Curvature corrected estimates for geodesic arc-length

2015/12/10 by Leo Brewin, Brewin, Leo
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Image and Object Detection Techniques #math.DG

paper · pdf · doi:10.48550/arxiv.1512.03461

arxiv created 2015/12/10 · openalex publication_date 2015/12/10 · arxiv updated 2015/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the convergence of metric and geometric properties of polyhedral surfaces

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