Optimal quadtree construction algorithms
Computer Vision, Graphics, and Image Processing
A comparison of sequential Delaunay triangulation algorithms
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Guaranteed-quality parallel Delaunay refinement for restricted polyhedral domains
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Concurrency and Computation: Practice & Experience
Parallel divide-and-conquer scheme for 2D Delaunay triangulation: Research Articles
Concurrency and Computation: Practice & Experience
A template for developing next generation parallel Delaunay refinement methods
Finite Elements in Analysis and Design
Parallel geometric algorithms for multi-core computers
Computational Geometry: Theory and Applications
Data-Parallel Octrees for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
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A generic parallel Delaunay triangulation scheme by means of zonal partition of points is presented. For efficient Delaunay triangulation, points are first partitioned into cells, each of which is allocated roughly equal number of points. The cells can be naturally grouped into zones, in which Delaunay triangulation is constructed by simultaneous point insertion cell by cell within each zone. Delaunay triangles/tetrahedra at the boundary between zones can be created in parallel by adding layers of cells at the boundary of each zone to ensure circumcircles(circumspheres) of boundary triangles(tetrahedra) contain no points in their interior. Redundant triangles(tetrahedra) at the boundary between zones can be easily eliminated by individual processors in a completely independent manner by means of the elegant minimum vertex allocation scheme, such that a simplex with k vertices belonging to zones (z1, z2,... zk) is allocated to zone z=min (z1, z2,... zk). A two-dimensional version of the algorithm has been coded in Intel Fortran VS2010. The parallel zonal insertion on a PC can boost the speed of the single-processor insertion by 4.5 times for the insertion of 200 million randomly generated points in 65.7s. The scalability of the parallel zonal insertion algorithm has also been tested on a proper multi-core machine with 12 processors running on OpenMP parallel directives with shared memory. Provided the number of zones is an integral multiple of the number of processors used, almost 100% scalability at 90% efficiency was observed for parallel insertion using 2, 4, 6, 8, 10 and 12 processors, and a 10.6 time speed up was recorded in a parallel insertion of 20 million points in 10x12=120 zones by 12 processors.