TY - GEN

T1 - Well-centered planar triangulation - An iterative approach

AU - Vanderzee, Evan

AU - Hirani, Anil N.

AU - Guoy, Damrong

AU - Ramos, Edgar

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram). This may be useful in scientific computing, for example, in discrete exterior calculus, in covolume method, and in space-time meshing. For some connectivities with no well-centered configurations, we present preprocessing steps that increase the possibility of finding a well-centered configuration. We show the results of applying our energy minimization approach to small and large meshes, with and without holes and gradations. Results are generally good, but in certain cases the method might result in inverted elements.

AB - We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram). This may be useful in scientific computing, for example, in discrete exterior calculus, in covolume method, and in space-time meshing. For some connectivities with no well-centered configurations, we present preprocessing steps that increase the possibility of finding a well-centered configuration. We show the results of applying our energy minimization approach to small and large meshes, with and without holes and gradations. Results are generally good, but in certain cases the method might result in inverted elements.

UR - http://www.scopus.com/inward/record.url?scp=84878193112&partnerID=8YFLogxK

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U2 - 10.1007/978-3-540-75103-8_7

DO - 10.1007/978-3-540-75103-8_7

M3 - Conference contribution

AN - SCOPUS:84878193112

SN - 9783540751021

T3 - Proceedings of the 16th International Meshing Roundtable, IMR 2007

SP - 121

EP - 138

BT - Proceedings of the 16th International Meshing Roundtable, IMR 2007

T2 - 16th International Meshing Roundtable, IMR 2007

Y2 - 14 October 2007 through 17 October 2007

ER -