GBGVD: Growth-based geodesic Voronoi diagrams

Abstract

Given a set of generators, the geodesic Voronoi diagram (GVD) defines how the base surface is decomposed into separate regions such that each generator dominates a region in terms of geodesic distance to the generators. Generally speaking, each ordinary bisector point of the GVD is determined by two adjacent generators while each branching point of the GVD is given by at least three generators. When there are sufficiently many generators, straight-line distance serves as an effective alternative of geodesic distance for computing GVDs. However, for a set of sparse generators, one has to use exact or approximate geodesic distance instead, which requires a high computational cost to trace the bisectors and the branching points. We observe that it is easier to infer the branching points by stretching the ordinary segments than competing between wavefronts from different directions. Based on the observation, we develop an unfolding technique to compute the ordinary points of the GVD, as well as a growth-based technique to stretch the traced bisector segments such that they finally grow into a complete GVD. Experimental results show that our algorithm runs 3 times as fast as the state-of-the-art method at the same accuracy level.