Higher order Voronoi diagrams and distance functions in art and visualization

Higher order Voronoi diagrams provide a useful tool for studying problems where more than one nearest site is of interest. Understanding and visualizing higher order Voronoi diagrams is more difficult than ordinary Voronoi diagrams and requires intelligent solutions. In this chapter we discuss several rendering techniques using color, line and texture to visualize higher order Voronoi diagrams in two and three dimensions. Such approaches have several interesting characteristics such as providing useful multi-dimensional information when even a small portion of the figure is available.