2014 Fiscal Year Final Research Report
Dimension-Change Principle for Robust Geometric Computation
| Project/Area Number |
24650015
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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 |
Software
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| Research Institution | Meiji University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | ロバスト計算 / 不可能立体 / 走査法 / 直線骨格線 / 位相優先法 / モアレ縞 / 立体錯視 / 高さ反転立体 |
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| Outline of Final Research Achievements |
We developed a principle for designing geometric algorithms by changing the spatial dimensions of the problems through many examples in the areas of shape design and shape analysis. This principle can be classified into two groups, one is to raise the dimension and the other is to decrease the dimension.
As for the dimension-decreasing principle, we constructed algorithms for pop-up card design, for moire pattern design, and for constructing mathematical model to explain classic geometric optical illusions including Muller-Lyer illusion and Poggendorf illusion in a unifying manner.
As for the dimension-raising principle, we constructed algorithms for realizing solids from "pictures of impossible objects" and their dynamic version, for designing pictures that appear to be mutually height reversing structures when they are seen from two special viewpoints, and for constructing straight skeletons of polygons and their weighted version efficiently and stably.
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| Free Research Field |
数理工学
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