How can I connect all Delaunay triangle to voronoi?

Question

I have a list of all triangle sharing an edge. How can I draw a voronoi diagram? I loop over the Delaunay triangles and compare it to vertex 1 = vertex 2 and vertex 2 = vertex 1, I. e. if there are the same edges. It also checks when vertex 1 = vertex 1 and vertex 2 = vertex 2. In the equation both side is a different triangle. It's the same loop from the boywer watson algorithm.

Answer 1

When two triangles are adjacent in the Delaunay triangulation, draw a line segment between the circumcenters of these triangles.

There is an easy to remember rule for the duality between Delaunay triangulations and Voronoi diagrams: The dimensions of the dual elements always sum up to the dimension of space. For example in 2D:

Delaunay <-> Voronoi

Triangle (2) + Point (0) = 2

Segment (1) + Segment (1) = 2

Point (0) + Cell (2) = 2

...similar in 3D.