I'm looking for an algorithm that computes the Voronoi regions of a set of points contained in a polygonal region with obstacles. What would be the most simple, straightforward way to implement this? For each region, I need an explicit description of the boundary, that is, the union of line segments and hyperbolic arcs that compose it. I'm aware that there are fast algorithms for this problem in the sense of running time (e.g. http://dl.acm.org/citation.cfm?id=161156 ) but I'm more interested in one that's easy to implement. To be honest, I'm not even sure how to find an easy algorithm for finding the shortest path map for this problem.