Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Dyer, Ramsay"'
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 presented in local coordinate charts for M, and ensure that H is a homeo
Externí odkaz:
http://arxiv.org/abs/1803.07642
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be d
Externí odkaz:
http://arxiv.org/abs/1612.02905
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 neighbourhood on which the Riemannian barycentric coordinates of a set of $n+1$ p
Externí odkaz:
http://arxiv.org/abs/1606.01585
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 that the result follows directly from structural properties of local f
Externí odkaz:
http://arxiv.org/abs/1506.06346
Computing Delaunay triangulations in $\mathbb{R}^d$ involves evaluating the so-called in\_sphere predicate that determines if a point $x$ lies inside, on or outside the sphere circumscribing $d+1$ points $p_0,\ldots ,p_d$. This predicate reduces to e
Externí odkaz:
http://arxiv.org/abs/1505.05454
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 structures such as Voronoi diagrams or Delaunay complexes. Our algorithm u
Externí odkaz:
http://arxiv.org/abs/1410.7012
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension $n$, and exploit these simplices to obtain criteria for triangulating compact Riemannian manifolds. These geometric simplices are defined us
Externí odkaz:
http://arxiv.org/abs/1406.3740
We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample points and an atlas on a compact manifold, a
Externí odkaz:
http://arxiv.org/abs/1311.0117
Publikováno v:
Int. J. Comput. Geom. Appl. 24, 125 (2014)
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 perturbed point set has quantifiable stability with respect to the metric
Externí odkaz:
http://arxiv.org/abs/1310.7696
Publikováno v:
Int. J. Comput. Geom. Appl. 23, 303 (2013)
We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of $\delta$-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulati
Externí odkaz:
http://arxiv.org/abs/1304.2947