Given any origami shape, Can It be mathematically defined say any function or equation that can satisfy all points of the origami shape ?
If so, How such functions for any origami can be derived with some general steps ?
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This question is quite unclear, but there is a lot of mathematics about origami, see here for example: http://erikdemaine.org/folding/ – Hans Lundmark Apr 25 '18 at 08:47
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1Origamis are very mathematical. MIT even has an open course ware course on them: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/index.htm It has lecture videos, too. – ploosu2 Apr 25 '18 at 14:42
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If you identify a point on the piece of paper you start with as a triple of coordinates (when you start folding paper, the thickness quickly becomes a factor, so I think you need to take the third dimension in account) and place the resulting shape in a coordinate system, it's obvious that you can then define a function mapping any point in the paper with the corresponding point in the resulting shape.
I'm not good at (not even particularly interested in) origami, but if you have a description of how to come from a piece of paper, containing all (including lifting, turning etc.) the transformations you should do to the piece of paper, I can't see a (theoretical) problem in using those on the coordinates to find a function, but I don't see use. And going the opposite way seems hard.
