| Issue |
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
|
|
|---|---|---|
| Page(s) | 105 - 120 | |
| DOI | https://doi.org/10.1051/m2an/2021088 | |
| Published online | 07 February 2022 | |
Numerical computation of the cut locus via a variational approximation of the distance function
1
Laboratoire Jean Kuntzmann (LJK), Université Joseph Fourier, Bâtiment IMAG, 700 Avenue Centrale, 38041 Grenoble Cedex 9, France
2
Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes, Bâtiment IMAG, 700 Avenue Centrale, 38041 Grenoble Cedex 9, France
3
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127 Pisa, Italy
* Corresponding author: edouard.oudet@univ-grenoble-alpes.fr
Received:
16
June
2020
Accepted:
20
December
2021
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.
Mathematics Subject Classification: 49J45 / 35R35 / 49M05 / 35J25
Key words: Calculus of variation / cut locus / relaxation / manifold
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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