| Project/Area Number |
15K12067
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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 |
Perceptual information processing
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| Research Institution | Meiji University |
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Principal Investigator |
Sugihara Kokichi 明治大学, 研究・知財戦略機構, 特任教授 (40144117)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 立体錯視 / 不可能立体 / 視覚モデル / 変身立体 / 錯覚 / 錯視効果 / 展開図 / ３Dプリンター / 図形の距離 / 厚みの制御 / ３Ｄプリンター / 数理工学 / 視覚情報処理 / 視覚の数理モデル |
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| Outline of Final Research Achievements |
The purpose of this research is to establish a design method for ambiguous cylinders, whose appearances change drastically when they are reflected in a plane mirror.
First, an equation system is constructed for finding the space curve that affects two given shapes when it is seen from two prespecified viewpoints. Next, an ambiguous cylinder is constructed as the surface swept by the space curve. Several heuristic methods were also constructed for controlling thickness of the ambiguous cylinders so that they appear to be as uniform as possible, and thus the cylinders are 3D printable. A method for drawing unfolded surface was also constructed.
On the basis of these methods, we also developed new types of impossible objects, such as "topology-disturbing objects", whose topology changes in the mirror, and "deformable objects", which appear to deform when viewpoint is moved. Thus, we establish a mathematical theory and a systematic design algorithm of "ambiguous cylinders".
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