An inverse distance-based potential field function for overlapping point set visualization

In this paper we address the problem of visualizing overlapping sets of points with a fixed positioning in a comprehensible way. A standard visualization technique is to enclose the point sets in isocontours generated by bounding a potential field function. The most commonly used functions are various approximations of the Gaussian distribution. Such an approach produces smooth and appealing shapes, however it may produce an incorrect point nesting in generated regions, e.g. some point is contained inside a foreign set region. We introduce a different potential field function that keeps the desired properties of Gaussian distribution, and in addition guarantees that every point belongs to all its sets´ regions and no others, and that regions of two sets with no common points have no overlaps. The presented function works well if the sets intersect each other, a situation that often arises in social network graphs, producing regions that reveal the structure of their clustering.