Optimizing triangulations by curvature equalization

An algorithm that attempts to improve a triangulation by shifting the vertices so that curvature within the triangles is nearly equal is presented. Unnecessary triangles are removed. The method is an effective way of guaranteeing that the triangle vertices are points of higher curvature, and that the triangle edges correspond to distinctive edges on the surfaces. Triangulations of surfaces with constant curvature-and hence no distinctive features-will gain nothing from this or any other optimization algorithm. As demonstrated by the results, the techinque of moving triangle vertices can improve some triangulation models. Greatest improvements occur with surfaces characterized by sharp edges, such as the pyramid and ridge models. Less improvement occurs on models that already approximate the surface topology and/or have less distinctive features