R. Ronfard and J. Rossignac, "Full-range Approximation of Triangulated Polyhedra." Computer Graphics Forum, vol. 15, no. 3, 1996.
I have made the following modifications to their algorithm:
1. When calculating the cost for an edge collapse, they arbitrarily choose which direction to collapse it in. This results in meshes not being simplified as far as they could be. Instead, I always test both collapse directions to see which one has the lower cost.
2. After collapsing vertex v1 to v2, they state that it is only necessary to recalculate costs for edges which have been modified, that is, those edges in the star of v1 or v2. This is incorrect. It is also necessary to recalculate the cost for any edge which shares a vertex with an edge in v1's star.
3. They define the local tesselation error for a face as being proportional to its angle of rotation. I replace the angle by 1-cos(angle). This has the same effect, and saves the need to evalate an acos.
4. Rather than always simplifying the entire mesh, I allow the user to select only a subset of the mesh to be simplified.
5. Their algorithm only works for closed meshes (meshes without a boundary). I have modified it to also work for open meshes.
6. I omit the relaxation step, since this would produce bad results for smoothed meshes.
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