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Kobbelt et al. published a paper some 20 years ago where they specified how solving Poisson equations on the positions of a mesh lead to removing noise. This can be used for reconstructing mesh topology on holes, smooth out noisy meshes, mesh joints...

I am trying to do something similar, but in my case the meshes are piecewise smooth:

enter image description here

What can I do at the corners so that they better reflect the geometry of the edges?

For the record what I am doing is splititng the mesh into fixed and mobile vertices, computing a cotan laplacian matrix and then solving for $Lx=0$ where x are the interleaved coordinates of the mobile vertices.

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  • $\begingroup$ It will not work with a Laplace equation. It may be better with $L^q$ where $q$ is large - my guess is that for $q\to \infty$ this becomes a sharp corner, but I am not sure. In your case probably a transport PDE will work better to create a sharp corner. It could also be that some low order and nonlinear operator works well. $\endgroup$
    – lightxbulb
    Commented Oct 9, 2023 at 6:06
  • $\begingroup$ By nature the Poisson equation gives you a smooth solution. I don't think you can get what you want with this method. Can you show the original point cloud maybe? $\endgroup$
    – user8469759
    Commented Oct 9, 2023 at 6:12
  • $\begingroup$ Also maybe variational methods might be useful in your case (the poisson equation is a specific case of those). $\endgroup$
    – user8469759
    Commented Oct 9, 2023 at 6:16
  • $\begingroup$ @user8469759 I am not using poisson reconstruction, there is no point cloud, I am working directly on meshes. $\endgroup$
    – Makogan
    Commented Oct 9, 2023 at 18:49
  • $\begingroup$ @lightxbulb Do you have a suggestion on what the operator could be? $\endgroup$
    – Makogan
    Commented Oct 9, 2023 at 18:50

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