Calculus of Variations and Geometric Measure Theory

F. Générau - E. Oudet - B. Velichkov

Numerical computation of the cut locus via a variational approximation of the distance function

created by velichkov on 22 Jun 2020
modified on 13 Nov 2026

[BibTeX]

Published Paper
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Inserted: 22 jun 2020
Last Updated: 13 nov 2026

Journal: ESAIM: M2AN
Year: 2022
Doi: https://doi.org/10.1051/m2an/2021088

Abstract:

We propose a new method for the numerical computation of the cut locus of a compact submanifold of $\mathbb{R}^3$ without boundary. The method is based on a convex variational problem with conic constraints, with proven convergence. We illustrate the versatility of our approach by the approximation of Voronoi cells on embedded surfaces of $\mathbb{R}^3$.


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