Chen-Gackstatter surface

[stla]

Hello,

I propose a game. Could you guess the shape of the ARAP parameterization space for the Chen-Gackstatter surface?

[stla]

Argh, we'll never know:

Error: Cannot solve linear system

[stla]

DCP perfectly gets the shape of the parameterization space:

[stla]

Hmm but it is not usable to map a radial checkerboard. This surface is strange.

[stla]

CGAL finds two borders of this mesh. However we see only one, no?

[sloriot]

To be honest, on the animation I see the hole moving while rotating and I don't understand what I see. About the two borders maybe the mesh contains more than what you expect.

[stla]

This mesh is obtained with a parametrization (r, t) with r in (0.2, 0.8) and t in (0, 2pi), and we use z=re^(itheta) in the formulas. I tried to change the bounds of (0.2, 0.8) and this gives very weird results. If I decrease 0.8 I see another border.

[stla]

Here are the two borders found by CGAL. Really strange.

[sloriot]

Can you share the mesh?

[stla]

Here is a non-binary PLY file of this mesh.
ChenGackstatter.ply.txt

[sloriot]

The mesh is self-interesting. It is folding on itself.

[stla]

I can get a non-self-intersecting version by alpha-wrapping the vertices 👍

[stla]

Ah but this new mesh does not have a border :-(