Edge search algorithm using vertices (2D and 3D) in the grid

Question

I have a grid with certain types of elements (e.g. triangular, tetra). For each element, I know all its vertices, i.e. A triangular two-dimensional element will have 3 vertices v1, v2 and v3, whose x, y, z-coordinates are known.

Question 1

I am looking for an algorithm that will return all edges ... in this case:

edge (v1, v2), edge (v1, v3), edge (v2, v3). Based on how many vertices each element has, the algorithm must efficiently determine edges.

Question 2

I use C ++, so what would be the most efficient way to store information about the edges returned by the above algorithm? For example, all that interests me is the tuple (v1, v2), which I want to use for some calculations, and then forget about it.

thank

Answer 1

You can use a half edge data structure.

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Answer 2

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Answer 3

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Here are some open source libraries that will do this for you (grok code for algorithms):

• CGAL Triangulation_2 and Triangulation_3 classes.
• Triangle (2D only) by Jonathan Richard Shevchuk
• Fast polygonal triangulation by Atul Narkhede and Dinesh Manocha