Consider this set of two dimensional generators (red polygons top left). A Voronoi diagram of these polygons is shown at bottom left. Now consider the same set of two dimensional generators on some "warped" surface (e.g. this banded surface at top right, where each shade of gray represents an amount by which a unit of distance is multiplied; i.e. white=1, black=5). The resulting Voronoi diagram is shown at bottom right.
These were created using a spreading algorithm where points on the boundary of the polygons "spread" at a constant rate. I can make these diagrams, but I would like to know how to explain them using correct terminology.
Can anyone express for me what is going on here in appropriate mathematical terms? (And I would appreciate it if you could correct any incorrect terminology used in posing the question).
I have read this post on Voronoi diagrams with different metric functions, but I don't think this quite what I am after.