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



Inserted: 22 jun 2020
Last Updated: 22 jun 2020

Year: 2020


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 $\mathbb{R}^3$.