更新TikZ文档，添加简介、配置项和多边形示例，修复README中的链接格式

PKM-er · Feb 27, 2025 · 00aaea6 · 00aaea6
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diff --git a/Other/说明/tikz绘图标准.md b/Other/说明/tikz绘图标准.md
@@ -2,6 +2,7 @@
 tags:
   - 数学
 ---
+# 简介
 ## 环境配置
 代码类型: tikz 
 ```
@@ -37,6 +38,7 @@ The following packages are available in `\usepackage{}`:
 会导致报错
 
 ---
+# 配置项
 ## 颜色
 TikZ 内置了一些常见的颜色方案，方便绘图时使用。这些颜色可以直接引用，也可以通过 `xcolor` 包扩展。以下是主要内置颜色方案：
 ### 常用颜色
@@ -186,7 +188,6 @@ TikZ 内置了一些常见的颜色方案，方便绘图时使用。这些颜色
 ---
 ## 颜色填充
 
-大多数情况都失败了, 但是有一次看到了一个偶然的成功案例
 ```
 % 填充阴影区域
 \begin{scope} \clip (0,-1.5) rectangle (1,0); \fill[black!20,opacity=0.7] plot[domain=0.01:1,smooth]({\x}, {ln(\x)}) -- (1,0) -- (0,0) -- cycle; \end{scope}
@@ -229,6 +230,88 @@ TikZ 内置了一些常见的颜色方案，方便绘图时使用。这些颜色
 
 
 
+---
+## Polygon
+
+You can use the geometric shapes given by the shapes.geometric library
+
+```latex
+\usetikzlibrary{shapes.geometric}
+
+\begin{tikzpicture}[mystyle/.style={draw,shape=circle,fill=blue}]
+\def\ngon{5}
+\node[regular polygon,regular polygon sides=\ngon,minimum size=3cm] (p) {};
+\foreach\x in {1,...,\ngon}{\node[mystyle] (p\x) at (p.corner \x){};}
+\foreach\x in {1,...,\numexpr\ngon-1\relax}{
+  \foreach\y in {\x,...,\ngon}{
+    \draw (p\x) -- (p\y);
+  }
+}
+\end{tikzpicture}
+```
+
+---
+One short tikz code without use of a library.
+
+```latex
+\documentclass[border=7mm]{standalone}
+\usepackage{tikz}
+\begin{document}
+\foreach \n in {3,...,7}
+  \tikz\foreach \i in {1,...,\n}
+    \fill (\i*360/\n:1) coordinate (n\i) circle(2 pt)
+      \ifnum \i>1 foreach \j in {\i,...,1}{(n\i) edge (n\j)} \fi;
+\end{document}
+```
+
+---
+For fun, a short code with `pst-poly` gets the desired result:
+
+```latex
+\documentclass[svgnames]{standalone}
+
+\usepackage{pst-poly}
+\usepackage{auto-pst-pdf}
+\begin{document}
+
+\psset{unit=3.5cm, dimen=middle, linejoin=1, dotsize=12pt}
+\begin{pspicture}(-1,-1)(1,1)
+    \providecommand{\PstPolygonNode}{\psdots[dotsize=12pt, linecolor=SteelBlue](1;\INode)
+    }
+    \rput(0,0){\PstPentagon[PolyName=A, linecolor=LightSteelBlue, linewidth=1.2pt] }
+    \rput(0,0){\PstPentagon[PolyName=A, PolyOffset=2] }
+\end{pspicture}
+
+\end{document}
+```
+
+**Upgrade:** An improved version, which itself calculate all necessary data from given number of nodes and angle of the first node position:
+```latex
+\documentclass[border=3mm,tikz]{standalone}
+
+\begin{document}
+\begin{tikzpicture}[
+ every node/.style={draw,shape=circle,fill=blue,text=white}]
+%%%% variable data data
+\def\numpoly{8}%number of nodes
+\def\startangle{30}%direction of the first node
+\def\pradious{33mm}
+%------- calculations of the positions angles
+\pgfmathparse{int(\startangle+360/\numpoly)}%
+    \let\nextangle=\pgfmathresult
+\pgfmathparse{int(\startangle-360/\numpoly+360)}%
+    \let\endtangle=\pgfmathresult
+%--- nodes
+    \foreach \i [count=\ii from 1] in {\startangle,\nextangle,...,\endtangle}
+\path (\i:\pradious) node (p\ii) {\ii};
+%--- interconnections
+    \foreach \x in {1,...,\numpoly}
+        \foreach \y in {\x,...,\numpoly}
+\draw (p\y) -- (p\x);
+    \end{tikzpicture}
+\end{document}
+```
+
 ---
 # 案例
 ## 2D
@@ -762,7 +845,104 @@ child {node {$y$}}
 ```
 
 
+## Automaton
+
+### tikz绘制自动机的状态转移图示例: 
+
+```tikz
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}
+
+  % 定义状态
+  \node (p0) at (0, 0) [circle, draw, double] {$p_0$}; % 接受状态
+  \node (p1) at (3, 0) [circle, draw] {$p_1$};
+  \node (p2) at (3, -3) [circle, draw] {$p_2$};
+  \node (p3) at (0, -3) [circle, draw] {$p_3$};
+
+  % 转移路径
+  \draw[->] (p0) to[loop above] node {0} ();
+  \draw[->] (p0) to[bend left] node[midway, above] {1} (p1);
+  \draw[->] (p0) to[bend left=15] node[midway, right] {2} (p2);
+  \draw[->] (p0) to[bend right] node[midway, left] {3} (p3);
+
+  \draw[->] (p1) to[loop above] node {0} ();
+  \draw[->] (p1) to[bend left] node[midway, right] {1} (p2);
+  \draw[->] (p1) to[bend left=15] node[midway, right] {2} (p3);
+  \draw[->] (p1) to[bend right] node[midway, above] {3} (p0);
+
+  \draw[->] (p2) to[loop below] node {0} ();
+  \draw[->] (p2) to[bend left] node[midway, below] {1} (p3);
+  \draw[->] (p2) to[bend left=15] node[midway, left] {2} (p0);
+  \draw[->] (p2) to[bend right] node[midway, right] {3} (p1);
+
+  \draw[->] (p3) to[loop below] node {0} ();
+  \draw[->] (p3) to[bend left] node[midway, left] {1} (p0);
+  \draw[->] (p3) to[bend left=15] node[midway, left] {2} (p1);
+  \draw[->] (p3) to[bend right] node[midway, below] {3} (p2);
+
+\end{tikzpicture}
+\end{document}
+```
+### 多边形
+```tikz
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}[mystyle/.style={draw, shape=circle, text=white, minimum size=6mm}
+]
+
+% Define the center of the pentagon
+\coordinate (center) at (0, 0);
 
+% Define nodes at equal angles around the center
+\foreach \i in {1, 2, 3, 4, 5} {
+    \node[mystyle] (q\i) at ({72*\i-72}:2cm) {$q_{\i}$}; % 72° spacing for pentagon
+}
+
+% Draw transitions between nodes
+\foreach \i [evaluate={\j=int(mod(\i,5)+1)}] in {1, 2, 3, 4, 5} {
+    \draw[->] (q\i) -- (q\j); % Connect nodes in a closed loop
+}
+
+\end{tikzpicture}
+\end{document}
+
+```
+
+### example
+```tikz
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}[->, shorten >=1pt, auto, node distance=1.5cm, thick]
+
+  % Define the states
+  \node (q2) at (180:1.5cm) [circle, draw, double] {$q_2$}; % q2 at 180° (leftmost point)
+
+  % Define the pentagon nodes using polar coordinates around q2
+  \foreach \i in {1, 2, 3, 4} {
+    \node (q\the\numexpr\i+2\relax) at ({180 - 72*\i}:1.5cm) [circle, draw] {$q_{\the\numexpr\i+2\relax}$};
+  }
+  \node (q1) [circle, draw, left of=q2] {$q_1$};
+  \node (q0) [circle, draw, left of=q1] {$q_0$};
+
+  % Draw the transitions
+  \path (q0) edge node {0} (q1)
+        (q1) edge node {0} (q2)
+        (q2) edge node {0} (q3)
+        (q3) edge node {0} (q4)
+        (q4) edge node {0} (q5)
+        (q5) edge node {0} (q6)
+        (q6) edge node {0} (q2);
+
+  % Start state arrow
+  \draw[->] (-5.5, -1) -- (q0);
+
+\end{tikzpicture}
+\end{document}
+```
 
 
 ---

diff --git a/Other/说明/插件配置说明.md b/Other/说明/插件配置说明.md
@@ -38,4 +38,6 @@ tags:
 此插件会导致markdown表格的公式输入bug, 暂时停止使用
 
 ## TikZJax
-2024-12-28 发现了一个新的插件可以渲染三维图像, 这在曲线曲面积分部分会很有用, 潜力待发掘
+[tikz绘图标准](Other/说明/tikz绘图标准.md)
+2024-12-28 发现了一个新的插件可以渲染三维图像, 这在曲线曲面积分部分会很有用, 潜力待发掘
+2025-02-25 现在使用TikzJax来绘制二维和三维函数图像，非必要不使用图片
diff --git a/README.md b/README.md
@@ -44,7 +44,7 @@
 		10. [bootstrap方法](概率论/bootstrap方法.md)
 		11. [随机过程及统计描述](---随机过程---.md)
 		12. [马尔可夫链](概率论/---马尔可夫链---.md)
-		13. [平稳随机过程](概率论/平稳随机过程.md)
+		13. [平稳随机过程](概率论/---平稳随机过程---.md)
 - [高等数学进阶](Other/-高等数学进阶-.md) (本库的补充)
 	- [复分析](Other/复分析/--复分析--.md)
 	- [抽象代数](Other/抽象代数/--抽象代数--.md)

diff --git a/_assets_/todo/数一真题问题清单.md b/_assets_/todo/数一真题问题清单.md
@@ -2,7 +2,7 @@
 tags:
   - todo
 ---
-- [ ] 有时候公式两边`$`缺失, 补全内容
+- [x] 有时候公式两边`$`缺失, 补全内容
 - [x] 单行公式的正则替换处理: 
 		替换表达式, 用于单行公式中添加开头的/displaystyle, 匹配lim sum int Sigma符号:
 	```
@@ -17,9 +17,8 @@ tags:
 	- [x] 首先将图床图片转为本地图片, 存储在`_assets_/Images`路径中
 	- [ ] 考虑能转成tikz的尽量不用图片
 - [ ] 使用分割线分题
-- [ ] 双链缺失文件
 - [ ] 问题和回答的标题修改
 	例如: `## (1)` 这是问题题号(1)作为二级标题, 紧跟着是对应解答的三级标题`### (1)` , 现在改为问题和题目都使用二级标题, 而解答使用`## (1)解` 这种形式
-- [ ] 指向本地视频文件的时间戳的链接, 如: [03:26](file:///C:/Users/wangpanfeng/Videos/01.%E6%95%B0%E5%AD%A6%E4%B8%80/08.2021%E5%B9%B4%E6%95%B0%E4%B8%80%E7%9C%9F%E9%A2%98/01.2021%E5%B9%B4%E8%80%83%E7%A0%94%E6%95%B0%E5%AD%A6%E7%9C%9F%E9%A2%98%E9%80%89%E6%8B%A9%E9%A2%98%EF%BC%88%E6%95%B0%E4%B8%80%EF%BC%89.mp4#t=03:26) ,暂时不需要处理
-- [ ] 指向不存在文件的双链, 暂时不需要处理
+- [x] 指向本地视频文件的时间戳的链接, 如: [03:26](file:///C:/Users/wangpanfeng/Videos/01.%E6%95%B0%E5%AD%A6%E4%B8%80/08.2021%E5%B9%B4%E6%95%B0%E4%B8%80%E7%9C%9F%E9%A2%98/01.2021%E5%B9%B4%E8%80%83%E7%A0%94%E6%95%B0%E5%AD%A6%E7%9C%9F%E9%A2%98%E9%80%89%E6%8B%A9%E9%A2%98%EF%BC%88%E6%95%B0%E4%B8%80%EF%BC%89.mp4#t=03:26) ,暂时不需要处理
+- [x] 指向不存在文件的双链, 暂时不需要处理