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non-planer surfaces to curved faces

K
kitwallace
Tue, Feb 11, 2020 9:01 AM

Really this is more a geometry question than OpenSCAD but I know you're a
knowledgable lot.

I've recently been playing with creating nets of solids with non-planar
faces.  When folded, such nets result in curved surfaces, but as polyhedra,
the non-planer surfaces are minimally triangulated.

http://forum.openscad.org/file/t229/random-n-prism.png

When constructed in a 2-D rigid material like card, all surfaces assume
curved shapes, though these are not necessarily uniquely defined - some
faces are bi or multi-stable indicating multiple solutions.

http://forum.openscad.org/file/t229/rpenta-r.jpg

I'd like to find some optimisation method which would produce a
triangulation of the solid which would satisfy the fixed edge length
constraints whilst minimising curvature (or something like that)

Any pointers?

--
Sent from: http://forum.openscad.org/

Really this is more a geometry question than OpenSCAD but I know you're a knowledgable lot. I've recently been playing with creating nets of solids with non-planar faces. When folded, such nets result in curved surfaces, but as polyhedra, the non-planer surfaces are minimally triangulated. <http://forum.openscad.org/file/t229/random-n-prism.png> When constructed in a 2-D rigid material like card, all surfaces assume curved shapes, though these are not necessarily uniquely defined - some faces are bi or multi-stable indicating multiple solutions. <http://forum.openscad.org/file/t229/rpenta-r.jpg> I'd like to find some optimisation method which would produce a triangulation of the solid which would satisfy the fixed edge length constraints whilst minimising curvature (or something like that) Any pointers? -- Sent from: http://forum.openscad.org/