Application of oriented methods for computing shortest paths and principal curvatures on triangle surfaces

Abstract

Abstract The paper considers two problems: computation of shortest paths on triangle surfaces and calculation of principal curvatures at vertices of triangle surfaces. A technique that allows us to compute smoother and shorter paths using intermediate admissible directions and linear interpolation of potential functions is proposed. Conventional methods that compute the curvature in nodes of triangle surfaces are based on processing only adjacent vertices. They are non stable because triangle meshes contain frequently oscillating errors in positions of the vertices. We propose a simple practical method that accounts for larger neighborhoods of vertices. The kriging method aimed to the sparse representation of specific surface parts (aesthetic regions) is sketched. Preliminary numerical results are presented.