3D Delaunay triangulation of 1 billion points on a PC

Of course, there is not enough memory on a PC with 16GB RAM, and tetrahedra constructed have to be output to leave rooms for the creation of new tetrahedra in the next round of point insertion. A segmental zonal insertion scheme is developed, in which large data sets of more than 100 million points are partitioned into zones, each of which is triangulated in turn by the parallel zonal insertion module. An overlapping zone between two steps of insertion has to be allowed to ensure Delaunay tetrahedra formed at the boundary between two insertion zones.Tetrahedra between zones can be easily eliminated by the minimum vertex allocation method. The collection of all the tetrahedra from each insertion zone/step will produce the required triangulation for the point set. As the work of each typical step for the insertion of an equal number of points is very much similar, the processing time bears roughly a linear relationship with the number of points in the set, at a construction rate of more than 5 million Delaunay tetrahedra per second for the triangulation of 1 billion randomly generated points. Segmental zonal insertion scheme to triangulate points zone by zone.Points within a zone are triangulated by a parallel insertion process.There is no limit to the number of points in the triangulation.Triangulation time is roughly linear with respect to the number of points in the set.More than 5 million tetrahedra are constructed per second for a set of 1 billion points.

[1]  Nikos Chrisochoides,et al.  Parallel Delaunay mesh generation kernel , 2003 .

[2]  H. Borouchaki,et al.  Fast Delaunay triangulation in three dimensions , 1995 .

[3]  Jean-Michel Moreau,et al.  A probabilistic result on multi-dimensional Delaunay triangulations, and its application to the 2D case , 2000, Comput. Geom..

[4]  S. H. Lo,et al.  Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain , 2005 .

[5]  Guy E. Blelloch,et al.  Design and Implementation of a Practical Parallel Delaunay Algorithm , 1999, Algorithmica.

[6]  S. H. Lo,et al.  3D Delaunay triangulation of non-uniform point distributions , 2014 .

[7]  Tilo Beyer,et al.  Parallel dynamic and kinetic regular triangulation in three dimensions , 2005, Comput. Phys. Commun..

[8]  P. George,et al.  OPTIMAL DELAUNAY POINT INSERTION , 1996 .

[9]  Mariette Yvinec,et al.  Voronoi Diagrams in Higher Dimensions under Certain Polyhedral Distance Functions , 1998, Discret. Comput. Geom..

[10]  Jianya Gong,et al.  ParaStream: A parallel streaming Delaunay triangulation algorithm for LiDAR points on multicore architectures , 2011, Comput. Geosci..

[11]  Tyng-Ruey Chuang,et al.  Parallel divide‐and‐conquer scheme for 2D Delaunay triangulation , 2006, Concurr. Comput. Pract. Exp..

[12]  H. Si.  Constrained Delaunay tetrahedral mesh generation and refinement , 2010 .

[13]  Ivana Kolingerová,et al.  Parallel Delaunay triangulation in E3: make it simple , 2003, The Visual Computer.

[14]  Ivana Kolingerová,et al.  Optimistic parallel Delaunay triangulation , 2002, The Visual Computer.

[15]  YingLiang Ma,et al.  A Parallelized Surface Extraction Algorithm for Large Binary Image Data Sets Based on an Adaptive 3-D Delaunay Subdivision Strategy , 2008, IEEE Transactions on Visualization and Computer Graphics.

[16]  David L. Millman,et al.  Parallel geometric algorithms for multi-core computers , 2010, Comput. Geom..

[17]  Jirí Zára,et al.  Parallel Delaunay triangulation in E2 and E3 for computers with shared memory , 2005, Parallel Comput..

[18]  S. H. Lo,et al.  Parallel Delaunay triangulation in three dimensions , 2012 .

[19]  Nikos Chrisochoides,et al.  Guaranteed-quality parallel Delaunay refinement for restricted polyhedral domains , 2004, Comput. Geom..

[20]  Olivier Devillers,et al.  Perturbations for Delaunay and weighted Delaunay 3D triangulations , 2011, Comput. Geom..

[21]  Tyng-Ruey Chuang,et al.  Efficient parallel implementations of near Delaunay triangulation with High Performance Fortran , 2004, Concurr. Pract. Exp..

[22]  Andrey N. Chernikov,et al.  A template for developing next generation parallel Delaunay refinement methods , 2010 .