| Project/Area Number |
10205205
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | The University of Tokyo |
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Principal Investigator |
SUGIHARA Kokichi University of Tokyo, Graduate School of Engineering, Professor, 工学系研究科, 教授 (40144117)
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| Co-Investigator(Kenkyū-buntansha) |
IMAI Toshiyuki Wakayama Univ., School of System Eng., Associate Professor, システム工学部, 助教授 (90213214)
YAMAMOTO Osami Aomori Univ., School of Eng., Lecturer, 工学部, 講師 (60200789)
HAYAMI Ken Univ. of Tokyo, Graduate School of Engineering, Associate Professor, 工学系研究科, 助教授 (20251358)
HIYOSHI Hisamoto Gunma Univ., School of Eng., Assistant, 工学部, 助手 (40323331)
NISHIDA Tetsushi University of Tokyo, Graduate School of Engineering, Assistant, 工学系研究科, 助手 (80302751)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥10,700,000 (Direct Cost: ¥10,700,000)
Fiscal Year 2000: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1999: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1998: ¥4,500,000 (Direct Cost: ¥4,500,000)
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| Keywords | robust computation / exact computation / precision-guaranteed computation / Voronoi diagram / interval algebra / evaluation of errors / area without zero points / lazy evaluation / 多面体の表現 / 誤差の伝幡 / 有限要素法 / 弾性変形 / ソリッドモデリング / 誤差吸収列 / 凸包 / 剰余演算 / 加速 |
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| Research Abstract |
Geometric algorithms are important techniques and have many applications in geographic information system, pattern recognition, robot motion planning, computer graphics and finite element analysis. They are studied in computational geometry, but are not necessarily robust against numerical errors. The goal of this project is to overcome this difficulty using precision-guaranteed computation.
We developed a new principle for designing numerically robust geometric algorithm. This principle consists of the evaluation of computational errors, exact-precision computation, acceleration of computation using floating- point filter, symbolic perturbation for avoiding degeneracy, and another acceleration method based on graphics hardware. This principle was applied to the construction of three-dimensional Delaunay diagrams and its application to mesh generation and the construction of a generalized Voronoi diagram for the evaluation of teamwork in sports.
For more difficult geometric problems such as the construction of the crystal Voronoi diagram, we developed another robust method. In this method, the geometric problem is reformulated in terms of a partial differential equation, and is solved using finite-difference method, the fast-marching method, in particular. We applied this method to the robot motion planning, in which the collision-free shortest path among enemy robots is computed, and could prove that our new method is more efficient than previous methods.
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