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1994 Fiscal Year Final Research Report Summary

Design of numerically robust geometric algorithms

Research Project

Project/Area Number 04452191
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 情報工学
Research InstitutionUniversity of Tokyo

Principal Investigator

SUGIHARA Kokichi  Univ. Tokyo, Faculty of Eng., professor, 工学部, 教授 (40144117)

Co-Investigator(Kenkyū-buntansha) IMAI Toshiyuki  Univ. Tokyo, Faculty of Eng., assistant, 工学部, 助手 (90213214)
HAYAMI Ken  Univ. Tokyo, Faculty of Eng., associate professor, 工学部, 助教授 (20251358)
Project Period (FY) 1992 – 1994
KeywordsCombinatorial Abstruction / Computational Geometry / Numerical Stability / Robustness / Voronoi Diagrams / Delaunay Decomposition / Combinatorial Geometry
Research Abstract

The design principle called "combinatorial abstraction", which was proposed by our research group for numerically robust geometric algorithms, has been studied from both theoretical and experimental points of view.
This principle was successfully applied to the problems of constructing ordinary Voronoi diagrams in two- and three-dimensional space, constructing generalized Voronoi diagrams for line segments and for polygons, constructing three-dimensional convex hulls, intersecting convex polyhedra, constructing Laguerre Voronoi diagrams, constructing arrangements of line segments, and constructing Voronoi diagrams for arbitrary figures. Furthermore, it was found that this principle is applicable if the objects admit topological properties that can be checked efficiently.
From a theoretical point of view, it became clear that the algorithm designed by this principle solves the geometric problem in the world of combinatorial geometry. From an experimental point of view, on the other hand, the computer programs made in this principle turned out to be completely robust in the sense that they never fail even if the arithmetic precision is poor.

  • Research Products

    (32 results)

All Other

All Publications (32 results)

  • [Publications] K.Sugihara: "Voronoi diagrams in a river" International Journal of Computational Geometry and Applications. 2. 29-48 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.K.Dey: "On good triangulations in three dimensions" International Journal of Computational Geometry and Applications. 2. 75-95 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "Construction of the Voronoi diagram for "one million"generators in single-precision arithmetic" Proceedings of the IEEE. 80. 1471-1484 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 谷口行信: "検出もれのない代数曲線の追跡法" 情報処理学会論文誌. 33. 1245-1253 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.K.Dey: "Delaunay triangulation in three dimensions with finite precision arithmetic" Computer Aided Geometric Design. 9. 457-470 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams" Computer Vision,Graphics,and Image Processing:Graphical Models and Image Processing. 55. 522-531 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 稲垣宏: "3次元ボロノイ図構成のためのの数値的に安定な逐次添加法" 情報処理学会論文誌. 35. 1-10 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Okabe: "Nearest neighbourhood operations with generalized Voronoi diagrams:a review" International Journal on Geographical Information Systems. 8. 43-71 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "Simpler proof of a realizability theorrem on Delaunay triangulations" Information Processing Letters. 50. 173-176 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "A robust topology-oriented incremental algorithm for Voronoi diagrams" International Journal of Computational Geometry and Applications. 4. 179-228 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 今井敏行: "誤差による破綻の心配のない線分 Voronoi 図構成算法" 情報処理学会論文誌. 35. 1966-1977 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "Robust gift wrapping for the three-dimensional convex hull" Journal of Computer and System Sciences. 49. 391-407 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊理正夫(監): "計算幾何学と地理情報処理,第2版" 共立出版, 294 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐々木建昭: "計算代数と計算幾何" 岩波書店, 166 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 杉原厚吉: "計算幾何工学" 培風館, 230 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 室田一雄: "離散構造とアルゴリズムIII" 近代科学社, 204 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sugihara: "Voronoi didgrams in a river" International Journal of Computational Geometry and Applications. vol.2. 29-48 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.K.Dey: "On good triangulations in three dimensions" International Journal of Computational Geometry and Applications. vol.2. 75-95 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: "Construction of the Voronoi diagram for "one million"generators in single-precision arithmetic" Proc. of the IEEE. vol.80. 1471-1484 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Taniguchi: "A robust method for tracing algebraic curves" Trans. of the Information Processing Society of Japan. vol.33, no.10. 1245-1253 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.K.Dey: "Delaunay triangulations in three dimensions with finite precision arithmetic" Computer Aided Geometric Design. vol.9. 457-470 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: "Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams" Computer Vision, Graphics, and Image Processing : Graphical Models and Image Processing. vol.55. 522-531 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Inagaki: "Robust algorithm for incremental construction of three-dimensional Voronoi diagrams" Trans. of the Information Processing Society of Japan. vol.35. 1-10 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A.Okabe: "Nearest neighborhood operations with generalized Voronoi diagrams : a review" International Journal on Geographical Information Systems. vol.8. 43-71 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: "Simpler proof of a realizability theorem on Delaunay triangulations" Information Processing Letters. vol.50. 173-176 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: "A robust topology-oriented incremental algorithm for Voronoi diagrams" International Journal of Computational Geometry and Applications. vol.4. 179-228 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Imai: "A failure-free algorithm for constructing Voronoi diagrams of line segments" Trans. of the Information Processing Society of Japan. vol.35. 1966-1977 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: "Robust gift wrapping for the three-dimensional convex hull" Journal of Computer and System Sciences. vol.49. 391-407 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Iri and T.Koshizuka(eds.): Kyoritsu-Shuppan. Computational Geometry and Geographic Information Processing, 2nd Edition, 294 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Sasaki et al.: Iwanami-Shoten.Tokyo. Computational Algebra and Computational Geometry, 166 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sugihara: Baifu-Kan, Tokyo. Computational Geometry in Finite Precision, 230 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Murota(ed.): Kindaikagaku-Sha, Tokyo. Discrete Structure and Algorithms III, 204 (1994)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1996-04-15  

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