1 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark
In this report, a technique for optimizing 3D triangulations is proposed. The method seeks to minimize an energy defined as a sum of energy terms for each edge in a triangle mesh. The main contribution is a novel per edge energy which strikes a balance between penalizing dihedral angle yet allowing sharp edges. The energy is minimized using edge swapping, and this can be done either in a greedy fashion or using simulated annealing. The latter is more costly, but effectively avoids local minima. The method has been used on a number of models. Particularly good results have been obtained on digital terrain models. It is demonstrated how the method has been able to recapture sharp edges which are clearly present in the data but not reflected by the original triangulation of the elevation points.
simulated annealing; optimization; data dependent triangulation