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I am very much happy after seeing some very good answers in this site. I am trying to design a algorithm for the construction of Delaunay Triangulation using Randomized Incremental Algorithm.(I wont expect everyone to know about this one), I need to design a triangle which stores points,edges and the triangles adjacent to it,also need to maintain a parent & children relation between the triangles and also edges with two opposite points to each of it(preferably in java) . I know its a bit complicated and not easy to understand but i cant explain the whole algorithm here in this site, so i would like to find some one who is familiar with this.

Thanks in advance.

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You might look at Lutz Kettner's paper, "Designing a Data Structure for Polyhedral Surfaces," (CiteSeer link). He uses the half-edge data structure. Here is CGAL's description of that structure:
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An alternative is the winged-edge data structure.

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