8 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…
The Singular Source of Vineyard Monodromy
Erin W. Chambers, Christopher Fillmore, Shankha Shubhra Mukherjee +3
Vineyards, or time-varying families of persistence diagrams, are widely used in topological data analysis (TDA) pipelines to track how topological features change and evolve as a p…
Braiding vineyards
Erin Chambers, Christopher Fillmore, Elizabeth Stephenson +1
In this work, we introduce and study what we believe is an intriguing and, to the best of our knowledge, previously unknown connection between two areas in computational topology,…
Error estimates for the interpolation and approximation of gradients and vector fields on protected Delaunay meshes in
David M. Williams, Mathijs Wintraecken
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or ap…
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…