| Project/Area Number |
04452191
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
情報工学
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| Research Institution | University of Tokyo |
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Principal Investigator |
SUGIHARA Kokichi Univ. Tokyo, Faculty of Eng., professor, 工学部, 教授 (40144117)
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| 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)
富岡 豊 東京大学, 工学部, 助手 (30188776)
伊理 正夫 東京大学, 工学部, 教授 (40010722)
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| Project Period (FY) |
1992 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1994: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1993: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1992: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Combinatorial Abstruction / Computational Geometry / Numerical Stability / Robustness / Voronoi Diagrams / Delaunay Decomposition / Combinatorial Geometry / 幾何アルゴリズム / 数値誤差対策 / ソリッドモデリング / 制約つきドロネー分割 / 幾何的アルゴリズム / 数値誤差 / 組合せ幾何学 / グリッド生成 / 凸包構成 / 交差図形 |
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| 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.
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