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Robust Implementation of 4-D Geometric Algorithm and Applications

Research Project

Project/Area Number 10450040
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionThe University of Tokyo

Principal Investigator

SUGIHARA Kokichi  Graduate School of Engineering, The University of Tokyo, Professor, 大学院・工学系研究科, 教授 (40144117)

Co-Investigator(Kenkyū-buntansha) INAGAKI Hiroshi  Toyota Advanced Institute of Technology, Dept. of Information Engineering, Associate Professor, 情報工学科, 助教授 (40213110)
NISHIDA Tetsushi  Graduate School of Engineering, The University of Tokyo, Assistant, 大学院・工学系研究科, 助手 (80302751)
HAYAMI Ken  Graduate School of Engineering, The University of Tokyo, Associate Professor, 大学院・工学系研究科, 助教授 (20251358)
IMAI Toshiyuki  Graduate School of Engineering, The University of Tokyo, Professor, システム工学部, 助教授 (90213214)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥13,100,000 (Direct Cost: ¥13,100,000)
Fiscal Year 2000: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1999: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥7,400,000 (Direct Cost: ¥7,400,000)
Keywords4-d convex hull / Delaunay diagram / crystal Voronoi diagram / exact computation / Lazy evolution / collision-avoidance path / 整数帰着法 / 記号摂動法 / ボロノイ図 / ドロネー分割 / 四面体メッシュ / 球面分割 / 記号慎動法
Research Abstract

The incremental algorithm for constructing 4-dimensional convex hull of points was re-designed into a numerically robust algorithm. In the new algorithm, all the decisions on the topological structure are done by exact arithmetic using about five-times longer expression of integers, and geometric degeneracy is avoided by the symbolic perturbation technique. Also the computation is accelerated by floating-point filter, in such a way that computation is first done in floating point arithmetic and is switched to the exact arithmetic only when the precision turns out to be insufficient, This algorithm was applied to robust implementations of algorithms for many 3-dimehsional geometric structures, including the Voronoi diagram, the Delaunay diagram, the Laguerre Delaunay diagram, farthest-point Delaunay diagram, intersections of half spaces. The resulting source codes were made open for public use in the supervisor's web page.
The other 4-dimensional geometric structure considered in this research is the time-space structure. In particular, robust algorithms for simulating crystal growth was designed and implemented using finite-difference techniques. This algorithm was applied to the construction of collision-free paths for a robust moving among hostile enemy robots.

Report

(4 results)
  • 2001 Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] H.Hiyoshi, K.Sugihara: "An inerpolant based on line segment Voronoi diagrams"Discrete and Computational Geometry, Lecture Notes in Computer Science. 1763. 119-128 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kokichi Sugihara: "Three-dimensional convex hull as a fruitful source of diagrams"Theoretical Computer Science. 235. 325-337 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Hiroshima, Y.Miyamoto, K.Sugihara: "Another proof of polynomial-time recognizability of Delaunay graphs"JEICE Transactions on Fundamentals. E83-A・4. 627-638 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Hiyoshi, K.Sugihara: "A sequence of generalized coordinate systems based on Voronoi diagrams and its application to interpolation"Proceedings of Geometric Modeling and Processing 2000. 129-137 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Hiyoshi, K.Sugihara: "Voronoi-based interpolation with higher continuity"Proceedings of the 16th Annual Symposium on Computational Geometry. 242-250 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 小林景, 杉原厚吉: "乗法重みつき結晶成長ボロノイ図の近似構成法とその応用"電子情報通信学会論文誌. J83-A-4. 1495-1504 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Okabe, B.Boots, K.Sugihara, S.N.Chiu: "Spatial Tessellations・・・Concepts and Applications of Voronoi Diagrams, Second Edition"John Wiley and Sons. 671+XVI (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. HIYOSHI and K. SUGIHARA: "An inerpolant based on line segment Voronoi diagrams"Discrete and Computational Geometry, Lecture Notes in Computer Science. 1763. 119-128 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K. SUGIHARA: "Three-dimensional convex hull as a fruitful source of diagrams"Theoretical Computer Science. Vol. 235. 325-337 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. HIROSHIMA, Y. MIYAMOTO and K. SUGIHARA: "Another proof of polynomial-time recognizability of Delaunay graphs"IEICE Transitions on Fundamentals. Vol. E83-A, No. 4. 627-638 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. HIYOSHI and K. SUGIHARA: "A sequence of generalized coordinate systems based on Voronoi diagrams and its application to interpolation"Proceedings of Geometric Modeling and Processing, (April, 2000, Hong Kong). 129-137 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. HIYOSHI and K. SUGIHARA: "Voronoi-based interpolation with higher continuity"Proceedings of the 16th Annual Symposium on Computational Geometry (June, 2000, Hong Kong). 242-250 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K. KOBAYASHI and K. SUGIHAR: "Approximation of multiplicatively weighted crystal growth Voronoi diagram and its application"The Transactions of IEICE. J83-A, No. 12. 1495-1504 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K. OKABE, B. BOOTS, K. SUGIHARA and S.-N. CHIU: "Spatial Tessellations Concepts and Applications of Voronoi Diagrams, Second Edition"John Wiley and Sons. 671 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Hiyoshi and K.Sugihara: "An inerpolant based on line segment Voronoi diagrams"Discrete and Computational Geometry,Lecture Notes in Computer Science. 1763. 119-128 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kokichi Sugihara: "Three-dimensional convex hull as a fruitful source of diagrams"Theoretical Computer Science. 235. 325-337 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Hiroshima,Y.Miyamoto and K.Sugihara: "Another proof of polynomial-time recognizability of Delaunay graphs"IEICE Transactions on Fundamentals. E83-A-4. 627-638 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Hiyoshi and K.Sugihara: "A sequence of generalized coordinate systems based on Voronoi diagrams and its application to interpolation"Proceedings of Geometric Modeling and Processing 2000. 242-250 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Hiyoshi and K.Sugihara: "Voronoi-based interpolation with higher continuity"Proceedings of the 16th Annual Symposium on Computational Geometry. 242-250 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 小林景,杉原厚吉: "乗法重みつき結晶成長ボロノイ図の近似構成法とその応用"電子情報通信学会論文誌. J83-A-4. 1495-1504 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 山本修身: "多項式の微分係数情報を付加した零点不在領域とNewton法"日本応用数理学会論文誌. 10・4. 65-90 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A.Okabe,B.Boots,K.Sugihara and S.-N.Chiu: "Spatial Tessellations---Concepts and Applications of Voronoi Diagrams,Second Edition"John Wiley and Sons. 671+xvi (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kokichi Sugihara: "Surface Interpolation Based on New Local Coordinates"Computer-Aided Design. 31. 51-58 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hisamoto Hiyoshi, Kokichi Sugihara: "Generalization of an interpolant using Voronoi diagrams in two directions"Proceedings of the International Conference on Shape Modeling and Applications. 154-161 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kokichi Sugihara: "Topology-Based Methods for Robust Geometric Computing"Proceedings of the Korea Istael Bi-National Conf. on Geometric Modeling and Computer Graphics in the World Wide Web Era. 1-7 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kokichi Sugihara: "Exact Computation of 4-D Convex Hulls with Pertutbation and Acceleration"Proceedings of the 7th Pacitic Conterence on Computer Graphics and Applications (Pacific Graphics '99). 70-79 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Tsuyoshi Minakawa Kokichi Sugihara: "Topology-Oriented Construction of Three-Dimensional Convex Hulls" Optimization Methods and Software. 10. 357-371 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kokichi Sugihara: "Degeneracy and Instability in Geometric Computation" Sixth IFIP WG 5.2 International Workshop on Geometric Modeling. 5-15 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kokichi Sugihara: "“Impossible Objects" Are Not Necessarily Impossible---Mathematic Study on Optical Illusion" Proceedings of Japan Conference on Discrete and Computational Geometry '98. 54-65 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ken Hayami: "Improvement of a Method for Identifying a Current Dipole in the Brain Using BEM and Nonlinear Optimization" International Symposium on Inverse Problems in Engineering Mechanics 1998. 449-458 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 杉原 厚吉: "FORTRAN計算幾何プログラミング" 岩波書店, 402 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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