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 |
|---|---|
| Title of host publication | Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012 |
| Publisher | Association for Computing Machinery, Inc |
| Pages | 71-76 |
| Number of pages | 6 |
| ISBN (Electronic) | 9783905674378 |
| Publication status | Published - 2012 Jul 29 |
| Externally published | Yes |
| Event | 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 - Lausanne, Switzerland Duration: 2012 Jul 29 → 2012 Jul 31 |
Other
| Other | 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 |
|---|---|
| Country | Switzerland |
| City | Lausanne |
| Period | 12/7/29 → 12/7/31 |
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ASJC Scopus subject areas
- Computer Vision and Pattern Recognition
- Human-Computer Interaction
- Computer Graphics and Computer-Aided Design
- Software
Cite this
Mathematical analysis on affine maps for 2D shape interpolation. / Kaji, S.; Hirose, Sampei; Sakata, S.; Mizoguchi, Y.; Anjyo, K.
Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. Association for Computing Machinery, Inc, 2012. p. 71-76.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Mathematical analysis on affine maps for 2D shape interpolation
AU - Kaji, S.
AU - Hirose, Sampei
AU - Sakata, S.
AU - Mizoguchi, Y.
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
SP - 71
EP - 76
BT - Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012
PB - Association for Computing Machinery, Inc
ER -