Minimal Surfaces and Principal Curvature Lines

Replies to This Discussion

Permalink Reply by David Rutten on October 31, 2016 at 3:21pm

Is there a question? Or an attachment?

Permalink Reply by Daniel Piker on November 1, 2016 at 11:02am

Hi Amir,

Yes - Kangaroo can generate accurate minimal surfaces, but I don't think that is the key issue here - the challenges of discretizing it into a PQ mesh will be the same whether it is approximately or exactly minimal.

No - the network of mesh edges in that image do not follow the principal curvature directions, since their topology comes from the initial base mesh, which generally won't match the topology needed for a principal curvature aligned net. A quad grid following the principal curvatures can only ever have vertices of even valence, while your mesh has several with valence 5. Also, the principal curvature lines generally won't even align with the edges of the surface, which complicates attempts to build a mesh following them.

Tools such as TMap from Evolute, or the QuadMesher in the Rhino WIP attempt to generate quad grids on surfaces, with options for aligning these with curvature. I know several people have also worked on tools for tracing principal curvature lines on meshes - not sure what the best one to use is though.

You only need a coarse and approximate net of curvature lines, as long as the topology is right, relaxing and planarizing the quads should help neaten everything up.