| 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)
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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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