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Article: 3D Delaunay triangulation of 1 billion points on a PC
Title  3D Delaunay triangulation of 1 billion points on a PC 

Authors  
Issue Date  2015 
Publisher  Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/finel 
Citation  Finite Elements in Analysis and Design, 2015, v. 102103, p. 6573 How to Cite? 
Abstract  Of course, there is not enough memory on a PC with 16 GB 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. 
Persistent Identifier  http://hdl.handle.net/10722/211001 
ISSN  2015 Impact Factor: 2.175 2015 SCImago Journal Rankings: 1.278 
DC Field  Value  Language 

dc.contributor.author  Lo, SH   
dc.date.accessioned  20150625T07:28:43Z   
dc.date.available  20150625T07:28:43Z   
dc.date.issued  2015   
dc.identifier.citation  Finite Elements in Analysis and Design, 2015, v. 102103, p. 6573   
dc.identifier.issn  0168874X   
dc.identifier.uri  http://hdl.handle.net/10722/211001   
dc.description.abstract  Of course, there is not enough memory on a PC with 16 GB 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.   
dc.language  eng   
dc.publisher  Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/finel   
dc.relation.ispartof  Finite Elements in Analysis and Design   
dc.title  3D Delaunay triangulation of 1 billion points on a PC   
dc.type  Article   
dc.identifier.email  Lo, SH: hreclsh@hkucc.hku.hk   
dc.identifier.authority  Lo, SH=rp00223   
dc.identifier.doi  10.1016/j.finel.2015.05.003   
dc.identifier.volume  102103   
dc.identifier.spage  65   
dc.identifier.epage  73   
dc.publisher.place  Netherlands   