Saturday, January 11, 2014

Algorithm to sort edge list of simple polygon for 2D and 3D

Sometimes it is handy to sort an edge list. In this case I needed an algorithm to test for concavity of a simple 3D polygon with just one face. You can also apply the procedure on 2D because it just sorts an edge list that could contain either 2D or 3D vertices.

The polygons were made in Blender v.2.67, so the script had to be written in Python and executed via the Run Script button in the text editor. I didn't want to use fancy algorithms to sort edges because we're dealing with simple polygons, so I ended up writing my own. As a side note, the edge-angle checkbox in Blender, which can be used to see if a polygon is convex or concave didn't work for me, so I had no other choice but to first sort edges before I can apply angle calculations on consecutive vertices. Suggestions for improvements are welcome and hopefully it helps someone else who had to deal with the same (or similar) issues in Blender!

The basic idea is that you build up your sorted edge list e step by step, starting by adding a first element. Next, there is a main loop that is as long as all the elements m contained in the unsorted edge list mesh.edges. Each edge contains a start vertex [0] and an end vertex [1]. What I did was: at each step you search for a match between the last inserted [1] of e and a target [0] of m. Sometimes, edges are added in a reversed direction in mesh.edges, so if the first search didn't find anything, than perhaps looking in the opposite direction (when [1] of m is equal to [1] of e but it was not already added to e), would result in a match. When this happens, the direction of the edge has to be switched, and a duplicate of the data is created to be able to switch the direction and add this switched direction into e. The drawback is that now, in the main search, the algorithm has to check if switched edges have not been added into e as well. I've tested it with meshes with 100+ vertices, and I didn't see any performance issues, but like I said before suggestions for improvements are more than welcome :)

Prerequisites:

  1. Be sure to be in Edit Mode.
  2. Be sure to be in Edge Select Mode.
  3. Be sure to have all edges selected.

Here is the script:

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