Add metrics for meshes #11
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…eliminary design)
luisfpereira
commented
Dec 20, 2024
| self.cutoff = cutoff | ||
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| super().__init__(shape) | ||
| self._graph = to_nx_edge_graph(shape) |
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edge_graph instead? maybe not, to keep code within class flexible.
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Inspired by #9, this PR brings in the first metrics for meshes (very preliminary design!).
Why? tldr: modularization!
An important step of scalable FMaps (Magnet, 2023) consists of approximating the Laplace-Beltrami eigenbasis.
An important step for approximating the Laplace-Beltrami eigenbasis is the construction of local basis functions (Nasikun, 2018).
An important step for the construction of local basis functions is the computation of distances between sampling points and the original mesh.
There's multiple ways of computing distances given a mesh.
I'm providing a common interface to compute those distances.
For now, I've implemented the
EuclideanMetricand theSingleSourceDijkstra. Variants of the second are low hanging fruits. (Magnet, 2023) implements a variant ofSingleSourceDijkstra.I hope this thread helps understanding a bit better the modularization steps I've started taking on scalable refactoring (51f6f50).
Of course I'm justifying this PR with scalable because it is the implementation we're pursuing at the moment requiring this, but needlessly to say these metrics will find a lot of applicability (e.g. the distance-based samplers we're discussing yesterday).
Other goals this PR will lead to: implementation of (Nasikun, 2018).
Still a draft because I need to think a bit more about the design and add other metrics.
Looking for your feedback @GiLonga, @gviga.