Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

Details Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

2003-02-06

arxiv.org/abs/physics/0302018v5

Computer Physics Communications 162, 9-23 (2004)

Physics

Biological Physics

29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibl

Scientific paper

10.1016/j.cpc.2004.06.066

We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.

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