| Project/Area Number |
16K12435
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
High performance computing
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| Research Institution | Wakayama University |
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Principal Investigator |
Imai Toshiyuki 和歌山大学, システム工学部, 教授 (90213214)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 計算幾何学 / 近似アルゴリズム / 位相情報 / 図形処理 / 高性能計算アプリケーション / 計算幾何 / Voronoi図 / Delaunay図 / 高機能計算アプリケーション / アルゴリズム |
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| Outline of Final Research Achievements |
This research pursues the possibility of a framework that guarantees topological correctness of figures efficiently by approximation algorithm in geometrical processing. In the construction of the Voronoi diagram for various figures, the existing algorithm for the point was used as the basis of the approximation. First, the geometrical processing based on the framework for the line segments or circles was succeeded.
Then, the intersection judgment of Bezier curves or arcs is also realized by this framework. We also construct the Voronoi diagrams for Bezier curve using those intersection judgments as parts of the algorithm. This proves that the arithmetic group that guarantees the strictness of the topological structure functions as a framework for geometrical processing. We also succeeded in crossing the (more generalized) NURBS curve. The Voronoi diagram for the NURBS curves will be constructed by this framework.
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| Academic Significance and Societal Importance of the Research Achievements |
一般的には近似をすれば近似解しか得られないとされてきた. 本研究では計算機で扱われる図形を, 具体的な角度や座標値のような実数値をとる計量情報と面や辺の接続関係を表す位相情報とに分離して扱い，近似アルゴリズムを位相情報を厳密に求めるためだけに使う．詳細な近似が必要なのは, 図形のごく一部の，位相情報を決定するのが困難な場合に限られるため，位相情報の厳密性と高速性が同時に得られた．ベジエ曲線分に対する交差判定や勢力圏図の構成は，原理的に厳密計算だけで実行できない．これに対して，位相情報だけでも厳密な図形処理を達成できたことは，図形処理において，大きな意義がある．
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