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Issue No.02 - March/April (1992 vol.12)
pp: 59-67
ABSTRACT
<p>A robust method for finding points of intersection of line segments in a 2-D plane is presented. The plane is subdivided by Delaunay triangulation to localize areas where points of intersection exist and to guarantee the topological consistency of the resulting arrangement. The subdivision is refined by inserting midpoints recursively until the areas containing points of intersection are sufficiently localized. The method is robust in the sense that it does not miss points of intersection that are easily detectable when costly line-pair checking is performed. The algorithm is adaptive in the sense that most of the computational cost is incurred for the areas where finding points of intersection is difficult.</p>
CITATION
Kokichi Sugihara, "An Intersection Algorithm Based on Delaunay Triangulation", IEEE Computer Graphics and Applications, vol.12, no. 2, pp. 59-67, March/April 1992, doi:10.1109/38.124289
REFERENCES
1. J.L. Bentley and T.A. Ottmann, "Algorithms for Reporting and Counting Geometric Intersections,"IEEE Trans. Computers, Vol. C-28, No. 9, Sept. 1979, pp. 643-647.
2. T. Ottmann, G. Thiemt, and C. Ullrich, "Numerical Stability of Geometric Algorithms,"Proc. 3rd Annual Conference on Computational Geometry, ACM, New York, 1987, pp. 119-125.
3. V. Milenkovic, "Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic,"Artificial Intelligence, Vol. 37, Nos. 1-3, Dec. 1988, pp. 377-401.
4. K. Sugihara and M. Iri, "Construction of the Voronoi Diagram for One Million Generators in Single-Precision Arithmetic," article presented at the First Canadian Conference on Computational Geometry, August 21-25, 1989, Montreal, Canada, and submitted for publication.
5. D.P. Dobkin, S.J. Friedman, and K.J. Supowit, "Delaunay Graphs Are Almost As Good As Complete Graphs,"Discrete and Computational Geometry, Vol. 5, No. 4, 1990, pp. 399-407.
6. T. Ohya, M. Iri, and K. Murota, "Improvements of the Incremental Method for the Voronoi Diagram with Computational Comparison of Various Algorithms,"J. Operations Research Society of Japan, Vol. 27, No. 4, Dec. 1984, pp. 306-336.
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