Convex decomposition of the great stellated dodecahedron

[stla]

Hello,

The convex decomposition works fine and it is fast. I'm using the code of the example. However I can't get it for the great stellated dodecahedron:

There's no crash, but after 3 minutes of computation the computation is not terminated. Here is the mesh file.

[stla]

Hmm if I take the mesh of the great stellated dodecahedron obtained by computing the alpha shape of the vertices, then the convex decomposition works. 62 convex parts are found. So there should be a problem in my above mesh. Maybe a self-intersection?

[stla]

Yes it self-intersects.

I noticed something. To sum up, I have two different mesh representations of the great stellated dodecahedron, and one of them self-intersects. If I use CGAL to compute the volume, I get two completely different results. Is it the one corresponding to the self-intersecting mesh which is not correct?

[stla]

Yes, the correct volume is obtained with the second mesh.

Therefore, shouldn't you add the non-self-intersecting property as a precondition for the volume calculation?

[stla]

Same for the area: it is wrong for the self-intersecting mesh.