Grasshopper

algorithmic modeling for Rhino

Hi everyone, i want to use delaunay on the sphere, and i try to use these two way to achieve my purpose.

But you can see very clear the two ways both has some defect.

Left one top of shape is broken, and the appearance isn't like delaunay.

Right one the edge is weir, because i draw a planar surface, then project it on the sphere.

Anyone could give me suggestion?

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Well, you're digging very deep into real hardcore mathmatics.I mean, people are writing thesis on this topic.

First my inner voice read voronoi instead of delaunay (which is very easy, at least with GH).Voronoi and delaunay a very close related but still I can't imagine a way to use the voronoi midpoints from GH to make a 3d-delaunay.
If I would, I'll also win probably a Nobel-Prize or something...

EDIT:Please note that it is not impossible to make a delaunay mesh on a sphere. It just requires a lot of work.

Hi Lucas

there are a way to create triangle line on the surface.

By changing the UV position of the surface, then recreate the mesh.

I think it's very similar to the Delaunay look like.

Thank for your explanation.

Regards 

Shuan

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Yeah, that's neat! Love it.

Great solution.

It seems, that David didn't want to implement another slow operation, so "convex hull" does only works in 2D. In other apps this operation often even works in 3D which will give - I suppose - the same result as your solution looks, which really looks good, also the triangulation seems to be perfect and suit the needs of a true delauney mesh.

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