A Robust Intersection Algorithm Based on Delaunay Triangulation

The paper presents a new robust method for finding points of intersection of line segments in the plane. In this method the subdivision of the plane based on the Delaunay triangulation plays the main role. First, the Delaunay triangulation spanning the end points of line segments is constructed. Next, for line segments that are not realized by Delaunay edges, midpoints are inserted recursively until the descendants of the line segments become realized by Delaunay edges or the areas containing points of intersection are sufficiently localized. The method is robust in the sense that in any imprecise arithmetic it gives a topologically consistent output, and is stable in the sense that it does not miss intersection that can be easily detected by naive pairwise check with the precision at hand.