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

François Générau (1) , Edouard Oudet (1) , Bozhidar Velichkov (2)

1 EDP - Equations aux Dérivées Partielles
2 Dipartimento di Matematica [Pisa]

We propose a new method for the numerical computation of the cut locus of a compact submanifold of ℝ3 without boundary. This 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 ℝ3.

Mots clés: Calculus of variation; cut locus; relaxation; manifold

Domaines: Mathématiques [math]

François Générau, Edouard Oudet, Bozhidar Velichkov. Numerical computation of the cut locus via a variational approximation of the distance function. ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (1), pp.105-120. ⟨10.1051/m2an/2021088⟩. ⟨hal-03560972⟩