Дискретизация функционально заданных поверхностей

Abstract

Surface discretization (triangulation) is a well- known topic of computational geometry. A triangulation of a set of points is a way of connecting them to form a simple triangle. The existing algorithms of triangulation differ in terms of their computational complexity, the frequency of the function evaluation (sampling), and the resulting mesh quality. High efficiency of a triangulation algorithm can be achieved by the use of optimization techniques, which can reduce the complexity of the basic algorithm. A new approach for accurate triangulation of functionally defined surfaces using perturbation functions is proposed. For analyzing how close the evolving meshes approaches the functionally defined surface two error metrics and uniformity are used. The metrics measure deviations of the vertices from the functionally defined surface and deviations of mesh normal from the normal of the functionally defined surface.