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We propose a new method for the numerical computation of the cut locus of a compact submanifold of ℝ 3  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 ℝ 3 .

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