Optimizing triangulations by curvature equalization

Triangulated irregular networks (TINs) are an attractive form of surface approximation because triangle vertices and edges may be adoptively selected to produce a good fit with a minimal number of triangles. Finding methods for selecting these vertices and edges, however, is still an active area of research. Numerous refinement algorithms have been proposed, but these may produce more triangles than necessary. In this paper we present an algorithm that attempts to improve a triangulation by shifting the vertices so that curvature within the triangles is nearly equal. In addition, unnecessary triangles are removed. We finish with results produced by running this algorithm on simple geometric surfaces and real terrain data.