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

François Générau 1 Edouard Oudet 1, * Bozhidar Velichkov 2 
* Corresponding author
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : 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.
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Submitted on : Monday, February 7, 2022 - 9:58:55 PM
Last modification on : Thursday, February 10, 2022 - 4:10:10 PM
Long-term archiving on: : Sunday, May 8, 2022 - 7:34:00 PM

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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, EDP Sciences, 2022, 56 (1), pp.105-120. ⟨10.1051/m2an/2021088⟩. ⟨hal-03560972⟩

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