Developable dome

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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Comment by Meryem Beny on January 28, 2021 at 4:10pm: Hello Daniel,

Could you please tell me how to launch the timer control? it says "just double click the kangaroo" but it doesn't seem to work ? it only shows: "enter a search keyword".

Many thanks

Comment by Annie Locke Scherer on December 7, 2018 at 6:46am: How do you generate "the approx solution"? Just taking a basic flat ron resch pattern or is the generation coming from the 3D surface?

Comment by Daniel Piker on October 1, 2014 at 11:12am: 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.

Comment by kipodi on October 1, 2014 at 11:04am: thanks for the reply Daniel, I can;t get it to work by just copying your def.

I get an error message saying that vector one and two equal zero..I tried culling out the zeros , didn't help.. I kept 1 as the "s" input for shift.

any idea?

Comment by Daniel Piker on July 5, 2014 at 11:07am: 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).