Line Simplification, Geometric Distortion, and Positional Error

Abstract

Line simplification is a generalization method that involves the selective elimination of vertices along a cartographic line. This procedure can introduce positional error by distorting line geometry. This study focuses on the quantification of this distortion with specific reference to the Douglas-Peucker line-simplification algorithm. Results based on US Geological Survey Digital Line Graph (DLG) data for streams and roads show that the algorithm is often suboptimal; that is, the amount of geometric distortion per eliminated vertex is generally not minimized. As the amount of simplification increases, the degree of suboptimality increases in absolute terms but declines in relative terms when compared to the entire distribution of possible distortion values. Significant differences in performance are observed for streams and roads, due to the higher error potential for roads as a function of their geometry.