4 papers
Simplicial subdivision of simplices of arbitrary dimension in spaces of constant curvature with bounded quality
Jean-Daniel Boissonnat, Hana Dal Poz Kourimska, Arijit Ghosh +1
In 1942, Freudenthal showed that a simplex in Euclidean space can be subdivided such that the quality (well-shapedness of the simplex, quantified in terms of e.g. fatness) of the s…
Generalized altitudes and their bounds
Hana Dal Poz Kourimska, Mathijs Wintraecken
We introduce generalized altitudes of a simplex, extending the usual vertex-to-opposite-face altitude to arbitrary pairs of opposite faces. These quantities encode the relative pos…
Bregman-Hausdorff divergence: strengthening the connections between computational geometry and machine learning
Tuyen Pham, Hana Dal Poz KouÅimská, Hubert Wagner
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures…
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…