Grasshopper

generative modeling for Rhino

In response to this discussion:

http://www.grasshopper3d.com/photo/mesh

I am posting my definition for generating an open foam mesh.

(I didn't post back at the time because there were some troubles with weaverbird back then and I was having to use some ugly workarounds, but now that is all fixed)

To sum up the approach -

take a random cloud of points

generate the 3d voronoi

scale the edges of the cells towards their centres, and also towards the centres of the faces.

connect these 2 sets of scaled edges with mesh quads and join

cull some of the outer faces

subdivide and smooth with weaverbird

(In the video there were some other variations on the smoothing/relaxation, both of the initial point positions and the final mesh, using hoopsnake and/or kangaroo)

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i feel like im witnessing the unraveling of all the secrets to meshs right infront of my eyes. :)

Ok, as i said before it can all be done with overdriven lines. This has some limitations (for now) : mesh is open (some more culling patterns needed), and connections must exist in voronoi3d connections (delaunay 3d) :( ... Its all done with dull culling, so it aint as tricky as before.

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and now closed with artificial triangles (not as elegant as it could be)

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so cool
what exactly is this one doing? folowing one path through the voronoi diagram?

It creates this geometry (inside) direct from lines. But there is only one limitation - endpoints of these lines and these lines must match voronoi 3d cells connections (delaunay 3d). Only if this condition is true , mesh will follow the line. 

what do you think about this, finally had a chance to explore for a minute, probably not as entertaining for your skill as it is for me, but I figured I would show you. basically I am moving the voronoi pieces away from each other then lofting together same faces. I know some parts are redundant in the definition, its my first rough try. I also am using a cluster I made, its in purple. 

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nice! i don't really understand this, but thanks for sharing 

will this also be in the "bonus" tab ;)

hey daniel,

Just curios ,.....

how did you achieve the voronoi for the delauney of the rabbit ... is it

3d voronoi based in the delaunay points and then intersected with the mesh ?

thx

It is the dual of the mesh. At each vertex, draw a polyline that unites all "centers" of the adjacent faces. "Center" can be defined in various ways.

This is a basic topological modification of a mesh. This is a weak dual.

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