| Project/Area Number |
05555027
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| Research Category |
Grant-in-Aid for Developmental Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | UNIVERSITY OF TOKYO |
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Principal Investigator |
SUGIHARA Kokichi University of Tokyo, Graduate School of Engineering, Professor, 大学院・工学系研究科, 教授 (40144117)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Toshiyuki University of Tokyo, Graduate School of Engineering, Assistant, 大学院・工学系研究科, 助手 (90213214)
HAYAMI Ken University of Tokyo, Graduate School of Engineering, Assistant Professor, 大学院・工学系研究科, 助教授 (20251358)
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| Project Period (FY) |
1993 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1994: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1993: ¥3,000,000 (Direct Cost: ¥3,000,000)
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| Keywords | computational geometry / numerical error / topology-oriented method / image processing / Voronoi diagram / 3-d convex hull / mesh generation / numerical stability / 衝突回避経路探索 / ドロネ-図 / 多角形ボロノイ図 / 骨格線抽出 / 幾何アルゴリズム / ドロネー図 / 凸多面体 / 交差図形 |
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| Research Abstract |
The topology-oriented method for designing geometric algorithms was applied to fundamental problems in computational geometry. This year in particular, numerically stable softwares for incremental constrution of the Voronoi diagrams for polygons, for Minkowski operations between polygons, and for divide-and-conquer construction of three-dimensional convex hulls were developed. Also the manuals of some of these softwares together with other ones developed previously were constructed.
A topology-oriented algorithm solves a geometric problem in the world of combinational geometry, and hence the output is not necessarily consistent with Euclidean geometry. The distance between the correct answer and the output was analyied both from a theoretically point of view and an experimental point of view.
Applications of the topology-oriented algorithm were also considered. The Delaunay tirangulation with numerical disturbance was applied to finite-element analysis, and a new scheme for the finite-element analysis was proposed. This scheme is practical in the sense that it works stably even if the Delaunay mesh is incomplete.
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