Interactive Computation of Discrete Generalized Voronoi Diagrams using Range Culling

We present an algorithm for fast computation of discrete generalized Voronoi diagrams. Given a set of geometric primitives, and a distance metric, our algorithm efficiently computes the Voronoi diagram along a uniform grid by evaluating distance fields. We use a multipass approach and divide the computation into intervals along each dimension. We present an efficient culling algorithm to reduce the region for distance-field computation and use conservative bounds on Voronoi regions in 2D and 3D to cull away primitives. We have implemented our algorithm on programmable graphics hardware and applied it to compute the discrete Voronoi diagram of complex 2D and 3D datasets. We compute the discrete Voronoi diagram of 20, 000 primitives on a 2D grid of size 1200× 1200 in less than 1 second. Our experimental results indicate a two to four times improvement over prior algorithms and implementations.