Cut Locus Construction using Deformable Simplicial Complexes

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2011

Standard

Cut Locus Construction using Deformable Simplicial Complexes. / Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas; Anton, François; Markvorsen, Steen.

2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2011. p. 134-141.

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2011

Harvard

Misztal, MK, Bærentzen, JA, Anton, F & Markvorsen, S 2011, 'Cut Locus Construction using Deformable Simplicial Complexes'. in 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, pp. 134-141., 10.1109/ISVD.2011.26

APA

Misztal, M. K., Bærentzen, J. A., Anton, F., & Markvorsen, S. (2011). Cut Locus Construction using Deformable Simplicial Complexes. In 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). (pp. 134-141). IEEE. 10.1109/ISVD.2011.26

CBE

Misztal MK, Bærentzen JA, Anton F, Markvorsen S. 2011. Cut Locus Construction using Deformable Simplicial Complexes. In 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE. pp. 134-141. Available from: 10.1109/ISVD.2011.26

MLA

Misztal, Marek Krzysztof et al. "Cut Locus Construction using Deformable Simplicial Complexes". 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE. 2011. 134-141. Available: 10.1109/ISVD.2011.26

Vancouver

Misztal MK, Bærentzen JA, Anton F, Markvorsen S. Cut Locus Construction using Deformable Simplicial Complexes. In 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE. 2011. p. 134-141. Available from: 10.1109/ISVD.2011.26

Author

Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas; Anton, François; Markvorsen, Steen / Cut Locus Construction using Deformable Simplicial Complexes.

2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2011. p. 134-141.

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2011

Bibtex

@inbook{2aa8f6e1680e4a33a1b38a0abd4ba46a,
title = "Cut Locus Construction using Deformable Simplicial Complexes",
publisher = "IEEE",
author = "Misztal, {Marek Krzysztof} and Bærentzen, {Jakob Andreas} and François Anton and Steen Markvorsen",
year = "2011",
doi = "10.1109/ISVD.2011.26",
isbn = "978-1-4577-1026-1",
pages = "134-141",
booktitle = "2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD)",

}

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 -