My intention today was to get the triangulate3d code written, but unfortunately, it looks like that isn't going to happen. Things have just been going really slow today. Thus, to adapt the schedule, I think I am going to combine the Triangulation and Finishing of Geometry conversion into a single stage. The combination of these two should be done by the time I laid out for Convert Geometry to be done.
The concept I have for the triangulation code is fairly straightforward. I intend to utilize the MakeMonotone algorithm given in deBerg et. al.'s computational geometry book. (I originally intended to use a Delaunay Triangulation, but I don't think that it's necessary to do all that work - we are given a polygon in 3D, so that makes the problem a little easier than a point cloud). Now, the problem I see is that the MakeMonotone algorithm (that is, break the polygon into y-monotone pieces, then triangulate each of these and combine) works on a 2D polygon. Normally, I thought it would be easiest simply to project the 3D polygon onto a 2D plane, but this doesn't work if the polygon wraps over on itself (consider a polygon like the following: http://www.cosy.sbg.ac.at/~held/projects/triang/spiral_01.gif
). Thus, my idea is to perform the following:
The problem will be to determine the mapping (Note: The removal of holes isn't trivial, but I have an algorithm for it somewhere... I just can't remember where it is at the moment. I will find it. So, I'm going to do everything else first, then add it in later.) I thought about an LSCM-unwrap type of algorithm, but that relies on user cuts. The thing is, that if the polygon is some kind of wierd 3D shape that loops back on itself, then it's no longer a polygon, and I probably can just ignore that case.
The code I have been working on today has been mostly to add a test application, so I can visualize the two versions of a polygon. Ideally, I want to create a split window. The top has the un-triangulated polygon, and the bottom has the triangulated one. To begin with, what I want to do is show the polygon in 3D in the top (the original polygon), then show the polygon in 2D after the mapping in the bottom. I am working on this application, which will be called apptri3dtest, as this is being written.
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