segaviv
commented
5 months ago Hi,
A local/global bijective parameterization is not guaranteed for LSCM in the case of free boundary, so for some meshes with high curvatures local flips and high distortion may occur (this can be mitigated by introducing singularities/extending the cut, but it is not within the scope of the course).
In some cases, limiting the choice of the fixed vertices to boundary vertices may help (i.e. find the two vertices on the boundary with maximal edge distance, and use them as the constrained vertices), but it does not guarantee the bijectivity of the parameterization.
I have a question about the LSCM case where we only fix 2 vertices. I implemented it as suggested, I fixed vertex 0 to a position and then picked one of the vertices that has maximal (edge) distance to vertex 0 to be fixed as well. The problem I have is that this mapping does not turn out to be bijective, the flattened mesh has some issues where the fixed vertices end up in the middle of other triangles and I get a few flipped triangles in the UV map. I've been working on this issue for quite some time now but don't see where I'm going wrong, especially because the sanity check presented in the assignment works, so if I fix the boundary, LCSM produces the exact same result as the cotangent Laplacian.
Can anyone give me a hint on what the problem could be here?
Thanks!