# Bi-harmonic diffusion to smooth weight maps over meshes.

- 05/2019 - #Jumble

# Research

[ C++ code ] for the experiment.

Goal: diffuse weight maps by using one or several steps of Jacobi iterations to solve the Biharmonic equation. For now I could solve using the bilaplacian L*M^-1*L operator with a sparse LU solver (note: Biharmonic functions minimize Laplacian energy). Trying to use Jacobi iterations doesn't really produce the results I was expecting. Mainly I have 3 problems:

- I don't converge unless I use an aggressive dampling with t = 0.6 to LERP between old and new values of one iteration of Jacobi.
- The results of this diffusion by Jacobi oscillate (produces slightly negative weights)
- deformation is C0 on boundaries :/

# Future work

Maybe the non negativity constraints in Alec's papers (bounding biharmonic weights) can help ?

There is also this paper: Multiscale Biharmonic kernels (Eurographics Raif M. Rustamov) to explore.

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