Body: <p>By open up I mean slightly open up so that a theoretical structure of panels with no width looks three-dimensional. The original structure being an ideal object where any number several panels can occupy the same region of space (plane).</p>
  
  <p>To concretize what I mean by rigid structure of panels, let's take what's on my profile picture. I'm including here a larger version of that object:</p>
  
  <p><a href="https://i.sstatic.net/m9Uxz.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/m9Uxz.jpg" alt="enter image description here"></a></p>
  
  <p>An origami figure is folded from a square and, unlike this simple example in the image, it can be very convoluted, with layers upon layers.</p>
  
  <p>Let's say that if I have an ideal, theoretical and flat model of an origami picture and by flat I mean the faces are on planes but not necessarily on a single plane. For example all of faces of the figure in the image would be in one plane, but there could be figures with more planes; think of animals with ears, flippers, etc.</p>
  
  <p>I would like to open up those parts that hinge on a theoretical segment (relatively easy) or curve or make a triangle of the corners of those faces that have two adjacent faces with no connections, open up a set of several faces that allow such opening of which the image is a good example.</p>
  
  <p>So far I have tried programming rules for different structures suchs as flaps, ends, wrap-arounds... However there are three no small problems. First, it's extremely challenging to take into account all the corner cases and possibilities. I suspect it sounds simpler that it really is, but I don't want to digress with explanations. Second, the code is not maintenable. It's difficult to put into words rules that have to be visualized. Third it's very difficult to unit test and debug.</p>
  
  <p>I strongly suspect that there must be some Artificial Intelligence techniques for doing this. Would you be so kind as to point me in the right direction? Just in a general way, without needing to go much into detail.</p>
  
  <p>Let me know if I should include more info or code.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-19T20:47:55.713Z
Comments.Text: Welcome to AI!  (I edited slightly, assuming "IA" was a typo... is this correct?)  Have you looked at Erik Demaine's work?  He's a major origami force, and wrote a nice paper on Algorithmic Combinatorial Game Theory.  You can [find his published papers here](http://erikdemaine.org/papers/).  This paper, [Geometric Folding Algorithms: Linkages, Origami, Polyhedra](http://erikdemaine.org/papers/GFALOP/)  looks like it might apply.
Comments.UserDisplayName: DukeZhou
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-24T15:58:38.260Z
Comments.Text: thanks @DukeZhou, there is a lot of info to take in there and it seems to have a more theoretical and geometrical approach, but I thank you for the link and I will take a closer look as soon as I have some spare time
Comments.UserDisplayName: DPM
Tags: <algorithm><heuristics>
Title: How to open up a rigid structure made of connected panels?
UserDisplayName: DPM
ThreadText: # How to open up a rigid structure made of connected panels?
  
  (Asked by: username_0 on 2018-01-19)
  
  By open up I mean slightly open up so that a theoretical structure of panels with no width looks three-dimensional. The original structure being an ideal object where any number several panels can occupy the same region of space (plane).
  
  To concretize what I mean by rigid structure of panels, let's take what's on my profile picture. I'm including here a larger version of that object:
  
  [![enter image description here](https://i.sstatic.net/m9Uxz.jpg)](https://i.sstatic.net/m9Uxz.jpg)
  
  An origami figure is folded from a square and, unlike this simple example in the image, it can be very convoluted, with layers upon layers.
  
  Let's say that if I have an ideal, theoretical and flat model of an origami picture and by flat I mean the faces are on planes but not necessarily on a single plane. For example all of faces of the figure in the image would be in one plane, but there could be figures with more planes; think of animals with ears, flippers, etc.
  
  I would like to open up those parts that hinge on a theoretical segment (relatively easy) or curve or make a triangle of the corners of those faces that have two adjacent faces with no connections, open up a set of several faces that allow such opening of which the image is a good example.
  
  So far I have tried programming rules for different structures suchs as flaps, ends, wrap-arounds... However there are three no small problems. First, it's extremely challenging to take into account all the corner cases and possibilities. I suspect it sounds simpler that it really is, but I don't want to digress with explanations. Second, the code is not maintenable. It's difficult to put into words rules that have to be visualized. Third it's very difficult to unit test and debug.
  
  I strongly suspect that there must be some Artificial Intelligence techniques for doing this. Would you be so kind as to point me in the right direction? Just in a general way, without needing to go much into detail.
  
  Let me know if I should include more info or code.
  
  **Tags:** algorithm, heuristics
  
  > **Comments:**
  > **username_1**: Welcome to AI!  (I edited slightly, assuming "IA" was a typo... is this correct?)  Have you looked at Erik Demaine's work?  He's a major origami force, and wrote a nice paper on Algorithmic Combinatorial Game Theory.  You can [find his published papers here](http://erikdemaine.org/papers/).  This paper, [Geometric Folding Algorithms: Linkages, Origami, Polyhedra](http://erikdemaine.org/papers/GFALOP/)  looks like it might apply.  
  > **username_0**: thanks @username_1, there is a lot of info to take in there and it seems to have a more theoretical and geometrical approach, but I thank you for the link and I will take a closer look as soon as I have some spare time  
  
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  ## 0 answers
  
  