlider = function(min, max, step, value) {
var slider = document.createElement(&#34;input&#34;);
slider.type = &#34;range&#34;;
slider.min = min;
slider.max = max;
slider.step = step;
slider.value = value;
slider.oninput = OnSliderInput;
slider.sliderActions = control.actions;
slider.sliderScene = this;
slider.className = &#34;rgl-slider&#34;;
slider.id = el.id + &#34;-slider&#34;;
el.rgltimer.Slider = slider;
slider.rgltimer = el.rgltimer;
el.appendChild(slider);
},
addLabel = function(labels, min, step, precision) {
var output = document.createElement(&#34;output&#34;);
output.sliderMin = min;
output.sliderStep = step;
output.outputPrecision = precision;
output.className = &#34;rgl-label&#34;;
output.id = el.id + &#34;-label&#34;;
el.rgltimer.Output = output;
el.rgltimer.outputLabels = labels;
el.appendChild(output);
},
addButton = function(which, label, active) {
var button = document.createElement(&#34;input&#34;),
onclicks = {Reverse: function() { this.rgltimer.reverse();},
Play: function() { this.rgltimer.play();
this.value = this.rgltimer.enabled ? this.inactiveValue : this.activeValue; },
Slower: function() { this.rgltimer.slower(); },
Faster: function() { this.rgltimer.faster(); },
Reset: function() { this.rgltimer.reset(); },
Step: function() { this.rgltimer.step(); }
};
button.rgltimer = el.rgltimer;
button.type = &#34;button&#34;;
button.value = label;
button.activeValue = label;
button.inactiveValue = active;
if (which === &#34;Play&#34;)
button.rgltimer.PlayButton = button;
button.onclick = onclicks[which];
button.className = &#34;rgl-button&#34;;
button.id = el.id + &#34;-&#34; + which;
el.appendChild(button);
};
if (typeof control.reinit !== &#34;undefined&#34; &amp;&amp; control.reinit !== null) {
control.actions.reinit = control.reinit;
}
el.rgltimer = new rgltimerClass(Tick, control.start, control.interval, control.stop,
control.step, control.value, control.rate, control.loop, control.actions);
for (var i=0; i &lt; components.length; i++) {
switch(components[i]) {
case &#34;Slider&#34;: addSlider(control.start, control.stop,
control.step, control.value);
break;
case &#34;Label&#34;: addLabel(control.labels, control.start,
control.step, control.precision);
break;
default:
addButton(components[i], buttonLabels[i], control.pause);
}
}
el.rgltimer.Tick();
};
/**
* Apply all registered controls
* @param { Object } el - DOM element of the control
* @param { Object } x - List of actions to apply
* @param { boolean } [draw=true] - Whether to redraw after applying
*/
rglwidgetClass.prototype.applyControls = function(el, x, draw) {
var self = this, reinit = x.reinit, i, control, type;
for (i = 0; i &lt; x.length; i++) {
control = x[i];
type = control.type;
self[type](el, control);
}
if (typeof reinit !== &#34;undefined&#34; &amp;&amp; reinit !== null) {
reinit = [].concat(reinit);
for (i = 0; i &lt; reinit.length; i++)
self.getObj(reinit[i]).initialized = false;
}
if (typeof draw === &#34;undefined&#34; || draw)
self.drawScene();
};
/**
* Handler for scene change
* @param { Object } message - What sort of scene change to do?
*/
rglwidgetClass.prototype.sceneChangeHandler = function(message) {
var self = document.getElementById(message.elementId).rglinstance,
objs = message.objects, mat = message.material,
root = message.rootSubscene,
initSubs = message.initSubscenes,
redraw = message.redrawScene,
skipRedraw = message.skipRedraw,
deletes, subs, allsubs = [], i,j;
if (typeof message.delete !== &#34;undefined&#34;) {
deletes = [].concat(message.delete);
if (typeof message.delfromSubscenes !== &#34;undefined&#34;)
subs = [].concat(message.delfromSubscenes);
else
subs = [];
for (i = 0; i &lt; deletes.length; i++) {
for (j = 0; j &lt; subs.length; j++) {
self.delFromSubscene(deletes[i], subs[j]);
}
delete self.scene.objects[deletes[i]];
}
}
if (typeof objs !== &#34;undefined&#34;) {
Object.keys(objs).forEach(function(key){
key = parseInt(key, 10);
self.scene.objects[key] = objs[key];
self.initObj(key);
var obj = self.getObj(key),
subs = [].concat(obj.inSubscenes), k;
allsubs = allsubs.concat(subs);
for (k = 0; k &lt; subs.length; k++)
self.addToSubscene(key, subs[k]);
});
}
if (typeof mat !== &#34;undefined&#34;) {
self.scene.material = mat;
}
if (typeof root !== &#34;undefined&#34;) {
self.scene.rootSubscene = root;
}
if (typeof initSubs !== &#34;undefined&#34;)
allsubs = allsubs.concat(initSubs);
allsubs = self.unique(allsubs);
for (i = 0; i &lt; allsubs.length; i++) {
self.initSubscene(allsubs[i]);
}
if (typeof skipRedraw !== &#34;undefined&#34;) {
root = self.getObj(self.scene.rootSubscene);
root.par3d.skipRedraw = skipRedraw;
}
if (redraw)
self.drawScene();
};
/**
* Set mouse mode for a subscene
* @param { string } mode - name of mode
* @param { number } button - button number (1 to 3)
* @param { number } subscene - subscene id number
* @param { number } stayActive - if truthy, don&#39;t clear brush
*/
rglwidgetClass.prototype.setMouseMode = function(mode, button, subscene, stayActive) {
var sub = this.getObj(subscene),
which = [&#34;left&#34;, &#34;right&#34;, &#34;middle&#34;][button - 1];
if (!stayActive &amp;&amp; sub.par3d.mouseMode[which] === &#34;selecting&#34;)
this.clearBrush(null);
sub.par3d.mouseMode[which] = mode;
};
/**
* The class of an rgl timer object
* @class
*/
/**
* Construct an rgltimerClass object
* @constructor
* @param { function } Tick - action when timer fires
* @param { number } startTime - nominal start time in seconds
* @param { number } interval - seconds between updates
* @param { number } stopTime - nominal stop time in seconds
* @param { number } stepSize - nominal step size
* @param { number } value - current nominal time
* @param { number } rate - nominal units per second
* @param { string } loop - &#34;none&#34;, &#34;cycle&#34; or &#34;oscillate&#34;
* @param { Object } actions - list of actions
*/
rgltimerClass = function(Tick, startTime, interval, stopTime, stepSize, value, rate, loop, actions) {
this.enabled = false;
this.timerId = 0;
/** nominal start time in seconds */
this.startTime = startTime;
/** current nominal time */
this.value = value;
/** seconds between updates */
this.interval = interval;
/** nominal stop time */
this.stopTime = stopTime;
/** nominal step size */
this.stepSize = stepSize;
/** nominal units per second */
this.rate = rate;
/** &#34;none&#34;, &#34;cycle&#34;, or &#34;oscillate&#34; */
this.loop = loop;
/** real world start time */
this.realStart = undefined;
/** multiplier for fast-forward or reverse */
this.multiplier = 1;
this.actions = actions;
this.Tick = Tick;
};
/**
* Start playing timer object
*/
rgltimerClass.prototype.play = function() {
if (this.enabled) {
this.enabled = false;
window.clearInterval(this.timerId);
this.timerId = 0;
return;
}
var tick = function(self) {
var now = new Date();
self.value = self.multiplier*self.rate*(now - self.realStart)/1000 + self.startTime;
self.forceToRange();
if (typeof self.Tick !== &#34;undefined&#34;) {
self.Tick(self.value);
}
};
this.realStart = new Date() - 1000*(this.value - this.startTime)/this.rate/this.multiplier;
this.timerId = window.setInterval(tick, 1000*this.interval, this);
this.enabled = true;
};
/**
* Force value into legal range
*/
rgltimerClass.prototype.forceToRange = function() {
if (this.value &gt; this.stopTime + this.stepSize/2 || this.value &lt; this.startTime - this.stepSize/2) {
if (!this.loop) {
this.reset();
} else {
var cycle = this.stopTime - this.startTime + this.stepSize,
newval = (this.value - this.startTime) % cycle + this.startTime;
if (newval &lt; this.startTime) {
newval += cycle;
}
this.realStart += (this.value - newval)*1000/this.multiplier/this.rate;
this.value = newval;
}
}
};
/**
* Reset to start values
*/
rgltimerClass.prototype.reset = function() {
this.value = this.startTime;
this.newmultiplier(1);
if (typeof this.Tick !== &#34;undefined&#34;) {
this.Tick(this.value);
}
if (this.enabled)
this.play(); /* really pause... */
if (typeof this.PlayButton !== &#34;undefined&#34;)
this.PlayButton.value = &#34;Play&#34;;
};
/**
* Increase the multiplier to play faster
*/
rgltimerClass.prototype.faster = function() {
this.newmultiplier(Math.SQRT2*this.multiplier);
};
/**
* Decrease the multiplier to play slower
*/
rgltimerClass.prototype.slower = function() {
this.newmultiplier(this.multiplier/Math.SQRT2);
};
/**
* Change sign of multiplier to reverse direction
*/
rgltimerClass.prototype.reverse = function() {
this.newmultiplier(-this.multiplier);
};
/**
* Set multiplier for play speed
* @param { number } newmult - new value
*/
rgltimerClass.prototype.newmultiplier = function(newmult) {
if (newmult != this.multiplier) {
this.realStart += 1000*(this.value - this.startTime)/this.rate*(1/this.multiplier - 1/newmult);
this.multiplier = newmult;
}
};
/**
* Take one step
*/
rgltimerClass.prototype.step = function() {
this.value += this.rate*this.multiplier;
this.forceToRange();
if (typeof this.Tick !== &#34;undefined&#34;)
this.Tick(this.value);
};&lt;/script&gt;
&lt;div id=&#34;unnamed_chunk_15div&#34; class=&#34;rglWebGL&#34;&gt;&lt;/div&gt;
&lt;script type=&#34;text/javascript&#34;&gt;
var unnamed_chunk_15div = document.getElementById(&#34;unnamed_chunk_15div&#34;),
unnamed_chunk_15rgl = new rglwidgetClass();
unnamed_chunk_15div.width = 673;
unnamed_chunk_15div.height = 481;
unnamed_chunk_15rgl.initialize(unnamed_chunk_15div,
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K9a3Vc7No7+/TIl7g8vdE0duNTbO/s5KxmqkeT1X39dcbLzaO0dtV5l/2Lnmvu6edr4hri7p+/iZrwrxfEKjFfHt7GwfHorgh3aOv/tm9oTX/O0Oup8nzf7Ton/ed4FXVR+MgMxnv1YTimOHf0fb66IARcCkIeJxYpLuHoqY9d2nNdJ/GVldWcdZHfNUJXD6+Ztp7PkVMlpcUnmTeBl2S632K9lVRFncqP0oPmtHtQTtq6qKnbGH7ZURkcHb3bAA7ewL679QP9Z+uL7785S9Hq13fjXl237q6+s9N8+mm+e2mefdHfmRigt3/2yi23PJOv1D1BmVvaVwHZHeJd2DqTdZfy/JfDXAOCHicUjRtvUGptrVyRVOofDWUmpUz/d5+uvfhZzXQR6M9y/WFr2Iq2vvUTFzyOOrHXnKw/+jOysSOHuZz4/VivWkeY/a+Xm6VatKV8ex9CdmkOfVszwyshK9//esxc/76XnwxNOW/cn39Xz75ydtf/dXmfuv3Ge+///7oOjf9OqLTomyFj467l4+T3YUee1wcAh6n4cmkyVxKEcX82irNKY3KPvCSj8drGp23WbPc0s/aIddn7pK1F2ceamV13UeTRgPn/uDtZs9E+Uz8GY6ud5+h1nw2xt9NTzn0+XRvi2Kx681p9hHqEfPx79XV1V9pmv/x2c/+iab5VNP8raZ5Ph3w2ig2xiOyDnk9JQ00+NvSjZUUnGnH6zHpsccFIeBxbFmn6Mq2jWmtCzcoLdo01tvaguYpa5sfl40re8vVE+uhua673E1UP43MLp+qtlNTO1iLsLPH97vo5esSR9Pdsx+qB1+lhf4zL0Qz7DqbEq9rKc/1su+9K2bmayWCxtp1sK7hhsM09N6mPvn44u/c3Hx0dfVfP/nJv3qf37/VNP2XvvRHFgS8/969IR79Q60t4dMbvrKl//4ebv3rIuNxQQh4HJVPeO5Th3ybJsF1Vsc065Nf22yv+R+RtTW9xT+aUgvH18updvGcfXZ6VlhmtJm72qyQGuHtO+Z517ee5MpsbWg+lL+0cJf2cVcLeLRkjee3XzZ1NhlwXZTw+/DDD6MYbdyi4vPfev36H7148W9+8if/8H1+/7Wm+YfT6T609ad61KNBr+uJ+IvSwbGgQIsn/QqmTzWPyyun7O0avXQDzg0Bj+NR6ydOoGop9imVdYtPSVOjcGaUVG21LHWmBoMfmuurVDZOd4kU8cN07dJudpuvp1fWTVVl8bervFeE1oOG6hfyzdq7tJ5t9ApG4x3ZhchdquXnPQ0xFu6/iOic147v0Yj/5s3N95rm97/ylWezQ+9qvuu3PPoGesx7d315pAJ7lTbtbZf1EpHxOHMEPI4kmnT9fS+od1PHd3Xqz/Kss1ld5WP6iPLKlo21E13K61RrZass17Pv+qJ2jZq3Vv5WvfczPf9xQbBzNZW1TTbUC1TvyMqK5Dz0kUcXx/s0CCW9QtRzUQfHG6g1e8Nh3/nOd25ubvxhtXHcv7v/4jea5uemp83Lt7/9be9Emcljf4atFQwuX7Kmc+rgrW8da+Vx5gh4PDqviRbtLU933zAma2CNRr43H/2yQNGyc2O9Lxrco+kbze7sCmB0vdbMxUR0Di95Ssu9TWI+vBfJ6dJy+R0e0EdP/H3WC1+num/d5lq7Ls3R69NFgzaBLX3j1atvfe5z/61p/sm2dL+6umqtm8f7GOavpeIHTdWjVY/FKlVZ8GOm/n7KCRPA+SDg8bhijDmizvvMNa1aGTx8oXuVw5yeND5Pys/dZbQ/qL3u4+ujh/mUtJkrgK3UmXE0akY/6HKnfATvwNf4utruWoI4OoHgzZs319fXUaguOueDjvxXr1//8y996T81zS9Op/vz58/92k796rFAoJ1Yqdjbrzje+bLxrT82XY/6Ws3VWLU7IeNxngh4PCIfY9ZwrIJcMdBvloLR8io9iC4CvEJL3KUrpsS3Vlx23sJcz+rh7NMl+3azwPvx+UveeTf07EH8/fEhFf913N7eNvd7ycS0+eELxfzfvLn5F8+e/f2bm19+9erXnz37/Z/92XenA/6b3/xmn64LdbHlfQyjoznqwFDdhbUt2+vTHA6/emttlWYsqPOLg+gG8L+EheshgWMi4PFY1pt7d+oEqr56tY2yCWvR4o+Az9pGPrFL/2ZNuiVDp8tz3bud9xxtjZH7nWP1sN6mzWN26LqXme6TUkT7zc1NTJuPr4eM/3tXV9+7vv7N168/vLr6xic+8Y+n0304/i5Vs1cGtzYfUL8vpa/GU9SBoSfsIw7lReHbVNTWM94H8n2yxdtUIfjIHTPAPAIejyLrhY7WdpxJI07azfIy5R3V2bteUJhla/pmE7LmD85+4j6N3T5tQtpOz/c+oazrfv8HUb+9z8iLGPaStJlv3Nz8z6ur999553rB0LtWVWjs33+n3sETX/h77hcBfnEwOoQfly+e8aOvfW2Vmi5l2t06FSo4k8tNPBICHo/CM9vXdndpUZyGbD32VsabSpEfPmDfLZh/Xob61rvoVO738sRScswPY5dT65e8aSfkhQV3GKHXg/hueKvNdQ1qx+vrf/Dq1W9dX69/4Rd+rmm+Nzt5/tmzZ57u+sNQJ0R2nacnMPUbVxO8tZn/Gl9QlqvjfX6uvhZJrtPm9Of2G/f5Kz648BiTPXE+CHgcXpzl9d/W1rlFV6e343001Ft1ihk1/RWW3Wwdkr6ozzp6TIykxiTw9eZyeXUe3KWdVWNeuu64TruQjT6NO9s3fYd374S8PbpnZ4OHvf9aX716pZH4b97cfPedd/76xz42RPgnZuL9fvdYf5C7VGReuavb9efRTayI09PTFWdnpQv8LyeO1CCROpPm3z1dgJ48431M4eRPBidBwOPwvOtPbV9NuFO7Km7xZXJqQq1nN4ZXl4APkGeRPPrE1ptla71d/tDz4FTMZ2MTl8hXrh9kTOE73/nO1dWVSteFb93cdF/84ptXr/7Cixe/3TR/fjrdP/jgg+wqIf6QyovC1tbrey/CnVnb0r64jsyWusUFZdb611S+dtssSy0A6WZ3r3ls59mRgCMj4HF4amGvU8GQiGT1dWfzrtdW2NVvKU/rEd6+9dnyZ5X1Rmbtm936pbOYX510hvzBaWR9z5h/+fKleto95n/j9et/fX393abpv/a15++8MzX0Hn8Y2dWeB212pej95PEb13izCgPovqu0GXFrFWq13k9/FR7bWzO+t7GeqS6Ex1MuMcWTRcDj8No0AN9uzpNXc8r7VPv7CwIVLVHi6ny9pNm0lRrWWa4fpIWqJuDF9ckvocDY+dW9//772YD6EPNDug+N+F9rmtvPfOZv3/fSTw29t1Y5p2zHx49Qz40y3i8r+811mC5uf2sb3+lVd8VmxPFnnP3oKeokOGZLmtV6cAQ8DkwD8HF2i7aRzs6REz5lKU7EWrXVptVxo+fxHUQ+xRn/+CfcauyzrO758+dleL9omn//7NnvffWr35runL+9vdVFoee3/23o6WkAKPsDU0N8dOqGqg6rD8APK/9UsjWWW9+0Lm278NgDN8f5KbgsBDwOLPpCIwlWqfh8m8bXlRNx7uvT+ngFfzaRfs8kVpeAd/If4lU+UdmyuoVJPxref6Bp/kbT/MXpdP/ggw80TLOyyv9eEzcbu1GJBV/b5lM+R1u30YhXZ37ZV1/+zZQt/pl3LK454kc83p8fDXeUCHgcWGdLn9WCUds9btcU+qzvV52xmpe3zzPx6fcs+T0srxw8n/TDd6dDfNLV1dUq1T0M2XJ23Z7NlOytN95b/HHLVA+25t/1aTTHD4v2evn3s7BDSJ8Ctf53Xog4iqVumELA48DinKvTZZx9VKE28vtt2qV7tVkMp7XlyDu3dbyYCU32x5YlfRldH3300Q4BH8vl9ccTEesPu94sHuw19Xz6ui4FvA+gHFxXl1LEsKZ5Zj8ui/m3afe5MPMuqXehtymBD3ujp5HumELA45BUYra1eXZxCtbtK6soojvqBBrnyt3OWdnkfJrsxzQ1OK0p9Mt9/etfV+/L2rYwyJLbO+rj2qLd3E4wrgx0i/cBZPkdjX6VTFYee2xn6z7iRk0Fnc94TRHQfzWOsGc80zOPGQQ8DmmVttqMk12cRtUtr1VzcaSqe2rQXQc/KJtpsp+VbFl5NoV+q+H4aONm9en0+/X+85XVQojZf+3mhje6Mmg3Z8/16Q9PJRkicXWLJmZmSys1NUS36093vtspXpS+9mmnO7/VU0sDgEDA45BaG3fXZKjoPtV06Ldp565svbJ6Ypef8rzJzij7WdGvY3QK/ZTh4Lh7VuZIUb1KRY7VW1B226hPfm2VcMoZ8sG75XuLYd1SjpqvrdZ9b61z3T71nmSzCrKehu6Bq0Uedcoe6kDA42DUUo9z3CptMBPRHmdY9dUr6XsrQa9T8NqqkKrTXk0l75ulyX6eFJAPar7f3t5mj+PteP09aLy/TSWNPeNVDF9tcV0KTGV8n1bS9xacWcaXo++60fv22+mFnfrT1bC9nluXVpEsf4fpnMdWBDwORmcu7Q3jbZ2sQ7JLq+T7VOhGZ8bOJmarYRQnQcX86HwunJXhdxTbwDf3JWsGV1dXL168uL43/HdruvepSe3tXc94765X290vBXrrDNAijjLjNaKkXqU4wPvAs0vJrNpd/Fl6x3t23akhA789Ore6semBW9VUMxGPhIDHwah/XrPkNHlejZU4MuJci+XizKv+1agnqkn1NNAv15s3b2I+fOwu8+rVq5ubmwj42HVmiPnPN82nm+bdd9/N7qtgHi1xc5c2GvaVltlhHuTrtAOhRvT970qz6vQtj3w/zNvN2WwDiczWBJT5kSNfpl/m/RRG37EEAY/D0HlK9bfVourTXPo4Uq35Pi2NiwO0D023bWk1LsXMFPooWPvrV1dvP/Wpr37sY11qvk/tgTaa8VpypjZ9dli2Xk4jPvoRugLIeubjakDjTZLdMprxms+/TitFZ5rmGgjw/8Yf/0lK2aMmBDwOI+bP9ymqfYZda4vW1LhfpSJ3cbb1YXiivRpbp9D/fNP875/4iX/ZNP/0ww81b27q0coZamqUxwHrYn85v0rwcfryMiJqM/jKjs7qLToVP9Ytq2JLnrXVOasQsgAAIABJREFUBohbVAGwDHtd+0qXykWwxh37IOBxAJoupxNiZ0VG46zqtbK1U7iPvsd3SfeabJ1C//Gm+bvvvvvPXr6McZn5eRXZ1Hoft/bIXG1uQtim1Wte/y6Oj6tP/VnG4/vBqusw+kyU/Wr0K859B4QypBX2esJTj88nAvsg4HEAOsPepf2227R9e5emDa9sK1XNpde5WFPnTvgqcHDbZs2PDL0v0Y7JGutZUz5u93lwcbDW3Pt0Oc2N74qad867630IQAeUc0ud9mXQTyyVk/WA5Qh4HED0q6uFFB3yGoP3VlS4S5uCKN1HGzq4dPPprlXvO/Bc93a5IjkrdRfNce86ygbdtfSjt33n4iJ1JmK9Gp1fK2QHtGNT92VmrN2n9D8ePW2G/CtDwGNfWr8bZ0OdrVabRUP9Lq0VrG3ve+9HO0Jx0bZWoR9dF7eQ173J2vFtqoToffKKWP0bgwI+6B79Tz70rr73+SejKfrR6B+ddhfXAVPXCtEHNjoXb2aC3sGx9K4yBDz25ac2PxvqxJqd1zTwqeync75K8wH/8uXLPR9foz/ZwPza9jXIxuNVp0FT89T+1gpPbSev7G8XTPxUTca4aBjdZ7Ycqhe/JTtgtbm13aMi4CtDwGNfmg8fJ1bfl7NNJeizE1YkepxzfRY0ajIzhX63ofeS8tK3BlYrXJVtsnZ8V5Suiz9aTW1TU159UUv+RH1PhJgwuC7K3Ppz9hv9v7qjpgIcrX+LT2JlCHjspdvcz2NlO3DE+bTfrBayTqVLlO7ME67VzBT6Q3XYaKDdIznojyqbC9LZtggRtNkm8T73TQ9VDjPNPKW1baq0LorqjLbjRx9cz3BJF8JB0IKvDAGPvXgLKfo/teOWAr5PrXytdPf4P1rrBEf2GEPvoyICo0NeXUee8eXiOt/UQHf0x9SQk993+XWJVtJ7zPt3fSZ/P7un+9byAAdEC74yBDx2p1NknB+16tfPiXFkm1YKKeA13kmjoVaPNPQ+am1la301h5eqbWeV2aamvML+Qb1NSvEubY2TTZeLJxy3ZPGvFfmrtOVSe5SyzaxkqQwBj92pLa5F8G2awOwBr4r0nv0aB2WP1yqNzrA71ND7KHUmRU9SmfFlAZzOtqXRn67T6nYd2T1kU1dtMK/Cdlm9h2jEa0XAyjaXi4DXbkw+yf8w79cYWvCVIeCxI58MH7eoQ3Jl+1736fQUjXUNT6rhwqZwVRoN+IN3zmfaVF7JJ7t1Vm/OR4ju0h7E6oIajTf1TrVWu2m9eDNDZXz81/fB8zp3803neA6t7cP0sPdlGbrT6kPAY0dxZsxq0g2ns5g3pzXxvZ12NT6qgG8ZgK9UOYX+sdO9t9pzbZpDpxH3OEC996rrootOrZ0bXdumpnz8ebebhfPmZcVqfJKdev7b2Ul8+kxpnOsx5txlq11QAQIeu9CqJK0bjgjXmjf/rke7zo8MwNctm0L/qJ3zono15RC7/tK8oz7yVUPswx/naOm6aG2rl17z5Jfv9lauBY2GuHrd1Tcw+onwLR7Uab/TO7TlSTIGXxkCHg+mQiI+rNinOXfa5b2chBzfUgOIs0nFPOD3KUm7Aw2ueyO+3Sxvp9s1dU7hPZrcHvBqjnepls6Shq96rUTr3aPpHL1ZcbVRxrzG8lXm+TEmr3DBXRkCHg+jqUBqJymnW1utq7OqAt4fRN899rPHsRy5c95FiZs27YmQzevs057Fnv2ar67JIuVGsV74Vt/qrCrO1q3wRrvWsyq58cjZdnN9al57b/9jNOIJ+MoQ8FhKZ6I4A/o0Oq36jSO1ZsmbSv5Q2ZUBKuMz7Iavj/8E9Lcacej1cPrU4+3F79q0M2ybJt95c1lWtj2SHsrLP2x9VlOprHTXgFe/OStQcwD13YPPqGcMvj4EPBaJs2H0CsaJQPPmNDHeA161wEYHNbvpPTRRAQX8cYbeR2nVRpe2jfFxdwW536ID1CLP2txeLC+rz6jegvm/6vKiQbJLhPjsqFdAQwnrtLFNf+hl6wR8fQh4bBetB1/q06dWeJx3sj7DOLH6LiDee1mWwUFlYgr9kYfeM+rNVvUbtdHXqTyt9zDp77m1yXfZ5Lj4r7I2HllD+50Vvp1JyvnvxjqUGDLwXjFdrKhN36cP5oHeMJbJVYiAxxblhKNV2l2m3SyRrfZEl7bs1HQ8v7tPs6fFUKWYYXfkofdSdHerme5bs0cSt1blxlvzK6tC723uSHGle2/V7uIANf1nUnzqu5pzF7P2tHW9LqM1lBDPPB7hgKWitk4jwMUh4DEpWj9lN2DWjBCda/QtnZU02V5V7TTeeaxXg+MZAv6RStLuRjPnlccR2/H3qda8xtc7W9KpIfl4KFV28ht9gZlK0s7MvItPViS0cn3mmkA9/96g16Xz/h31y9f74bIQ8BgX58TRdoZ3afq3NIanWUg6TKc5FRjRyfQYLwbHdcKh9yla7K6FcF6OyXec09+nZq1n80viz74Mdf0sb4vr35iLtzZxY7dZF2/mmiB+dHxXdSSXr9ObsvzufFovDgGPce3YDpU+crmyIrXBB9d10uw217trnC87b6IaJ5k2v4QXV+5STTqlflkAp00L7VS0sU+zTeMBs5Z99nnxmfzatEbprnUoWrOncjpT/eS+VkXrArzC3c7vycJOfgL+4hDwyMVMojLd40zUp0IiZcBr/LK1TeSyZrp3468frao2MEorPlora6O8964p5a5Pj1cVOX06NMluqgycZqFuHeHWRcbMYT5r1R85WzS/XPkpnj94hx+BEyLgsSFOc2W6a/VtPx3wapG0qSaXd4HGMV7Ze3SAH3hU6819Y7vNknZZxusPVevTFPwRwxpNH13jvko7ysSFwtYZJ/Oz83pbgKoHX6UikqNVdOZF8335PBj62y4OAY//byrd1XbXf9s0F0k3rlK9T5+FpJOpn7PUz+8XDcBxqHO77I3vNpfMtWkL9mziiO64vt/OVamcRWw2SB+fha0ZHB8rfV5idZ/+q2EFDeerU60vAlgdFT78r9eijXmWXxYQ8BeHgMcPTaV7v9k1p3Z5Fs9aHK81PIr2slHiq5Ue6eUAUzQ7pAzsMuB9C0Tv0vfLXF3LeqKXne2jn4VM/ERf3XeXxAHqkI8nps9jf/8Z9D115n+Qkn75m8bl+MUh4J86jSBOpXs2dqjZc342CVqY66fOfmKbjbaYfwccR7YSRH+u0cbNbmxtT+Tedp3RNUE0sn21fT+9o+udbaM8avSO3v/vhXR0/aGZd9qKZskn60Fr6En3S0TAP2magjt1IV9etndpDXF0+mWP1qepdnEGjPvG6S975NY684EjG23ExzWuMl6ZHT3hGnTXZNKsi1t17rIhLadV8lNN+akrA39AXTr3VpQi/qt+hSVvwtZ5f9nBC4/E+SDgn7StV+Xl6aaz3S1HA17nTTXQy75KnV45a+AkNHCeBXxnZRazKwDvJPdV9R6Tmoqv2fWluN7VWvnsMzjVqlaRiT5dl7dppkt8mvqxPejmPahRTgv+EhHwT9rWIfDyZNHaGvcy4GMSkFb7qBBH9iDqxifgcSrxZ7y2nQ8V5GoW60pUDffeMjVa/BH2ynj9zU81030Pm+hU18XucONUwPu91mmrJ11qd6nOndfIm9cumPGXvV3LD8aZIOCftK35Otq13qWSn9l5JE6I2mOmtyGA8ufGCfShC3uAQ1HjO/J4ZWWVPdqV9NEDv0rubJvEsmRTRK8308up7Hp8Vb/p0uqS+SccQwZ6Mm1ayKfnsPVzXX54tyLgLxEB/3QtmRY7GvAe3tm37tJu8RpoLAfaVeKbAXicVvy5qnit99Wrlexd99F21x5u3gVVziT1TvXvJ8ryco5qb7VuWpufX06C8R8dh8XQgI6cnz2XbZG3/L166F1wcgT807VkDu1oF32ctsoR9Eh0n0ak6Uh+mG+TdYCXAexhlbaWyQbdO6tzp954LW33e7295w36EE3tqYZyfEzKHiy17+/SZvD6vNylGs8qv6PVKPHT/eM8E+E7lMTpCfjLRMA/UVOVNTNlBrdpxlw5gq6eeZ3p2rG1cDH/iAF4nIlY5+arPzrbTU4Br2iP4jYahtdY+9oq1kWCxph68I563aX8DGZ9+57ZWvIeHzSV1tfT9tieGv+ameE/j4C/RAT8UxQdektWyJQR7pU0PP69kaHGhM6Afp7SWYmAx/koN5TLZtSr316Ncj/MH0fj4sr7Mh1VSC7rRfPH1+a2flhWM39tO8lm/RC67PD1fjuXluLTeokI+Kdo6uq+lF3se1R79Y/els/543dpJZKfVnx8cd9XAhyOr5rT9Wu7KTJbo1S99Vf1tlGsB+3ocrgQj+aX2l2xvm74bvQEROeBZgboGXrfQ/Y84+uDvDkE/CUi4DEnu+T3KwNVnte3NLan7gE1ZbIyHZqQfLQXAiyRrYz35m/kpTrJFd5t2oxuPVaJVhPlfEpK3OIL5JTxbbF5q6b7+U/s7cPVWWE7fQBVdaofu2jYAZ/WS0TAY062R5Z37GufyvivN+hbq+up1kbc4s2OQ7UtgEMpq9h6wKvXPXJ0ZdsptUVZiKBOr2jcl1PiFf+xpL614a0uLaLTI2h9Xb/ZcNeT72xqvd+yf/ubgL9EBDy20OlDBbNEDRF9kd1FI4g670RbRNOXjvg6gEVUyKFMenWPq8XcW0f9aCd81geWVaHRd8uO/alHa20ZS5um0OvBYyKef1S1e96es+QI+EtEwGOOx/ZowPfpRKNV9dF1HwdEI0PTfTVCXz4UcCamqthqbaeGnFSJ2e+VPVq2XMUL0mXf1Sy/VdrovXw0lYda2abM6n7X5zH7KSrms09dKQL+EhHwmNMW8+T9uzo9RcZr2a7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&lt;/script&gt;
&lt;p id=&#34;unnamed_chunk_15debug&#34;&gt;
You must enable Javascript to view this page properly.&lt;/p&gt;
&lt;script&gt;unnamed_chunk_15rgl.start();&lt;/script&gt;
&lt;p&gt;Finally we can construct a 2D coordinate system on the plane and project
the intersection positions onto that.&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r&#34;&gt;# find pair of orthogonal tangent vectors of plane
uv = Morpho::tangentPlane(mean_vec)
# centre our points on mean
sp=scale(intersections, scale = F, center=T)
DotProduct=function(a,b) sum(a*b)
# find coordinates w.r.t. to our two basis vectors
xy=data.frame(u=apply(sp, 1, DotProduct, uv[[1]]),
v=apply(sp, 1, DotProduct, uv[[2]]))
# maintain consist x-y aspect ratio
plot(xy, pch=19, asp=1, main = &amp;quot;Position of Axon intersection in plane&amp;quot;,
xlab=&amp;quot;u /µm&amp;quot;, ylab=&amp;quot;v /µm&amp;quot;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/articles/2019-09-nat/index_files/figure-html/unnamed-chunk-16-1.png&#34; width=&#34;480&#34; /&gt;&lt;/p&gt;</description></item><item><title>Hello R Markdown</title><link>https://natverse.github.io/post/2015-07-23-r-rmarkdown/</link><pubDate>Thu, 23 Jul 2015 21:13:14 -0500</pubDate><guid>https://natverse.github.io/post/2015-07-23-r-rmarkdown/</guid><description>
&lt;div id=&#34;r-markdown&#34; class=&#34;section level1&#34;&gt;
&lt;h1&gt;R Markdown&lt;/h1&gt;
&lt;p&gt;This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see &lt;a href=&#34;http://rmarkdown.rstudio.com&#34; class=&#34;uri&#34;&gt;http://rmarkdown.rstudio.com&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;You can embed an R code chunk like this:&lt;/p&gt;
&lt;pre class=&#34;r&#34;&gt;&lt;code&gt;summary(cars)
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
fit &amp;lt;- lm(dist ~ speed, data = cars)
fit
##
## Call:
## lm(formula = dist ~ speed, data = cars)
##
## Coefficients:
## (Intercept) speed
## -17.579 3.932&lt;/code&gt;&lt;/pre&gt;
&lt;/div&gt;
&lt;div id=&#34;including-plots&#34; class=&#34;section level1&#34;&gt;
&lt;h1&gt;Including Plots&lt;/h1&gt;
&lt;p&gt;You can also embed plots. See Figure &lt;a href=&#34;#fig:pie&#34;&gt;1&lt;/a&gt; for example:&lt;/p&gt;
&lt;pre class=&#34;r&#34;&gt;&lt;code&gt;par(mar = c(0, 1, 0, 1))
pie(
c(280, 60, 20),
c(&amp;#39;Sky&amp;#39;, &amp;#39;Sunny side of pyramid&amp;#39;, &amp;#39;Shady side of pyramid&amp;#39;),
col = c(&amp;#39;#0292D8&amp;#39;, &amp;#39;#F7EA39&amp;#39;, &amp;#39;#C4B632&amp;#39;),
init.angle = -50, border = NA
)&lt;/code&gt;&lt;/pre&gt;
&lt;div class=&#34;figure&#34;&gt;&lt;span id=&#34;fig:pie&#34;&gt;&lt;/span&gt;
&lt;img src=&#34;https://natverse.github.io/post/2015-07-23-r-rmarkdown_files/figure-html/pie-1.png&#34; alt=&#34;A fancy pie chart.&#34; width=&#34;672&#34; /&gt;
&lt;p class=&#34;caption&#34;&gt;
Figure 1: A fancy pie chart.
&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;</description></item><item><title>Architecture</title><link>https://natverse.github.io/gallery/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/gallery/</guid><description>
&lt;p&gt;Note that you can find example code to generate many of the figures below at &lt;a href=&#34;https://github.com/natverse/nat.examples&#34; target=&#34;_blank&#34;&gt;https://github.com/natverse/nat.examples&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;
&lt;link rel=&#34;stylesheet&#34; href=&#34;https://natverse.github.io/css/hugo-easy-gallery.css&#34; /&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/architecture/01_arch_natverse-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/architecture/01_arch_natverse-thumb.png&#34; alt=&#34;01_arch_natverse&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;01_arch_natverse&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/architecture/01_arch_natverse.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/architecture/02_arch_datatypes-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/architecture/02_arch_datatypes-thumb.png&#34; alt=&#34;02_arch_datatypes&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;02_arch_datatypes&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/architecture/02_arch_datatypes.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
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&lt;div class=&#34;pswp__share-modal pswp__share-modal--hidden pswp__single-tap&#34;&gt;
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&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;visualization&#34;&gt;Visualization&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/visualisation/Visualise%20neurons-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/visualisation/Visualise%20neurons-thumb.png&#34; alt=&#34;Visualise neurons&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;Visualise neurons&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/visualisation/Visualise%20neurons.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;registrations&#34;&gt;Registrations&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/registrations/01_Template%20brains%20and%20bridges-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/registrations/01_Template%20brains%20and%20bridges-thumb.png&#34; alt=&#34;01_Template brains and bridges&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;01_Template brains and bridges&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/registrations/01_Template%20brains%20and%20bridges.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/registrations/02_Bridging%20map-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/registrations/02_Bridging%20map-thumb.png&#34; alt=&#34;02_Bridging map&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;02_Bridging map&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/registrations/02_Bridging%20map.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/registrations/06_Registration%20with%203D%20models-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/registrations/06_Registration%20with%203D%20models-thumb.png&#34; alt=&#34;06_Registration with 3D models&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;06_Registration with 3D models&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/registrations/06_Registration%20with%203D%20models.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;nblast-examples&#34;&gt;NBLAST examples&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/nblast/00_Mirroring%20comparison-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/nblast/00_Mirroring%20comparison-thumb.png&#34; alt=&#34;00_Mirroring comparison&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;00_Mirroring comparison&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/nblast/00_Mirroring%20comparison.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/nblast/01_NBLAST%20fly%20example-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/nblast/01_NBLAST%20fly%20example-thumb.png&#34; alt=&#34;01_NBLAST fly example&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;01_NBLAST fly example&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/nblast/01_NBLAST%20fly%20example.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/nblast/02_NBLAST%20fish%20example-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/nblast/02_NBLAST%20fish%20example-thumb.png&#34; alt=&#34;02_NBLAST fish example&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;02_NBLAST fish example&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/nblast/02_NBLAST%20fish%20example.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/nblast/03_NBLAST%20mouse%20example-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/nblast/03_NBLAST%20mouse%20example-thumb.png&#34; alt=&#34;03_NBLAST mouse example&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;03_NBLAST mouse example&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/nblast/03_NBLAST%20mouse%20example.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;bridging-between-datasets&#34;&gt;Bridging between datasets&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/bridging/03_Bridge%20image%20data-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/bridging/03_Bridge%20image%20data-thumb.png&#34; alt=&#34;03_Bridge image data&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;03_Bridge image data&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/bridging/03_Bridge%20image%20data.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/bridging/04_Bridge%20skeletons-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/bridging/04_Bridge%20skeletons-thumb.png&#34; alt=&#34;04_Bridge skeletons&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;04_Bridge skeletons&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/bridging/04_Bridge%20skeletons.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/bridging/08_Match%20neurons%20across%20datasets-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/bridging/08_Match%20neurons%20across%20datasets-thumb.png&#34; alt=&#34;08_Match neurons across datasets&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;08_Match neurons across datasets&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/bridging/08_Match%20neurons%20across%20datasets.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;volumes&#34;&gt;Volumes&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/volumes/01_Autosegmentation-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/volumes/01_Autosegmentation-thumb.png&#34; alt=&#34;01_Autosegmentation&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;01_Autosegmentation&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/volumes/01_Autosegmentation.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/volumes/02_Sub-volume%20connectivity-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/volumes/02_Sub-volume%20connectivity-thumb.png&#34; alt=&#34;02_Sub-volume connectivity&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;02_Sub-volume connectivity&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/volumes/02_Sub-volume%20connectivity.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/volumes/03_Compare%20insect%20brains-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/volumes/03_Compare%20insect%20brains-thumb.png&#34; alt=&#34;03_Compare insect brains&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;03_Compare insect brains&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/volumes/03_Compare%20insect%20brains.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;neuroanatomy&#34;&gt;Neuroanatomy&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neuroanatomy/01_Measure%20neuroanatomy-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neuroanatomy/01_Measure%20neuroanatomy-thumb.png&#34; alt=&#34;01_Measure neuroanatomy&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;01_Measure neuroanatomy&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neuroanatomy/01_Measure%20neuroanatomy.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neuroanatomy/03_Manually%20sort%20neurons-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neuroanatomy/03_Manually%20sort%20neurons-thumb.png&#34; alt=&#34;03_Manually sort neurons&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;03_Manually sort neurons&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neuroanatomy/03_Manually%20sort%20neurons.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neuroanatomy/04_Prune%20neurons-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neuroanatomy/04_Prune%20neurons-thumb.png&#34; alt=&#34;04_Prune neurons&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;04_Prune neurons&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neuroanatomy/04_Prune%20neurons.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;neurogeometry&#34;&gt;Neurogeometry&lt;/h2&gt;
&lt;p&gt;
&lt;div class=&#34;gallery caption-position-bottom caption-effect-slide hover-effect-zoom hover-transition&#34; itemscope itemtype=&#34;http://schema.org/ImageGallery&#34;&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neurogeometry/02_Neurogeometry-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neurogeometry/02_Neurogeometry-thumb.png&#34; alt=&#34;02_Neurogeometry&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;02_Neurogeometry&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neurogeometry/02_Neurogeometry.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neurogeometry/05_Find%20EM%20neuron-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neurogeometry/05_Find%20EM%20neuron-thumb.png&#34; alt=&#34;05_Find EM neuron&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;05_Find EM neuron&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neurogeometry/05_Find%20EM%20neuron.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neurogeometry/06_Find%20genetic%20lines-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neurogeometry/06_Find%20genetic%20lines-thumb.png&#34; alt=&#34;06_Find genetic lines&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;06_Find genetic lines&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neurogeometry/06_Find%20genetic%20lines.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;div class=&#34;box&#34;&gt;
&lt;figure itemprop=&#34;associatedMedia&#34; itemscope itemtype=&#34;http://schema.org/ImageObject&#34;&gt;
&lt;div class=&#34;img&#34; style=&#34;background-image: url(&#39;https://natverse.github.io/images/gallery/neurogeometry/07_Discover%20neurons-thumb.png&#39;);&#34; &gt;
&lt;img itemprop=&#34;thumbnail&#34; src=&#34;https://natverse.github.io/images/gallery/neurogeometry/07_Discover%20neurons-thumb.png&#34; alt=&#34;07_Discover neurons&#34; /&gt;
&lt;/div&gt;
&lt;figcaption&gt;
&lt;p&gt;07_Discover neurons&lt;/p&gt;
&lt;/figcaption&gt;
&lt;a href=&#34;https://natverse.github.io/images/gallery/neurogeometry/07_Discover%20neurons.png&#34; itemprop=&#34;contentUrl&#34;&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;/p&gt;</description></item><item><title>Contribute to the natverse</title><link>https://natverse.github.io/contribute/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/contribute/</guid><description>
&lt;p&gt;We want the natverse to expand. No matter your current skills it&amp;rsquo;s possible to contribute to the natverse by adding your own code, reporting bugs, requesting features and giving us your feedback. We are all ears, and we are keen to make the natverse easier to use as well as expanding its capabilities, and improving interaction with other toolkits / languages.&lt;/p&gt;
&lt;h2 id=&#34;show&#34;&gt;Show and tell&lt;/h2&gt;
&lt;p&gt;Get in touch and let us know if these tools have been useful, and what you have used them for! We are always super interested to see our tools used by others. If you use &lt;a href=&#34;https://twitter.com&#34; target=&#34;_blank&#34;&gt;twitter&lt;/a&gt;, you can mention &lt;a href=&#34;https://twitter.com/gsxej&#34; target=&#34;_blank&#34;&gt;@gsxej&lt;/a&gt; and &lt;a href=&#34;https://twitter.com/as_bates&#34; target=&#34;_blank&#34;&gt;@as_bates&lt;/a&gt; in a tweet. Alternatively,
you can write the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user&lt;/a&gt; group with your use case.&lt;/p&gt;
&lt;p&gt;If you have some nice code, it would be great if you could make a pull request for the appropriate package. You could add an example to
the documentation for a function or make a short &lt;a href=&#34;http://r-pkgs.had.co.nz/vignettes.html&#34; target=&#34;_blank&#34;&gt;vignette&lt;/a&gt; in &lt;a href=&#34;https://rmarkdown.rstudio.com/&#34; target=&#34;_blank&#34;&gt;R Markdown&lt;/a&gt;. We can even add you example to the
natverse &lt;a href=&#34;https://natverse.github.io/gallery/&#34;&gt;Gallery&lt;/a&gt; help inspire others.&lt;/p&gt;
&lt;h2 id=&#34;cite&#34;&gt;Cite our papers&lt;/h2&gt;
&lt;p&gt;Citing appropriate papers is a key way to support the natverse. As usual
citations are the general currency of academic credit and the best way to
justify ongoing support of the natverse. Don&amp;rsquo;t worry though, natverse
development is currently well supported by core funding from the Medical Research Council as well as grant support from ERC and the Wellcome Trust.&lt;/p&gt;
&lt;p&gt;You can extract a generic citation for the natverse or specific citation info
for any of the packages like so:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;citation(&#39;natverse&#39;)
citation(&#39;flycircuit&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;If unsure, please contact the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user&lt;/a&gt; group.&lt;/p&gt;
&lt;h2 id=&#34;answers&#34;&gt;Answer community questions&lt;/h2&gt;
&lt;p&gt;The simplest way to help out is to answer questions posed by our user community. We are trying to this, but you might get there first, and it would be great if you could pay forward any help received! We have an active &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user&lt;/a&gt; Google group.&lt;/p&gt;
&lt;h2 id=&#34;issues&#34;&gt;File issues&lt;/h2&gt;
&lt;p&gt;If you think you&amp;rsquo;ve found a bug, first create a minimal, &lt;a href=&#34;https://stackoverflow.com/help/minimal-reproducible-example&#34; target=&#34;_blank&#34;&gt;reproducible example&lt;/a&gt;
Then file it on the GitHub repo of the appropriate package or add to the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user&lt;/a&gt; Google forum. For example, for nat, you could create an issue &lt;a href=&#34;https://github.com/natverse/nat/issues&#34; target=&#34;_blank&#34;&gt;here&lt;/a&gt;. See the &lt;a href=&#34;https://natverse.github.io/help/&#34;&gt;help&lt;/a&gt; page for more details.&lt;/p&gt;
&lt;h2 id=&#34;docs&#34;&gt;Contribute documentation&lt;/h2&gt;
&lt;p&gt;Anyone with a GitHub account can help improve our documentation.
We have worked hard to ensure that all the functions in our packages have
up to date documentation; many also have examples and there are also
a number of longer form articles/vignettes. However, if you see a typo, bug, missing cross-reference, opportunity to add an example, or anything else that could be improved in this documentation, then we would be delighted if you make a suggestion.&lt;/p&gt;
&lt;p&gt;Each page in the online documentation includes a
link at the top of the form &lt;code&gt;Source: R/neuron-io.R&lt;/code&gt;. Clicking on this takes you to GitHub where you can then edit the source code. If you do this, you
will automatically make a &lt;a href=&#34;https://help.github.com/en/articles/about-pull-requests&#34; target=&#34;_blank&#34;&gt;pull request&lt;/a&gt;
that will invite us to incorporate your edits.&lt;/p&gt;
&lt;h2 id=&#34;bugs&#34;&gt;Contribute code to an existing package&lt;/h2&gt;
&lt;p&gt;If you are a middling-to-experienced programmer, you might want to pitch in with R package development. Before you do a pull request, best practice would be to file an issue and make sure someone from our team agrees that it&amp;rsquo;s a problem and you have a good solution. When it comes to how you should write your code, a great place to look is the &lt;a href=&#34;http://style.tidyverse.org/&#34; target=&#34;_blank&#34;&gt;tidyverse style guide&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;new&#34;&gt;Contribute new packages and libraries to the natverse&lt;/h2&gt;
&lt;p&gt;If you are an experienced programmer, you might want to contribute your own R packages, or a library in a different programming language to the natverse project! Good ideas include:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;talking to new, remote data repositories we have missed&lt;/li&gt;
&lt;li&gt;adding a new analysis capability to the natverse&lt;/li&gt;
&lt;li&gt;linking natverse functionality to other programming language
&lt;ul&gt;
&lt;li&gt;for example by using &lt;a href=&#34;https://www.mathworks.com/matlabcentral/fileexchange/5051-matlab-r-link&#34; target=&#34;_blank&#34;&gt;MATLAB R-Link&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;&lt;/li&gt;
&lt;li&gt;improving integration of the natverse with other analysis suites e.g.
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://www.treestoolbox.org/&#34; target=&#34;_blank&#34;&gt;TREES toolbox&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;Philipp Schlegel&amp;rsquo;s Python 3 library &lt;a href=&#34;https://github.com/schlegelp/navis&#34; target=&#34;_blank&#34;&gt;NAVis&lt;/a&gt; is a great example of expanding the natverse mentality into another programming language.&lt;/li&gt;
&lt;/ul&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;The easiest way to contribute large amounts of code to the natverse is as an &lt;a href=&#34;http://r-pkgs.had.co.nz/&#34; target=&#34;_blank&#34;&gt;R package&lt;/a&gt;. R packages are discrete bundles of code. It is preferable to develop logically related sets of functions as separate packages because this simplifies development, ease troubleshooting and divides the natverse into units within which users can search for the more specific code examples or functions that they want.&lt;/p&gt;
&lt;p&gt;If you would like to contribute a large amount of new code to the project, get in touch with &lt;a href=&#34;https://www2.mrc-lmb.cam.ac.uk/group-leaders/h-to-m/gregory-jefferis/&#34; target=&#34;_blank&#34;&gt;Gregory Jefferis&lt;/a&gt;.&lt;/p&gt;</description></item><item><title>Get help!</title><link>https://natverse.github.io/help/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/help/</guid><description>
&lt;p&gt;Thanks for using the natverse. We&amp;rsquo;re sorry you&amp;rsquo;re having trouble, but
we&amp;rsquo;re here to help! To get help as quickly as possible, please read the following.&lt;/p&gt;
&lt;h2 id=&#34;search&#34;&gt;Search&lt;/h2&gt;
&lt;p&gt;The first thing is to see if anyone has had your problem before:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Search our &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;.&lt;/li&gt;
&lt;li&gt;Search GitHub for &lt;a href=&#34;https://github.com/search?q=user%3Anatverse&amp;amp;type=Issues&#34; target=&#34;_blank&#34;&gt;issues across the whole natverse&lt;/a&gt;.
You can add your own terms to the search in the search box in the top left of that page.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;If that solves your problem, then great!&lt;/p&gt;
&lt;h2 id=&#34;known-problems&#34;&gt;Known Problems&lt;/h2&gt;
&lt;p&gt;If you need more help with a known problem:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;If you found a relevant thread on the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;:
please reply to that.&lt;/li&gt;
&lt;li&gt;If you found a GitHub issue:
please reply to that with more details (you&amp;rsquo;ll need a GitHub login) or just &lt;em&gt;like&lt;/em&gt; it to let us know you&amp;rsquo;re having trouble too.&lt;/li&gt;
&lt;li&gt;If you&amp;rsquo;re not sure:
ask a new question on the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;
linking to what you have found.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;new-problems&#34;&gt;New Problems&lt;/h2&gt;
&lt;p&gt;If it looks like a new problem then:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;If you just have a question:
please ask the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;.&lt;/li&gt;
&lt;li&gt;If you need to report a &lt;em&gt;new&lt;/em&gt; bug:
please file a GitHub issue for the relevant package.&lt;/li&gt;
&lt;li&gt;If you&amp;rsquo;re not sure:
please just ask the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;! If your
problem &lt;em&gt;is&lt;/em&gt; a bug or a feature request, you can easily return here and
report it - and we may be able to point you to an existing report or workaround.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;good-questions-and-bug-reports&#34;&gt;Good Questions and Bug Reports&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Be specific&lt;/li&gt;
&lt;li&gt;Include the code that triggered the problem&lt;/li&gt;
&lt;li&gt;If at all possible, make a minimal &lt;strong&gt;repr&lt;/strong&gt;oducible &lt;strong&gt;ex&lt;/strong&gt;ample (a &lt;em&gt;reprex&lt;/em&gt;)&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;It will be much easier for us to help if we can run a &lt;em&gt;reprex&lt;/em&gt; on
our own machine without your data. You might want to use sample data
from a nat package to help, or refer to publicly available data online.&lt;/p&gt;
&lt;p&gt;You can use the &lt;a href=&#34;https://reprex.tidyverse.org/&#34; target=&#34;_blank&#34;&gt;reprex&lt;/a&gt; package to help
and read the &lt;a href=&#34;https://www.tidyverse.org/help/&#34; target=&#34;_blank&#34;&gt;Get help!&lt;/a&gt;
section of the tidyverse site for more information on this.&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Thanks for your help!&lt;/em&gt;&lt;/p&gt;
&lt;h2 id=&#34;general-r-questions&#34;&gt;General R questions&lt;/h2&gt;
&lt;p&gt;You may find that your question is more of a general R issue than a natverse
issue. We&amp;rsquo;ll always try to help, but you may also want to check out other sources of support:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;p&gt;&lt;a href=&#34;https://www.r-project.org/help.html&#34; target=&#34;_blank&#34;&gt;&lt;strong&gt;r-help&lt;/strong&gt;&lt;/a&gt;: The core R project&amp;rsquo;s information about
finding help. The mailing lists have a reputation for being a bit brusque but if you ask
a good question you can get a response very quickly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;a href=&#34;http://community.rstudio.com&#34; target=&#34;_blank&#34;&gt;&lt;strong&gt;community.rstudio.com&lt;/strong&gt;&lt;/a&gt;: This is a friendly
place to ask general questions albeit with a focus on the &lt;a href=&#34;https://www.tidyverse.org&#34; target=&#34;_blank&#34;&gt;tidyverse&lt;/a&gt;
and other packages written by the rstudio team.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;a href=&#34;https://stackoverflow.com&#34; target=&#34;_blank&#34;&gt;&lt;strong&gt;Stack Overflow&lt;/strong&gt;&lt;/a&gt;. Google will often bring you here. It can
be a good place to ask questions about specific code issues.&lt;/p&gt;&lt;/li&gt;
&lt;/ul&gt;</description></item><item><title>Getting started</title><link>https://natverse.github.io/home/band_two/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/home/band_two/</guid><description>&lt;p&gt;To get started, take a look at our &lt;a href=&#34;gallery/&#34; target=&#34;_blank&#34;&gt;Gallery&lt;/a&gt; or the &lt;a href=&#34;https://elifesciences.org/articles/53350&#34; target=&#34;_blank&#34;&gt;natverse paper&lt;/a&gt;.
Explore our resources for &lt;a href=&#34;learn/&#34; target=&#34;_blank&#34;&gt;learning the natverse&lt;/a&gt; and &lt;a href=&#34;help/&#34; target=&#34;_blank&#34;&gt;get help&lt;/a&gt; if you have a problem. We also have a friendly &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;user forum&lt;/a&gt; that you can use to request input from developers and other users.&lt;/p&gt;</description></item><item><title>Getting started</title><link>https://natverse.github.io/install/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/install/</guid><description>
&lt;h2 id=&#34;installation&#34;&gt;Installation&lt;/h2&gt;
&lt;p&gt;The natverse runs on top of R. If you have never installed R see the First time
install and Step by Step illustrated guide at the bottom of this page.&lt;/p&gt;
&lt;h3 id=&#34;basic-install&#34;&gt;Basic Install&lt;/h3&gt;
&lt;p&gt;Install core natverse packages to get started by doing&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;install.packages(&amp;quot;natmanager&amp;quot;)
natmanager::install(&#39;core&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;h3 id=&#34;full-install&#34;&gt;Full Install&lt;/h3&gt;
&lt;p&gt;Install all the packages in the natverse by running:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;install.packages(&amp;quot;natmanager&amp;quot;)
natmanager::install(&#39;natverse&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You may need to make a GitHub account and personal access token
(GITHUB_PAT) if you have not done this previously. See the &lt;a href=&#34;#github-rate-limiting&#34;&gt;GitHub Rate limiting&lt;/a&gt; and &lt;a href=&#34;#step-by-step-installation-guide&#34;&gt;Step by Step Installation Guide&lt;/a&gt; sections below.&lt;/p&gt;
&lt;h2 id=&#34;run&#34;&gt;Run&lt;/h2&gt;
&lt;p&gt;To load the core natverse and make it available in your current R session:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;library(natverse)
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;You can check everything is working with some simple plots:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;# plot some test data (?kcs20 for details)
# Drosophila Kenyon cells processed from raw data at http://flycircuit.tw
head(kcs20)
open3d()
plot3d(kcs20, col=type)
# get help
?nat
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;To find our more, explore our resources for &lt;a href=&#34;../learn&#34;&gt;learning the natverse&lt;/a&gt;.&lt;/p&gt;
&lt;h2 id=&#34;update&#34;&gt;Update&lt;/h2&gt;
&lt;p&gt;To update all natverse packages (and their dependencies):&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;library(natverse)
# see what needs updating
natverse_update()
# actually update
natverse_update(update = TRUE)
# ... or if you don&#39;t want to answer any yes/no questions
natverse_update(update = TRUE, upgrade=&#39;always&#39;)
&lt;/code&gt;&lt;/pre&gt;
&lt;h2 id=&#34;troubleshooting&#34;&gt;Troubleshooting&lt;/h2&gt;
&lt;h3 id=&#34;github-rate-limiting&#34;&gt;GitHub Rate limiting&lt;/h3&gt;
&lt;p&gt;Unfortunately installing the full natverse suite makes many calls to the GitHub
API, which is rate limited unless you have a GitHub account and present a
&lt;code&gt;GITHUB_PAT&lt;/code&gt; authentication token. The &lt;code&gt;natmanager&lt;/code&gt; package will attempt to
use a built-in PAT if you do not have one. However, if multiple users are
installing the natverse simultaneously, you may get errors like&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;Using github PAT from envvar GITHUB_PAT
Error: Failed to install &#39;unknown package&#39; from GitHub:
HTTP error 401.
Bad credentials
Rate limit remaining: 56/60
Rate limit reset at: 2020-02-27 19:21:26 UTC
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;To avoid these errors, do&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;natmanager::check_pat()
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;and this will guide you through the process of obtaining your own &lt;code&gt;GITHUB_PAT&lt;/code&gt;
and telling R about it. See also the illustrated guide below.&lt;/p&gt;
&lt;h3 id=&#34;other-install-issues&#34;&gt;Other install issues&lt;/h3&gt;
&lt;p&gt;If you have any installation issues, some general tips:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Start a clean R session&lt;/li&gt;
&lt;li&gt;Start a clean R session if you had to update natmanager&lt;/li&gt;
&lt;li&gt;make sure that you have recent R (&amp;gt;=3.6.0 recommended, R&amp;gt;=3.3.0 at a minimum)&lt;/li&gt;
&lt;li&gt;try updating installed packages (&lt;code&gt;update.packages(ask=F)&lt;/code&gt; will update everything)&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Still no luck?&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;most install issues will be general R issues rather than anything
specific to the natverse, so Google is your friend.&lt;/li&gt;
&lt;li&gt;Search the &lt;a href=&#34;https://groups.google.com/forum/#!forum/nat-user&#34; target=&#34;_blank&#34;&gt;nat-user google group&lt;/a&gt;.&lt;/li&gt;
&lt;li&gt;&amp;hellip; or use it to ask for help.&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id=&#34;first-time-install-prerequisites&#34;&gt;First time install - Prerequisites&lt;/h2&gt;
&lt;p&gt;To install this package you need to have &lt;code&gt;R&lt;/code&gt; and &lt;code&gt;RStudio&lt;/code&gt; installed. Detailed
instructions for each operating system are given below. You will also need a
valid GitHub account to install the full suite of natverse packages. You will be
prompted to do this by the natmanager package, but we recommend following the
illustrated &lt;a href=&#34;#step-by-step-installation-guide&#34;&gt;Step by Step Installation Guide&lt;/a&gt;.&lt;/p&gt;
&lt;h3 id=&#34;mac-os-x&#34;&gt;Mac OS X&lt;/h3&gt;
&lt;ol&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;R&lt;/code&gt; from here:
&lt;a href=&#34;http://cloud.r-project.org/bin/macosx/&#34; target=&#34;_blank&#34;&gt;r-installation&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;RStudio&lt;/code&gt;, from here:
&lt;a href=&#34;https://rstudio.com/products/rstudio/download/#download&#34; target=&#34;_blank&#34;&gt;RStudio-installation&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Start &lt;code&gt;RStudio&lt;/code&gt; from Launchpad&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;To use the rgl package for 3D visualisation you may also need to install
the &lt;a href=&#34;https://www.xquartz.org/&#34; target=&#34;_blank&#34;&gt;Xquartz X11 system&lt;/a&gt;, which is also available by
following links from the &lt;a href=&#34;https://cloud.r-project.org/bin/macosx/&#34; target=&#34;_blank&#34;&gt;CRAN Mac OS X page&lt;/a&gt;.&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;h3 id=&#34;windows&#34;&gt;Windows&lt;/h3&gt;
&lt;ol&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;R&lt;/code&gt; from here:
&lt;a href=&#34;http://cloud.r-project.org/bin/windows/base/&#34; target=&#34;_blank&#34;&gt;r-installation&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;RStudio&lt;/code&gt;, for Windows from here:
&lt;a href=&#34;https://rstudio.com/products/rstudio/download/#download&#34; target=&#34;_blank&#34;&gt;RStudio-installation&lt;/a&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Start &lt;code&gt;RStudio&lt;/code&gt; from Programs menu&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;h3 id=&#34;linux-ubuntu&#34;&gt;Linux (Ubuntu)&lt;/h3&gt;
&lt;ol&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;R&lt;/code&gt;, in terminal type below:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r,&#34;&gt;sudo apt-get install libopenblas-base r-base
&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Install &lt;code&gt;RStudio&lt;/code&gt;, in terminal type below:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r,&#34;&gt;sudo apt-get install gdebi
cd ~/Downloads
wget https://download1.rstudio.org/rstudio-xenial-1.1.419-amd64.deb
sudo gdebi rstudio-xenial-1.1.419-amd64.deb
&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;Start &lt;code&gt;RStudio&lt;/code&gt;, in terminal type below:&lt;/p&gt;
&lt;pre&gt;&lt;code class=&#34;language-r,&#34;&gt;rstudio
&lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;h2 id=&#34;step-by-step-installation-guide&#34;&gt;Step by Step Installation Guide&lt;/h2&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step0.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step1.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step2.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step3.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step4.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step5.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step6.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step7.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step8.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step9_10.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&#34;https://natverse.github.io/images/installation_images/Step11.png&#34; alt=&#34;&#34; /&gt;&lt;/p&gt;</description></item><item><title>Learn the natverse</title><link>https://natverse.github.io/learn/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/learn/</guid><description>
&lt;p&gt;To see some examples of the natverse in action take a look at our
&lt;a href=&#34;https://natverse.github.io/gallery&#34;&gt;Gallery&lt;/a&gt;. Alternatively if you&amp;rsquo;d rather see some code right away,
then read one of the
introductory &lt;a href=&#34;https://natverse.github.io/news&#34;&gt;articles&lt;/a&gt;. If these look interesting, then we recommend
reading (or at least skimming) the &lt;a href=&#34;#natverse-paper&#34;&gt;natverse paper&lt;/a&gt; for a more in depth introduction. You can then browse documentation for the
core &lt;a href=&#34;https://natverse.github.io/nat/&#34; target=&#34;_blank&#34;&gt;nat package&lt;/a&gt; and work through some
&lt;a href=&#34;https://github.com/jefferis/nat.examples&#34; target=&#34;_blank&#34;&gt;example code&lt;/a&gt;.&lt;/p&gt;
&lt;hr /&gt;
&lt;p&gt;&lt;a href=&#34;https://elifesciences.org/articles/53350&#34;&gt;&lt;img src=&#34;../images/natverse_manuscript4.png&#34;&#34; align=&#34;right&#34; height=&#34;300&#34;/&gt;&lt;/a&gt;&lt;/p&gt;
&lt;h2 id=&#34;natverse-paper&#34;&gt;natverse paper&lt;/h2&gt;
&lt;p&gt;To understand what the natverse can do and how it is organised, the best
resource is a paper currently available at elife :
&lt;a href=&#34;https://elifesciences.org/articles/53350&#34; target=&#34;_blank&#34;&gt;Bates, Manton et al (2020)&lt;/a&gt;.
This describes all the main natverse packages and how they fit together. It also
provides numerous worked examples based on data from a range of species, including flies, fish and mice.&lt;/p&gt;
&lt;div style=&#34;clear:both;&#34;&gt;&lt;/div&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;nat-documentation&#34;&gt;nat documentation&lt;/h2&gt;
&lt;p&gt;&lt;img src=&#34;nat-pkgdown.png&#34; align=&#34;right&#34; height=&#34;300&#34; /&gt;&lt;/p&gt;
&lt;p&gt;To get started with some actual code, take a look at the documentation for the
&lt;a href=&#34;https://natverse.github.io/nat&#34; target=&#34;_blank&#34;&gt;&lt;strong&gt;nat&lt;/strong&gt; (NeuroAnatomy Toolbox)&lt;/a&gt; package, which is the core of the natverse:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Read the &lt;a href=&#34;https://natverse.github.io/nat/reference/nat-package.html&#34; target=&#34;_blank&#34;&gt;overview package documentation&lt;/a&gt;
(&lt;code&gt;?nat&lt;/code&gt; in R)&lt;/li&gt;
&lt;li&gt;Read the &lt;a href=&#34;https://natverse.github.io/nat/articles/neurons-intro.html&#34; target=&#34;_blank&#34;&gt;Introduction to neurons&lt;/a&gt; article
&lt;ul&gt;
&lt;li&gt;There are several other useful &lt;a href=&#34;https://natverse.github.io/nat/articles&#34; target=&#34;_blank&#34;&gt;articles&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;&lt;/li&gt;
&lt;li&gt;Check out the thematically organised &lt;a href=&#34;https://natverse.github.io/nat/reference/&#34; target=&#34;_blank&#34;&gt;function reference documentation&lt;/a&gt;.
&lt;ul&gt;
&lt;li&gt;Most help pages include examples.&lt;/li&gt;
&lt;/ul&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;There is extensive sample code and data available including:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://github.com/jefferis/nat.examples&#34; target=&#34;_blank&#34;&gt;nat.examples&lt;/a&gt; has detailed
examples for data sets from a range of model organisms and techniques&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://github.com/jefferis/frulhns&#34; target=&#34;_blank&#34;&gt;frulhns&lt;/a&gt; analysis of sexually dimorphic circuits&lt;/li&gt;
&lt;/ul&gt;
&lt;div style=&#34;clear:both;&#34;&gt;&lt;/div&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;bridging-and-mirroring-registrations&#34;&gt;Bridging and Mirroring registrations&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://www.biorxiv.org/content/10.1101/006353v1?versioned=true&#34;&gt;&lt;img src=&#34;../images/manton_biorxiv.png&#34;&#34; align=&#34;right&#34; height=&#34;300&#34; /&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;We introduced the concept of bridging registrations between template
brains in &lt;a href=&#34;https://www.biorxiv.org/content/10.1101/006353v1?versioned=true&#34; target=&#34;_blank&#34;&gt;Manton et al, bioRxiv, 2014&lt;/a&gt;.
This allows a huge amount of neuroanatomical
data from different labs acquired using both light and electron microscopy
to brought into a common space for shared analysis. The natverse provides
efficient tools to move data from one template brain to another. The original
version of this paper introduces and motivates our general approach with many examples.
The natverse supports a range of different registration tools and formats
including thin plate splines, &lt;a href=&#34;https://www.nitrc.org/projects/cmtk&#34; target=&#34;_blank&#34;&gt;CMTK&lt;/a&gt;,
&lt;a href=&#34;http://stnava.github.io/ANTs/&#34; target=&#34;_blank&#34;&gt;ANTs&lt;/a&gt; and the Saalfeld lab&amp;rsquo;s
&lt;a href=&#34;https://github.com/saalfeldlab/template-building/wiki/Hdf5-Deformation-fields&#34; target=&#34;_blank&#34;&gt;h5 format&lt;/a&gt;.&lt;/p&gt;
&lt;div style=&#34;clear:both;&#34;&gt;&lt;/div&gt;
&lt;hr /&gt;
&lt;p&gt;&lt;a href=&#34;http://dx.doi.org/10.1016/j.neuron.2016.06.012&#34;&gt;&lt;img src=&#34;../images/costa-nblast-scaled-p1clusters.png&#34; align=&#34;right&#34; height=&#34;300&#34; /&gt;&lt;/a&gt;&lt;/p&gt;
&lt;h2 id=&#34;nblast&#34;&gt;NBLAST&lt;/h2&gt;
&lt;p&gt;NBLAST is a fast and sensitive algorithm for comparing neuron structure. It is
described in an open access publication, &lt;a href=&#34;http://dx.doi.org/10.1016/j.neuron.2016.06.012&#34; target=&#34;_blank&#34;&gt;Costa et al, Neuron (2016)&lt;/a&gt;. Read the paper
to understand how the algorithm works and to see many examples of its use.&lt;/p&gt;
&lt;p&gt;You can also see the &lt;a href=&#34;http://rmarkdown.rstudio.com/&#34; target=&#34;_blank&#34;&gt;R Markdown&lt;/a&gt; reports
used to generate &lt;a href=&#34;https://github.com/jefferislab/NBLAST_figures/&#34; target=&#34;_blank&#34;&gt;all the figures for the paper&lt;/a&gt;.&lt;/p&gt;
&lt;div style=&#34;clear:both;&#34;&gt;&lt;/div&gt;
&lt;hr /&gt;
&lt;h2 id=&#34;learning-r&#34;&gt;Learning R&lt;/h2&gt;
&lt;p&gt;Naturally you will need to learn some basics of the R language to use the
natverse. There are a huge number of books and online resources now available.
The tidyverse website has some good suggestions, see
&lt;a href=&#34;https://www.tidyverse.org/learn/&#34; target=&#34;_blank&#34;&gt;https://www.tidyverse.org/learn/&lt;/a&gt;. Resources that we recommend include:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;http://swirlstats.com&#34; target=&#34;_blank&#34;&gt;http://swirlstats.com&lt;/a&gt; (an interactive way to get started for complete beginners)&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.rstudio.com/resources/cheatsheets/&#34; target=&#34;_blank&#34;&gt;https://www.rstudio.com/resources/cheatsheets/&lt;/a&gt; (a quick way to find key functions for data munging tasks)&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;http://adv-r.had.co.nz&#34; target=&#34;_blank&#34;&gt;http://adv-r.had.co.nz&lt;/a&gt; (chapters 1-7 are a good investment if you plan to spend much time in R)&lt;/li&gt;
&lt;/ul&gt;</description></item><item><title>Neuroanatomical data analysis</title><link>https://natverse.github.io/home/band_one/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/home/band_one/</guid><description>&lt;p&gt;The natverse is a &lt;a href=&#34;https://natverse.github.io/packages&#34;&gt;collection of interoperable R packages&lt;/a&gt; to import, visualise, analyse, manipulate and export 3D neuroanatomical data, including neurons, brains and brain regions. It has been used to study brain and circuit organisation in species from flies to fish and mice. You can install quickly like this:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;install.packages(&#39;natmanager&#39;)
natmanager::install(&#39;core&#39;) # basic install
natmanager::install(&#39;natverse&#39;) # or full install
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;See the &lt;a href=&#34;https://natverse.github.io/install&#34;&gt;install page&lt;/a&gt; for full details, especially if you are new to R.&lt;/p&gt;</description></item><item><title>Publications</title><link>https://natverse.github.io/publications/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/publications/</guid><description>
&lt;div id=&#34;citations-when-using-the-natverse&#34; class=&#34;section level2&#34;&gt;
&lt;h2&gt;Citations when using the natverse&lt;/h2&gt;
&lt;p&gt;If you use the natverse in your work, please cite us. Currently the most appropriate
citations are:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;General natverse, Bridging and Mirroring registrations: &lt;span class=&#34;citation&#34;&gt;[1]&lt;/span&gt; &lt;a href=&#34;https://doi.org/10.7554/eLife.53350&#34;&gt;10.7554/eLife.53350&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;NBLAST: &lt;span class=&#34;citation&#34;&gt;[2]&lt;/span&gt; &lt;a href=&#34;https://doi.org/10.1016/j.neuron.2016.06.012&#34;&gt;10.1016/j.neuron.2016.06.012&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/div&gt;
&lt;div id=&#34;publications-using-the-natverse&#34; class=&#34;section level2&#34;&gt;
&lt;h2&gt;Publications using the natverse&lt;/h2&gt;
&lt;!-- Note that for some reason I needed to use the absolute path + here in the YAML header--&gt;
&lt;!-- although in this snippet, the bare filename without any path worked as expected --&gt;
&lt;p&gt;The following 27 publications used the natverse or its direct ancestor
(the R &lt;a href=&#34;https://github.com/jefferis/AnalysisSuite&#34;&gt;AnalysisSuite&lt;/a&gt;).
If you use a natverse package in one of your papers, then please let us know.
You can even add a bibtex formatted record for your publication straight to the
top of our bibliography file
by &lt;a href=&#34;https://github.com/natverse/natverse_hugo/edit/dev_pages/content/publications/natverse-papers.bib&#34;&gt;following this link&lt;/a&gt;. Thanks!&lt;/p&gt;
&lt;hr /&gt;
&lt;div id=&#34;refs&#34; class=&#34;references&#34;&gt;
&lt;div id=&#34;ref-bates2020&#34;&gt;
&lt;p&gt;[1] A.S. Bates, J.D. Manton, S.R. Jagannathan, M. Costa, P. Schlegel, T. Rohlfing, G.S. Jefferis, The natverse, a versatile toolbox for combining and analysing neuroanatomical data, eLife. 9 (2020) e53350. doi:&lt;a href=&#34;https://doi.org/10.7554/eLife.53350&#34;&gt;10.7554/eLife.53350&lt;/a&gt;.&lt;/p&gt;
&lt;/div&gt;
&lt;div id=&#34;ref-Costa:2016aa&#34;&gt;
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&lt;/div&gt;
&lt;/div&gt;</description></item><item><title>What&#39;s in a name?</title><link>https://natverse.github.io/home/band_three/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/home/band_three/</guid><description>&lt;p&gt;The natverse is named by analogy to the &lt;a href=&#34;https://tidyverse.org&#34; target=&#34;_blank&#34;&gt;tidyverse&lt;/a&gt; a collection of R packages that try to enable simple and efficient general data analysis.&lt;/p&gt;</description></item><item><title>natverse packages</title><link>https://natverse.github.io/packages/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://natverse.github.io/packages/</guid><description>
&lt;h2 id=&#34;core-natverse&#34;&gt;Core natverse&lt;/h2&gt;
&lt;div class=&#34;package-section&#34;&gt;
&lt;div class=&#34;package-section-info&#34;&gt;
&lt;p&gt;The core natverse includes the packages that you&#39;re likely to use in analysis of neuroanatomical data.
As of natverse 0.2.1, the following packages
are included in the core natverse:&lt;/p&gt;
&lt;/div&gt;
&lt;div class=&#34;packages&#34;&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/nat/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-nat_logo.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/nat/&#34;&gt;nat&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
NeuroAnatomy Toolbox (nat) enables analysis and visualisation of 3D biological image data, especially traced neurons.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/nat/&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/nat.nblast/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-natnblast.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/nat.nblast/&#34;&gt;nat.nblast&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Extends package &#39;nat&#39; (NeuroAnatomy Toolbox) by providing a collection of NBLAST-related functions for neuronal morphology comparison (Costa et al.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/nat.nblast/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/nat.templatebrains/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-nattemplatebrains.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/nat.templatebrains/&#34;&gt;nat.templatebrains&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Extends package &#39;nat&#39; (NeuroAnatomy Toolbox) by providing objects and functions for handling template brains.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/nat.templatebrains/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/rcatmaid/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-catmaid.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/rcatmaid/&#34;&gt;catmaid&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
This package provide access to the API exposed by the CATMAID (C ollaborative A nnotation T oolkit for M assive A mounts of I mage D ata) web tool.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/rcatmaid/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/neuprintr/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-neurprintr.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/neuprintr/&#34;&gt;neuprintr&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Access to the neuprint connectome analysis service, including functions to fetch skeletons, synapses and ROIs, query connectivity data and develop new low level queries.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/neuprintr/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://jefferis.github.io/drvid/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-drvid.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://jefferis.github.io/drvid/&#34;&gt;drvid&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
API access to the &#39;DVID&#39; (Distributed, Versioned, Image-oriented Dataservice).
&lt;/p&gt;
&lt;a href=&#34;https://jefferis.github.io/drvid/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/neuromorphr/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-neuromorphr.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/neuromorphr/&#34;&gt;neuromorphr&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Access to the NeuroMorpho online repository (version 7.7 ) for single-cell neuron morphology data, enabling users to easily find and use neurons from this repository with nat family packages.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/neuromorphr/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/elmr/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-elmr.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/elmr/&#34;&gt;elmr&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Provides tools to move between adult brain EM and light level data, emphasising the interaction between the CATMAID web application and the R Neuroanatomy Toolbox package.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/elmr/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://natverse.github.io/nat.flybrains/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-natflybrains.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://natverse.github.io/nat.flybrains/&#34;&gt;nat.flybrains&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Includes 3D brain surfaces, bridging and mirroring registrations, and neuropil segmentations for various template brains.
&lt;/p&gt;
&lt;a href=&#34;https://natverse.github.io/nat.flybrains/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;http://natverse.github.io/flycircuit/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-flycircuit.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;http://natverse.github.io/flycircuit/&#34;&gt;flycircuit&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Functions and data for spatial analysis and annotation of neurons from the &#39;FlyCircuit&#39; collection available online at http://flycircuit.tw.
&lt;/p&gt;
&lt;a href=&#34;http://natverse.github.io/flycircuit/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;a href=&#34;https://github.com/jefferis/nabor/&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;https://natverse.github.io/images/hex-nabor.png&#34; alt=&#34;&#34;&gt;&lt;/img&gt;&lt;/a&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://github.com/jefferis/nabor/&#34;&gt;nabor&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
An R wrapper for &#39;libnabo&#39;, an exact or approximate k nearest neighbour library which is optimised for low dimensional spaces (e.g. 3D).
&lt;/p&gt;
&lt;a href=&#34;https://github.com/jefferis/nabor/&#34; aria-hidden=&#34;true&#34;&gt;Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;p&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;/div&gt;&lt;/p&gt;
&lt;p&gt;The natverse also includes many other packages with more specialised usage. They are not loaded automatically with &lt;code&gt;library(natverse)&lt;/code&gt;, so you&amp;rsquo;ll need to load each one with its own call to &lt;code&gt;library()&lt;/code&gt;.&lt;/p&gt;
&lt;h2 id=&#34;external-toolboxes&#34;&gt;External toolboxes&lt;/h2&gt;
&lt;p&gt;The following are the external toolboxes that play well with the &lt;code&gt;natverse&lt;/code&gt;:
&lt;div class=&#34;package-section&#34;&gt;
&lt;div class=&#34;package-section-info&#34;&gt;&lt;/p&gt;
&lt;p&gt;&lt;/div&gt;&lt;/p&gt;
&lt;div class=&#34;packages&#34;&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;&#34; alt=&#34;&#34;&gt;&lt;/img&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://cran.r-project.org/package=rgl&#34;&gt;rgl&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Provides medium to high level functions for 3D interactive graphics, including functions modelled on base graphics (plot3d(), etc.) as well as functions for constructing representations of geometric objects (cube3d(), etc.).
&lt;/p&gt;
&lt;a href=&#34;https://cran.r-project.org/package=rgl&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;&#34; alt=&#34;&#34;&gt;&lt;/img&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://cran.r-project.org/package=igraph/&#34;&gt;igraph&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Routines for simple graphs and network analysis.
&lt;/p&gt;
&lt;a href=&#34;https://cran.r-project.org/package=igraph&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;&#34; alt=&#34;&#34;&gt;&lt;/img&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://cran.r-project.org/package=alphashape3d&#34;&gt;alphashape3d&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Implementation in R of the alpha-shape of a finite set of points in the three-dimensional space.
&lt;/p&gt;
&lt;a href=&#34;https://cran.r-project.org/package=alphashape3d&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;&#34; alt=&#34;&#34;&gt;&lt;/img&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://cran.r-project.org/package=Rvcg&#34;&gt;Rvcg&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
Operations on triangular meshes based on &#39;VCGLIB&#39;.
&lt;/p&gt;
&lt;a href=&#34;https://cran.r-project.org/package=Rvcg&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&#34;package&#34;&gt;
&lt;img class=&#34;package-image&#34; src=&#34;&#34; alt=&#34;&#34;&gt;&lt;/img&gt;
&lt;div class=&#34;package-info&#34;&gt;
&lt;h3&gt;&lt;a href=&#34;https://cran.r-project.org/package=Morpho&#34;&gt;Morpho&lt;/a&gt;&lt;/h3&gt;
&lt;p&gt;
A toolset for Geometric Morphometrics and mesh processing.
&lt;/p&gt;
&lt;a href=&#34;https://cran.r-project.org/package=Morpho&#34; aria-hidden=&#34;true&#34;&gt;
Learn more ...&lt;/a&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;p&gt;&lt;/div&gt;
&lt;/div&gt;&lt;/p&gt;
&lt;h2 id=&#34;get-help&#34;&gt;Get help&lt;/h2&gt;
&lt;p&gt;If you’re asking for help, reporting a bug, or requesting a new feature, you’re more likely to succeed if you include a good reproducible example, which is precisely what the &lt;a href=&#34;https://natverse.github.io/help/#reprex&#34; target=&#34;_blank&#34;&gt;reprex&lt;/a&gt; package is meant for. You can learn more about reprex, along with other tips on how to help others help you in the &lt;a href=&#34;https://natverse.github.io/help/&#34; target=&#34;_blank&#34;&gt;help section&lt;/a&gt;.&lt;/p&gt;</description></item></channel></rss>