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.
Keywords: Calculus of variation, cut locus, relaxation, manifold
@article{M2AN_2022__56_1_105_0,
author = {G\'en\'erau, Fran\c{c}ois and Oudet, Edouard and Velichkov, Bozhidar},
title = {Numerical computation of the cut locus \protect\emph{via} a variational approximation of the distance function},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {105--120},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {1},
doi = {10.1051/m2an/2021088},
mrnumber = {4376271},
zbl = {1485.49020},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021088/}
}
TY - JOUR AU - Générau, François AU - Oudet, Edouard AU - Velichkov, Bozhidar TI - Numerical computation of the cut locus via a variational approximation of the distance function JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 105 EP - 120 VL - 56 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021088/ DO - 10.1051/m2an/2021088 LA - en ID - M2AN_2022__56_1_105_0 ER -
%0 Journal Article %A Générau, François %A Oudet, Edouard %A Velichkov, Bozhidar %T Numerical computation of the cut locus via a variational approximation of the distance function %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 105-120 %V 56 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021088/ %R 10.1051/m2an/2021088 %G en %F M2AN_2022__56_1_105_0
Générau, François; Oudet, Edouard; Velichkov, Bozhidar. Numerical computation of the cut locus via a variational approximation of the distance function. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 1, pp. 105-120. doi: 10.1051/m2an/2021088
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