Hoping I'm not misunderstanding the concept here, but it is my understanding that Voronoi Diagrams and Delaunay Tesselations are 'dual' to one another, owing to the fact that each' solution makes computational of the other's solution trivial.
What I'm looking to understand is, why? I mean, it obviously happens, but is there some kind of mathematical proof or principle that justifies that convenient coincidence? Or is it just that, a coincidence?
I suppose, the voronoi quality of 'each vertex is equidistant from the 3 closest points' means that any matching triangulation is a delaunay triangulation (there is no point closer than the closest points), but I am hoping for something more... in-depth? Is there such a thing?
To clarify: the question is not about what them being dual means, like the suggested duplicate. The question is why they behave as duals.