Curvature corrected estimates for geodesic arc-length
Differential Geometry
2015-12-14 v1
Abstract
We will develop simple relations between the arc-lengths of a pair of geodesics that share common end-points. The two geodesics differ only by the requirement that one is constrained to lie in a subspace of the parent manifold. We will present two applications of our results. In the first example we explore the convergence of Gaussian curvature estimates on a simple triangular mesh. The second example demonstrates an improved error estimate for the area of a Schwarz lantern.
Cite
@article{arxiv.1512.03461,
title = {Curvature corrected estimates for geodesic arc-length},
author = {Leo Brewin},
journal= {arXiv preprint arXiv:1512.03461},
year = {2015}
}