Delaunay Surface

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?

Attachments:

DelaunaySurface.gh, 18 KB

Replies to This Discussion

Permalink Reply by Lucas Becker on September 7, 2014 at 2:30pm

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.

Permalink Reply by Shaun on September 24, 2014 at 4:30am

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

Attachments:

07.jpg, 1.2 MB
06.png, 113 KB

Permalink Reply by Lucas Becker on September 25, 2014 at 12:58pm

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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