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If you have an image sheet of facets and data to indicate which point on each facet should connect with other points on the other facets, is it possible to position those facets in 3D space based on the connecting points? Essentially turning 2D images into 3D objects. Similar to paper craft folding.

Matt W
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  • Can you provide visual example? – yossico Aug 14 '16 at 12:21
  • I was hoping for an algorithm I can base my code on. For an example of what I imagine: http://cdn.acidcow.com/pics/20091112/cat_papercraft_04.jpg – Matt W Aug 14 '16 at 12:37
  • I feel like the solution should be reasonably simple but can't figure it out. – Matt W Aug 14 '16 at 12:53
  • WOW, After seeing your example image I have no clue... :-\ – yossico Aug 14 '16 at 13:05
  • In essence, points on that sheet must connect to a limited number of other points without distorting their parent facet. I can't help but think that the problem is analogous to pulling strings connecting those points. – Matt W Aug 14 '16 at 13:08
  • It's a paper folding problem. Interesting. Off-hand, it seems to me that it would not be too hard, but I haven't tried it. A [*first Wikipedia search*](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=paper+folding+algorithm) doesn't seem to address it. – Mike Dunlavey Aug 14 '16 at 13:27

1 Answers1

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No. You are missing the convex/concave information.

Each 3d point can be determined by solving a simultaneous equation. Unfortunately it will have two solutions, an 'out of the page' or 'into the page' solution.

With this additional information, its still not a trivial problem. you need to determine the order of the folds, calculate the required fold angle and apply rotational matrix transformations to the joined vertices recursively.

Also, your paper craft example is the simplest version of the problem, with each fold on a single axis. Some paper folds rely on the bendyness of the paper eg inside/outside reverse folds

http://www.origami-instructions.com/origami-inside-and-outside-reverse-folds.html

My feeling is that, if you include enough information for a unique solution in the 'instructions' file, you would basically have just invented a rather long winded 3d file format, rather than achieve you goal of (presumably) automatically generate 3D models from paper folding instructions

Ewan
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  • What if certain information, such as initial facing direction and connections sequence were provided? – Matt W Aug 14 '16 at 15:45
  • Yeah, like I say, its then just a matter of solving the equations in turn and modifying the vertexes each time. There is another edge case with right angles you have 3 possible solutions, but you can choose the smallest angle – Ewan Aug 14 '16 at 15:51
  • Sounds like you've done this before..? – Matt W Aug 14 '16 at 16:45
  • I don't mind an algorithm to fold paper. That would be awesome. I just don't know how to do it in code. And yes, that's essentially what I'm looking for, hence the papercraft link. I've no problem with requiring all folds to be 'backwards', such that shapes like footballs are possible. The cat face would be tricky but, I think, possible. – Matt W Aug 14 '16 at 22:15
  • In an attempt to sub-divide the problem, I've posted this question: http://stackoverflow.com/questions/38955073/position-3-polygons-together-in-3d – Matt W Aug 15 '16 at 12:28