Arbitrary order principal directions and how to compute them
Computational Geometry
2021-11-11 v1 Graphics
Abstract
Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R^3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces.
Keywords
Cite
@article{arxiv.2111.05800,
title = {Arbitrary order principal directions and how to compute them},
author = {Julie Digne and Sébastien Valette and Raphaëlle Chaine and Yohann Béarzi},
journal= {arXiv preprint arXiv:2111.05800},
year = {2021}
}