Conference paper
Cut Locus Construction using Deformable Simplicial Complexes
Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark1
Department of Informatics and Mathematical Modeling, Technical University of Denmark2
Geometry, Department of Mathematics, Technical University of Denmark3
Department of Mathematics, Technical University of Denmark4
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 geodesics 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, [1]) 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 [2].
The method, however, is generic and can be easily adapted to construct cut loci for other manifolds of genera other than 1.
Language: | English |
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Publisher: | IEEE |
Year: | 2011 |
Pages: | 134-141 |
Proceedings: | 8th International Symposium on Voronoi Diagrams in Science and Engineering |
ISBN: | 1457710269 , 9781457710261 , 0769544835 and 9780769544830 |
Types: | Conference paper |
DOI: | 10.1109/ISVD.2011.26 |
ORCIDs: | Bærentzen, Jakob Andreas , Anton, François and Markvorsen, Steen |
Approximation methods Cut locus Farthest site Voronoi diagram Image edge detection Joining processes Manifolds Measurement Piecewise linear approximation Riemannian 2D manifolds Topology Voronoi diagrams collision detection mechanism computational geometry cut locus construction deformable interface tracking deformable simplicial complexes generalised Voronoi diagram geodesic Voronoi diagram interface topology control kinetic structures medial axis skeleton