Issue with Geodesic Distance Computation

[whb007]

Hello. Thank you for sharing your code.

However, I believe I’ve encountered an issue with the geodesic distance computation. I used the following code:
solver = pp3d.MeshHeatMethodDistanceSolver(vertices, faces)
dist = solver.compute_distance(2)

to compute the geodesic distance on a simple mesh with the following data:

`v 0 0 0
v 1 -3 0
v 2 0 0
v 1 3 0

f 1 2 3
f 1 3 4`

The result I obtained was:
[1.51446671 2.71666474 0. 2.71666474]

However, this result seems incorrect given the simple planar configuration of the mesh. I would greatly appreciate it if you could take a look and let me know whether this is expected behavior, or if there might be an issue with the implementation or usage.

Thank you again for your time and effort in making the code available.

[nzfeng]

Am I correct that your mesh has only 4 vertices and 2 triangle faces?

Because the heat method is based on solving a partial differential equation, the accuracy of the solution depends on how "refined" the domain is (as with all PDEs). In this case, the number of degrees of freedom (the number of vertices) is very few relative to the precision we are probably asking for on these two triangles. On such a coarse mesh, the scalar diffusion step of the heat method, in particular, will not be too reliable. If you refine your mesh -- tessellate the rhombus with more triangles -- you should get much lower relative error!