36 citations · 92 across the 8 of their papers we have counts for
11 papers
Local criteria for triangulation of manifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh +1
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are pr…
An obstruction to Delaunay triangulations in Riemannian manifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh +1
Delaunay has shown that the Delaunay complex of a finite set of points of Euclidean space triangulates the convex hull of , provided that satisfies a mild…
Barycentric coordinate neighbourhoods in Riemannian manifolds
Ramsay Dyer, Gert Vegter, Mathijs Wintraecken
We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourho…
An elementary approach to tangent space variation on Riemannian submanifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We give asymptotically tight estimates of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifolds. We show…
A probabilistic approach to reducing the algebraic complexity of computing Delaunay triangulations
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
Computing Delaunay triangulations in involves evaluating the so-called in\_sphere predicate that determines if a point lies inside, on or outside the sphere circ…
Only distances are required to reconstruct submanifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh +1
In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data stru…
Riemannian simplices and triangulations
Ramsay Dyer, Gert Vegter, Mathijs Wintraecken
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension , and exploit these simplices to obtain criteria for triangulating…
Delaunay triangulation of manifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean spa…
Delaunay stability via perturbations
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting pert…
The Stability of Delaunay Triangulations
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of -generic point sets are thick. Equipped…
Constructing Intrinsic Delaunay Triangulations of Submanifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the s…