Question

I have a a mesh, with certain types of elements (e.g. triangular, tetra). For each element I know all its vertices i.e. a triangular 2D element will have 3 vertices v1, v2 and v3 whose x,y,z coords are known.

Question 1

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

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

Question 2

I am using C++, so, what will be the most efficient way to store the information about the edges returned by the above algorithm? Example, all I am interested in is a tuple (v1, v2) that I want to use for some computation and then forget about it.

Thank you

Answer 1

You can use the half-edge data structure.

Basically your mesh also has a list of edges, and there is one edge structure per pair of verts in each direction. That means if you have verts A and B then there are two edge structures stored somewhere, one for A->B and one for B->A. Each edge has 3 pointers, one called previous, one called next and one called twin. Following the next and previous pointers walks you around the edges of the triangle or polygon in the mesh. Calling twin takes you to the adjacent edge in the adjacent polygon or triangle. (Look at the arrows int he picture) This is the most useful and verbose edge data structure I know of. I’ve used it to smooth meshes by creating new edges and updating the pointers. Btw, each edge should also point to a vertex so it knows where it is in space.