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Application of the delaunay triangulation to geometric intersection problems

  • Kokichi Sugihara
II Mathematical Programming II.1 Computational Geometry
  • 106 Downloads
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)

Abstract

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.

Keywords

Line Segment Voronoi Diagram Numerical Error Computational Geometry Delaunay Triangulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Kokichi Sugihara
    • 1
  1. 1.Department of Mathematical Engineering and Information PhysicsUniversity of TokyoTokyoJapan

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