# To FlatFold a Curved-folding paper

Hi,@DanielPiker

I am trying to generate a curved-folding paper on a Hyperbolic paraboloid
However, I can’t flat it to be like a paper.

It is basically a continuation of this topic: Developable Surface Optimization with Kangaroo 2

In my opinion, I think the problem is that the sum of each vertices neighboring angles is not 2π.(show in the panel in the picture). So far, I tried to use “On Curve” and “Hinge” to achieve that, but it didn’t work.

Do you have any way to make sure that each vertices neighboring angles is sum to 2π ??
like “developablize”(in kangaroo 1) can force to angles sum up to 360 ??

Best,

curved-folding.gh (53.8 KB)

1 Like

The easiest way to make sure angles around each vertex sum to pi is to flatten a copy of the mesh, and then use EqualLength on corresponding pairs of edges of the flat and folded mesh, while using an OnPlane goal to keep the flat one flat. You need a triangulated mesh for this to work.

Hi,@DanielPiker

Recently, I am back to doing this project and try to more complex curved folding origami.

The first problem is how do I can speed zombie of kangaroo solver up ?
Because I am try to find out the proper parameter of kangaroo goal in attach file
I using zombie solver to run for like 13mins result in wasting my time to figure out the proper parameter.

The other question is that how can I unfold the folded mesh better?
I tried to test your way to keep the same length of mesh.
In the picture, I tried to unfold mesh with same edge length of mesh before.
but the meshes were deformed by PullToCurve.

next time, I will try to produce developable surface better by add angle constraints
because I read the Tomohiro Tach’s paper and know that ,in the crease pattern, the left and right ruling lines emanate at the same angle from the tangent vector of th curve, meaning that the rulings are drawn such that they reflect at the curve.
Do you have any suggestion??

The first attach is to generate developable sufaces between crease patterncomplex developable surfaces.gh (132.1 KB)
The second is to unfold the curved-folding origami, is to unfold the work of first file.unfold mesh.gh (540.7 KB)