A systematic review of algorithms with linear-time behaviour to generate Delaunay and Voronoi tessellations
نویسندگان
چکیده
Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay and/or Voronoi tessellations is presented.
منابع مشابه
Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations
A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...
متن کاملImproved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation
Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by non-linear optimisation algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared to conventional random initialisation, certain low-discrepancy point distributions help convergence towards more spatially regular resu...
متن کاملMeshing the Universe: Identifying Voids in Cosmological Simulations Through In Situ Parallel Voronoi Tessellation
Mesh tessellations are effective constructs for the visualization and analysis of point data, because they transform sparse discrete samples into dense and continuous functions. We present a prototype method for computing a Voronoi tessellation in parallel from large particle datasets; the same method, in principle, is applicable to the Delaunay. Computing large tessellations is computationally...
متن کامل2D Centroidal Voronoi Tessellations with Constraints
We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation. We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges. The clipping itself i...
متن کاملThe Duality of Geodesic Voronoi/Delaunay Diagrams For An Intrinsic Discrete Laplace-Beltrami Operator on Simplicial Surfaces
An intrinsic discrete Laplace-Beltrami operator on simplicial surfaces S proposed in [2] was established via an intrinsic Delaunay tessellation on S. Up to now, this intrinsic Delaunay tessellations can only be computed by an edge flipping algorithm without any provable complexity analysis. In the paper, we show that the intrinsic Delaunay triangulation can be obtained from a duality of geodesi...
متن کامل