Mesh singularities example

Hi @DanielPiker
I was checking some of the examples from Kangaroo’s github page, and realized how nice the avatar picture is:

Is there an example file which creates these convenient singularities?
Thank you for the reply.

Hi Djordje,

Most meshes can be made to look better with some subdivision/relaxation/smoothing, but creating initial coarse quad meshes with nice placement of singularities is a bit of an art.

There are some automated approaches, including the QuadMesh command (QuadMesh prototype command available in latest WIP).

For something like that avatar image though, where the underlying geometry is something very symmetrical (in this case it is a surface with the topology of a gyroid), I find the best way to get a good mesh is to design the initial coarse quadrangulation manually, respecting the symmetry of the form (by coarse I mean with the minimal number of quads that can form the desired singularities - ie they cannot be grouped into larger rectangular patches). Applying quad subdivision (eg Catmull-Clark) to such a coarse mesh does not change these irregular vertices.

Meshes which follow principal curvature directions usually look good. Personally I like the look of meshes where all the irregular vertices are of even valence (and the singularities in the principal curvature field are only ever of even valence).