Restricted Delaunay Triangulation from 3D Voronoi Component

Howdy!

I would like to construct the restricted Delaunay triangulation of points on a surface by using the 3D Voronoi diagram.

My current code for doing so is slow. The attached example takes me 30 sec to execute on my Windows 8 virtual box on my MacBook Air (not the ideal environment but I think this metric still points to inefficiency).

I imagine that the connectivity / adjacency of the cells is calculated while created the 3D Voronoi diagram. Would it be possible to access this information without breaching the user agreement by decompiling and rewriting the Voronoi3D component? Is there a better way to construct the restricted Delaunay triangulation?

My current procedure for constructing the restricted Delaunay triangulation is:

1. find the intersection two cells with respect to each other and

2. if the result is not empty, intersect the result with the surface

3. if the result is not empty, connect points of the two cells

Thanks very much!

Attachments:

intersectSrfXVoronoi_4.gh, 10 KB

Replies to This Discussion

Permalink Reply by David Rutten on May 27, 2015 at 3:15pm

It is certainly a violation of the license agreement to decompile Grasshopper.

The Grasshopper voronoi algorithm relies on the Delaunay algorithm for adjacency information. These methods are available in the SDK so you should be able to call them directly and continue where they leave off.

Delaunay is much faster than voronoi so my advice would be to start with an unconstrained delaunay triangulation and adjust it whenever it violates the constraints. Have a look at the Grasshopper.Kernel.Geometry.Voronoi and Grasshopper.Kernel.Geometry.Delaunay namespaces. Specifically the Connectivity and Solver classes.

Permalink Reply by Tess on May 27, 2015 at 4:02pm

Hi David,

Thanks for the lightning fast reply! I looked at the Solvers for both Grasshopper.Kernel.Geometry.Voronoi and Grasshopper.Kernel.Geometry.Delaunay. Both operate on Node2List but I'm looking to solve a 3D problem. Are there solvers that take Node3List?

Thanks again!

Tess

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