algorithmic modeling for Rhino
An origami dome using a generalization of one of Ron Resch's folding patterns. Inspired by the work of Tomohiro Tachi (http://www.tsg.ne.jp/TT/cg/). An approximate solution is generated geometrically, then the 'developablize' force in Kangaroo is used to optimize it so that angles around each vertex sum to 360° (which they do to within 0.00003°)
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How do you generate "the approx solution"? Just taking a basic flat ron resch pattern or is the generation coming from the 3D surface?
Kipodi - For the VertexNeighbours(VN) component you need to not flatten, the C output.
The N output is giving a tree which contains a list of neighbours for each of the vertex inputs in a separate branch, so by grafting C we make sure that the central vertices are in a matching tree.
Hi Kipodi,
Here's an approach to get the angle defect at each internal vertex of a mesh:
For a developable surface the result should be zero.
I've shown it here with an icosahedron -there are 5 equilateral triangles around each vertex, so each is 60° short of a full turn.
Also - I think it's kind of neat to see how the total of all these angle defects for any closed mesh without topological handles will always add up to 720° (Gauss-Bonnet theorem).
hey Daniel, nice work,just a question.. how do I check that angles around each vertex sum to 360°?
May the force be with you.
Amazing work!Really!
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