Fast Voronoi modeling

Abstract

The common way to construct Voronoi tessellations is to compare the distances between given reference points using a given distance function. To generalize this distance-function concept we expand an existing approach which defines distance functions by their ``unit circles''. Our new approach allows modeling the ``unit circles'' by a closed Spline curve. Changing the control polygon directly affects the tessellation's appearance. Typically generalized Voronoi diagrams are represented by Voronoi vertices and curves separating the individual tiles. To obtain interactive modeling we extended an existing hardware accelerated rendering approach computing a bitmap-representation using different colors for individual tiles. With our extension, we are able to use our Spline distance representations as input for a growing process. This growing process easily takes into account weighting approaches like multiplicative, additive, and even free functional weighting.