| Project/Area Number |
17K14580
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Design engineering/Machine functional elements/Tribology
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| Research Institution | Chuo University (2019)
Meiji University (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 表面メッシュ / 骨格線 / 位相保存 / 形状モデリング / 幾何形状処理 |
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| Outline of Final Research Achievements |
We propose an algorithm of homotopy-preserving curve-skeleton extraction for surface meshes embedded in 3-dimensional space. The proposed method computes curve-skeletons that have the same homotopy type of the solid bounded by the given surface mesh. While it is easy to preserve the homotopy type if we have volume meshes, we achieve the homotopy preservation even without computing volume meshes. Our algorithm is based on extraction methods using edge contractions and we derive novel conditions on edge contractions for the homotopy preservation. There exist meshes that cannot be contracted into curve-skeleton with the same homotopy type, but we also propose a solution to this problem by modifying the edge split operation.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，位相保存の保証を持つロバストな骨格線抽出法を開発した．骨格線は形状モデリングや形状解析において多くの応用を持つ構造であり，この理論保証やロバスト化は映像産業や製造業での課題解決にも役立つことが期待できる．
また，幾何形状処理の分野では，辺縮約がどのような位相的性質を保存できるかについての研究が続けられているが，本研究は新しい保存可能な性質を導いた．これは，辺縮約の新たな応用先の開拓にもつながるものである．
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