Best data-dependent triangulations (Q1576443)

The first step in evaluation a surface is to construct a triangulation of the data. A ``good'' triangulation can help to solve many problems, i.e., in scattered data interpolation and approximation, or in applications recovering 3-D objects. Therefore, in this paper, as a measure of the quality of triangulation methods various differential geometrical properties, namely integral absolute Gaussian curvature, integral absolute mean curvature and area are considered. A comparison is made with data-dependent triangulation methods existing in the literature. The most promising criterion seems to be minimizing absolute mean curvature.