Application of the delaunay triangulation to geometric intersection problems
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The paper presents a new robust method for finding intersections of line segments in the plane. This method first constructs the Delaunay triangulation spanning the end points of line segments, and next recursively inserts the midpoints in the line segments that are not realized by Delaunay edges, 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 arrangement as the output, and is stable in the sense that it does not miss intersections that can be easily detected by naive pairwise check with the precision at hand.
KeywordsLine Segment Voronoi Diagram Numerical Error Computational Geometry Delaunay Triangulation
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