2001 Fiscal Year Final Research Report Summary
Robust Implementation of 4-D Geometric Algorithm and Applications
| Project/Area Number |
10450040
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | The University of Tokyo |
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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)
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| 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)
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| Project Period (FY) |
1998 – 2000
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| Keywords | 4-d convex hull / Delaunay diagram / crystal Voronoi diagram / exact computation / Lazy evolution / collision-avoidance path |
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| 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.
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