Name
Abstract | ||
|---|---|---|
In this paper we present a method for appproximating cut loci for a given point p on Riemannian 2D manifolds, closely related to the notion of Voronoi diagrams. Our method finds the cut locus by advecting a front of points equally distant from p along the geodesies originating at p and finding the lines of self-intersections of the front in the parametric space. This becomes possible by using the deformable simplicial complexes (DSC), method for deformable interface tracking. DSC provide a simple collision detection mechanism, allows for interface topology control, and does not require the domain to have disk topology. We test our method for tori of revolution and compare our results to the benchmark ones from . The method, however, is generic and can be easily adapted to construct cut loci for other manifolds of genera other than 1. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/ISVD.2011.26 | Voronoi Diagrams in Science and Engineering |
Keywords | Field | DocType |
disk topology,cut locus construction,interface topology control,deformable interface tracking,deformable simplicial complexes,appproximating cut locus,parametric space,simple collision detection mechanism,voronoi diagram,deformable simplicial complex,point p,cut locus,collision detection,measurement,manifolds,topology,kinetics,simplicial complex,skeleton,voronoi diagrams,computational geometry,edge detection,medial axis | Topology,Collision detection,Computational geometry,Medial axis,Torus,Cut locus,Voronoi diagram,Geodesic,Manifold,Mathematics | Conference |
ISBN | Citations | PageRank |
978-0-7695-4483-0 | 2 | 0.38 |
References | Authors | |
5 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marek Krzysztof Misztal | 1 | 72 | 4.57 |
| Jakob Andreas Bærentzen | 2 | 58 | 7.67 |
| Francois Anton | 3 | 60 | 11.19 |
| Steen Markvorsen | 4 | 3 | 1.54 |