In this paper, we present and evaluate a Voronoi method for partitioning continuous information spaces. We define the formal characteristics of the problem and discuss several well-known partitioning methods and approaches. We submit that although they all partially solve the problem, they all have shortcomings. As an alternative, we offer an approach based on an adaptive version of the multiplicatively weighted Voronoi diagram. The diagram is ‘adaptive’ because it is computed backwards; that is, the generators' weights are treated as dependent rather than independent variables. We successfully test this adaptive solution using both ideal-typical (artificial) and empirical data. Since the resultant visualizations are meant to be used by human subjects, we then discuss the results of a usability experiment, positioning the adaptive solution against a commonly used rectangular solution and the classic nonweighted Voronoi solution. The results indicate that in terms of usability, both the rectangular and the adaptive Voronoi solution outperform the standard Voronoi solution. In addition, although subjects are better able to gage rectangular area relationships, only the adaptive Voronoi solution satisfies all geometric constraints of weight-proportional partitioning.

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Traditional application of Voronoi diagrams for space partitioning results in Voronoi regions, each with a specific area determined by the generators' relative locations and weights. Particularly in the area of information space (re)construction, however, there is a need for inverse solutions; i.e., finding weights that result in regions with predefined area ratios. In this paper, we formulate an adaptive Voronoi solution and propose a raster-based optimization method for finding the associated weight set. The solution consists of a combination of simple, fixed-point iteration with an optional spatial resolution refinement along the regions' boundaries using quadtree decomposition. We present the corresponding algorithm and its complexity analysis. The method is successfully tested on a series of ideal-typical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.