No Fuzzy Creep! A Clustering Algorithm for Controlling Arbitrary Node Movement

A perennial problem in vector overlay is fuzzy creep. Commercial vector overlay algorithms resolve near intersections of lines employing arbitrary node movement to align two chains at nodes selected randomly in the area of an epsilon band. While this solution is effective in reducing the number of sliver polygons, it introduces distortion. In some situations this distortion may be tolerable, but in others it may produce positional errors that are unacceptable for the cartographic or analytical purpose. Our research aims to provide an extension of overlay processing that provides a solution for GIS uses that require more exact control over node movement. The key to this is a robust, non-distorting cluster analysis. The cluster algorithm we present fulfills two goals: 1) it selects nodes based on an nearness heuristic, 2) it allows the user to fix the position of one data set's nodes and moves the other data set's nodes to match these position. In this paper we review existing cluster algorithms from the computational geometry and analytical cartography literature, evaluating their heuristics in terms of the potential to avoid fuzzy creep. Grouping the algorithms into a bit-map and fuzzy-detection types, we discuss the advantages and disadvantages of each approach for controlled near intersection detection. Based on the results of this analysis, we present a algorithm for non-distortive geometric match processing, the basis for our work on geometric match processing. 1. THE PROBLEM WITH FUZZY CREEP Vector overlay is utilized for a diverse range of purposes to combine geographic information. These purposes place numerous positional accuracy demands that we find are only partially served by existing vector overlay algorithms. All geographic data contains some positional inaccuracy, processing should not increase inaccuracy. We find there is ample need for vector processing algorithms that provide more control. A crucial problem in current vector overlay algorithms is fuzzy creep (Pullar, 1990; Pullar, 1991; Pullar, 1993; Zhang & Tulip, 1990). Fuzzy creep is