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

Journal of Physics Conference Series, vol. 2514, pp. 012005

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.

Authors 4

1. Nikolai D. Botkin corresponding

   Technical University of Munich

   Affiliation as printed

   Mathematical Faculty, Technical University of Munich, Boltzmannstraße 3, 85748 Garching b. München, Germany

2. Laszlo Kovacs

   TUM Klinikum · Technical University of Munich

   Affiliation as printed

   Research Group-Computer Aided Plastic Surgery (CAPS), Department of Plastic Surgery and Hand Surgery, Klinikum rechts der Isar, Technical University of Munich, Ismaninger Straße 22, 81675 München, Germany

3. Stefan Raith Aachen Clinic of Oral and Maxillofacial Surgery

   RWTH Aachen University

   Affiliation as printed

   Clinic of Oral and Maxillofacial Surgery, RWTH Aachen University, Pauwelsstraße 30, 52074 Aachen, Germany

4. A. Volf

   TUM Klinikum · Technical University of Munich

   Affiliation as printed

   Research Group-Computer Aided Plastic Surgery (CAPS), Department of Plastic Surgery and Hand Surgery, Klinikum rechts der Isar, Technical University of Munich, Ismaninger Straße 22, 81675 München, Germany