### Abstract

This paper gives a simple mathematical framework for 2D shape interpolation methods that preserve rigidity. An interpolation technique in this framework works for given the source and target 2D shapes, which are compatibly triangulated. Focusing on the local affine maps between the corresponding triangles, we describe a global transformation as a piecewise affine map. Several existing rigid shape interpolation techniques are discussed and mathematically analyzed through this framework. This gives us not only a useful comprehensive understanding of existing approaches, but also new algorithms and a few improvements of previous approaches.

Original language | English |
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Title of host publication | Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012 |

Editors | Dieter W. Fellner |

Publisher | Association for Computing Machinery, Inc |

Pages | 71-76 |

Number of pages | 6 |

ISBN (Electronic) | 9783905674378 |

Publication status | Published - Jul 29 2012 |

Event | 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 - Lausanne, Switzerland Duration: Jul 29 2012 → Jul 31 2012 |

### Other

Other | 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 |
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Country | Switzerland |

City | Lausanne |

Period | 7/29/12 → 7/31/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Vision and Pattern Recognition
- Human-Computer Interaction
- Computer Graphics and Computer-Aided Design
- Software

### Cite this

*Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012*(pp. 71-76). Association for Computing Machinery, Inc.

**Mathematical analysis on affine maps for 2D shape interpolation.** / Kaji, Shizuo; Hirose, S.; Sakata, S.; Mizoguchi, Yoshihiro; Anjyo, K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012.*Association for Computing Machinery, Inc, pp. 71-76, 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012, Lausanne, Switzerland, 7/29/12.

}

TY - GEN

T1 - Mathematical analysis on affine maps for 2D shape interpolation

AU - Kaji, Shizuo

AU - Hirose, S.

AU - Sakata, S.

AU - Mizoguchi, Yoshihiro

AU - Anjyo, K.

PY - 2012/7/29

Y1 - 2012/7/29

N2 - This paper gives a simple mathematical framework for 2D shape interpolation methods that preserve rigidity. An interpolation technique in this framework works for given the source and target 2D shapes, which are compatibly triangulated. Focusing on the local affine maps between the corresponding triangles, we describe a global transformation as a piecewise affine map. Several existing rigid shape interpolation techniques are discussed and mathematically analyzed through this framework. This gives us not only a useful comprehensive understanding of existing approaches, but also new algorithms and a few improvements of previous approaches.

AB - This paper gives a simple mathematical framework for 2D shape interpolation methods that preserve rigidity. An interpolation technique in this framework works for given the source and target 2D shapes, which are compatibly triangulated. Focusing on the local affine maps between the corresponding triangles, we describe a global transformation as a piecewise affine map. Several existing rigid shape interpolation techniques are discussed and mathematically analyzed through this framework. This gives us not only a useful comprehensive understanding of existing approaches, but also new algorithms and a few improvements of previous approaches.

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M3 - Conference contribution

AN - SCOPUS:84890907681

SP - 71

EP - 76

BT - Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012

A2 - Fellner, Dieter W.

PB - Association for Computing Machinery, Inc

ER -