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Re: [cgal-discuss] overlapping in 3D triangulation


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  • From: Camille Wormser <>
  • To:
  • Subject: Re: [cgal-discuss] overlapping in 3D triangulation
  • Date: Tue, 15 Jan 2008 09:44:26 +0100


Basically, this is a polyhedron with five vertices, (0,10,0), (0,0,0), (2,5,6),
(5,7,0) and (1,-1,-4). The simplest triangulation will contain just two tetrahedrons (excluding the cells that contain infinite vertices). However, I find that the result contains overlapping cells, for example, cell [1 0 3 4] overlaps with cell [2 1 3 4]. Is this common to the 3D triangulation feature of CGAL? Or did I misinterpret the result?

Note that 0 is the index of the infinite vertex, in the 9 lines which compose the list of tetrahedra. This means, from your output, that there are 3 tetrahedrons (the ones without 0, which share edge 2-4) and 6 outer faces (the ones with 0). On the other hand, in the last 9 lines of the output, the numbers 0 to 8 represent the 9 tetrahedra that have been listed above:
for example, first line 5 1 6 2 refers to first tet 1 0 3 4 and means
the tet opposite to vertex 1 is tet 5
the tet opposite to vertex 0 is tet 1
the tet opposite to vertex 3 is tet 6
the tet opposite to vertex 4 is tet 2



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