Compared FMM with Euclidean distance on a non-uniform mesh without holes. The results show that, although there are some differences, it is minimal. This thus indicates that the FMM is accurately calculating the distance.
I managed to get the Gaussian FMM to work. With this, it now somewhat simulates the energy preservation process of heat diffusion. There are multiple parameters that we can tune to get it to look more like an actual heat diffusion process. The animations below are based on parameters that I thought looked best, without any actual testing or comparison with true energy preservation.
I think this looks the best out of all the examples, since there it is a clean triangular mesh.
This mesh struggles a bit since there are multiple obtuse angles.
This one is very slow because of the shear number of vertices there are.
It's hard to see, but at the beginning, it's not very accurate due to the irregular triangular mesh.
This one struggles a bit because of the large difference in size between the various triangles.
This one also struggles because of the difference in size of the triangles.
As you can see from the animations, there are multiple cases where it fails in its approximation due to irregularities with the mesh. I think this can be somewhat fixed by further tuning the parameters as well as coming up with a better way to create the triangular mesh.
The FMM algorithm is largely based off the example that Professor Chen showed in the last meeting. Though I haven't tested it yet, I think that because of the nature of the algorithm, getting it to work with a 3D mesh would be trivial.
All code for this can be found on my GitHub page, linked below. The main FMM stuff is in the vtk_fmm.py file, while the visualizations is in the diffusion_colormap_display.py file.
Heat-Diffusion/VTK-FMM at main ยท Jakl3/Heat-Diffusion
Also, I uploaded it to GitHub since I like to share my work with my family and friends, and GitHub is convenient for that. If you would like me to remove it from GitHub, or to make the repository private, please let me know!