Mathematical analysis on affine maps for 2D shape interpolation

S. Kaji, Sampei Hirose, S. Sakata, Y. Mizoguchi, K. Anjyo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

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 languageEnglish
Title of host publicationComputer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012
PublisherAssociation for Computing Machinery, Inc
Pages71-76
Number of pages6
ISBN (Electronic)9783905674378
Publication statusPublished - 2012 Jul 29
Externally publishedYes
Event11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 - Lausanne, Switzerland
Duration: 2012 Jul 292012 Jul 31

Other

Other11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
CountrySwitzerland
CityLausanne
Period12/7/2912/7/31

Fingerprint

Interpolation
Rigidity

ASJC Scopus subject areas

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

Cite this

Kaji, S., Hirose, S., Sakata, S., Mizoguchi, Y., & Anjyo, K. (2012). Mathematical analysis on affine maps for 2D shape interpolation. In 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, 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 proceedingConference contribution

Kaji, S, Hirose, S, Sakata, S, Mizoguchi, Y & Anjyo, K 2012, Mathematical analysis on affine maps for 2D shape interpolation. in 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, 12/7/29.
Kaji S, Hirose S, Sakata S, Mizoguchi Y, Anjyo K. Mathematical analysis on affine maps for 2D shape interpolation. In Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. Association for Computing Machinery, Inc. 2012. p. 71-76
Kaji, S. ; Hirose, Sampei ; Sakata, S. ; Mizoguchi, Y. ; Anjyo, K. / Mathematical analysis on affine maps for 2D shape interpolation. Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. Association for Computing Machinery, Inc, 2012. pp. 71-76
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