2013 Fiscal Year Final Research Report
Moduli space of motions of geometric objects
| Project/Area Number |
23654054
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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 |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
OCHIAI Hiroyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (90214163)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 変形 / リー群 / 補間 / 運動群 / 離散微分幾何 / 映像 / 曲面 / 曲線 |
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| Research Abstract |
Computer Graphics produces a scene. It is a collection of large data, depending on the time variable.
In this research, we study the structure of the space of scenes, in terms of geometry and Lie theory. The groups acting on the objects are the central role of this study. The example of such groups are Euclidean motion groups, orthogonal groups, rotation groups, and affine transformation groups. We give an interpretation of these groups into several subgroups or the matrix exponential image of subspaces as a basic tool of interpolation and blend in the graphics, such as SLERP (spherical linear interpolation) and ARAP (as rigid as possible). This analysis enables us to understand the previous method as well as to generalize and to improve the quality and speed of the interpolation.
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