Cut Locus Construction using Deformable Simplicial Complexes
Publication: Research - peer-review › Article in proceedings – Annual report year: 2011
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Cut Locus Construction using Deformable Simplicial Complexes. / Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas; Anton, François; Markvorsen, Steen.
In: 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2011. p. 134-141.Publication: Research - peer-review › Article in proceedings – Annual report year: 2011
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RIS
TY - GEN
T1 - Cut Locus Construction using Deformable Simplicial Complexes
A1 - Misztal,Marek Krzysztof
A1 - Bærentzen,Jakob Andreas
A1 - Anton,François
A1 - Markvorsen,Steen
AU - Misztal,Marek Krzysztof
AU - Bærentzen,Jakob Andreas
AU - Anton,François
AU - Markvorsen,Steen
PB - IEEE
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://i.cs.hku.hk/~isvd2011/
U2 - 10.1109/ISVD.2011.26
DO - 10.1109/ISVD.2011.26
SN - 978-1-4577-1026-1
BT - 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)
T2 - 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)
SP - 134
EP - 141
ER -