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cs.CG2024
Manifolds of positive reach, differentiability, tangent variation, and attaining the reach
André Lieutier, Mathijs Wintraecken
This paper contains three main results. Firstly, we give an elementary proof of the following statement: Let be a (closed, in both the geometrical and topological sense of the…
cs.CG2024
A free lunch: manifolds of positive reach can be smoothed without decreasing the reach
Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken
Assumptions on the reach are crucial for ensuring the correctness of many geometric and topological algorithms, including triangulation, manifold reconstruction and learning, homot…
cs.CG2024
When alpha-complexes collapse onto codimension-1 submanifolds
Dominique Attali, Mattéo Clémot, Bianca B. Dornelas +1
Given a finite set of points sampling an unknown smooth surface , our goal is to triangulate based solely on . Assuming $\m…