Equal Triangular Length On Mesh Surface

Hi, there. I am trying to use Kangaroo2 to get a equal length edge on this mesh surface, which is similar to Fuksas’s Milan Expo project. However, I guess the Kangaroo2 is not getting what I want. Any Help will be appreciated!
Equal Triangular Length With Kangaroo2.gh (144.0 KB)



Input to show goal input as a mesh is missing.
And if you want equal length use equal length goal as well.

Hi! I follow your suggestions and it starts to work now, but the geometry starts to collapse in the middle and the edge is not being filled with triangle. Any idea how to fix it?
Equal Triangular Length With Kangaroo2.gh (148.3 KB)


Hi @brucehesp

It is not geometrically possible to have a triangular mesh with equal edge lengths on a smoothly curving surface like this.
For a mesh on a smooth surface - in areas of positive Gaussian curvature, the angles around each vertex need to sum to slightly less than 360°, and in areas of negative Gaussian curvature they need to sum to slightly more.
If you have only equilateral triangles, these small variations in angle sum aren’t possible, you can only make jumps of 60° by changing the number of triangles around a point. Any number of triangles other than 6 around a vertex results in a big kink or spike.

Non planar quad meshes on the other hand can form smooth surfaces with equal edge lengths, because the angles are free to change.

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Hi, Daniel. I understand that it not possibles to get exactly the same length for each edge. My goal is to archive the similar results as Fuksas’s Milan expo, which is to make most of edges to have the same length.

I think maybe you’re looking for mesh relaxation. Try using MeshMachine linked in this post

The Fuksas pavilion has the topology of a triangulated quad grid, so I don’t think remeshing is what @brucehesp is after here.
Are you after just similar lengths?