PARAMETRIC TILINGS AND SCATTERED DATA APPROXIMATION

Abstract

This paper is concerned with methods for mapping meshes in ℝ3 to meshes in ℝ2 in such a way that the local geometry of the mesh is as far as possible preserved. Two linear methods are analyzed and compared. The first, which is more general and more stable, is based on convex combinations while the second is based on minimizing weighted squared lengths of edges. These methods can be used to approximate scattered data points in ℝ3 with smooth parametric spline surfaces.