4 papers
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…
Delaunay-like Triangulation of Smooth Orientable Submanifolds by L1-Norm Minimization
Dominique Attali, André Lieutier
In this paper, we study the shape reconstruction problem, when the shape we wish to reconstruct is an orientable smooth d-dimensional submanifold of the Euclidean space. Assuming w…
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…
A free lunch: manifolds of positive reach can be smoothed without decreasing the reach
Hana Dal Poz KouÅimská, 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…