Mathematical analysis on affine maps for 2D shape interpolation

S. Kaji; S. Hirose; S. Sakata; Y. Mizoguchi; K. Anjyo

Mathematical analysis on affine maps for 2D shape interpolation

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

Department of Engineering and Design

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

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

Publication series

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

Other

Other	11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
Country	Switzerland
City	Lausanne
Period	12/7/29 → 12/7/31

ASJC Scopus subject areas

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

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Kaji, S., Hirose, S., Sakata, S., Mizoguchi, Y., & Anjyo, K. (2012). Mathematical analysis on affine maps for 2D shape interpolation. In D. W. Fellner (Ed.), Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012 (pp. 71-76). (Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012). Association for Computing Machinery, Inc.

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

Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. ed. / Dieter W. Fellner. Association for Computing Machinery, Inc, 2012. p. 71-76 (Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012).

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

Kaji, S, Hirose, S, Sakata, S, Mizoguchi, Y & Anjyo, K 2012, Mathematical analysis on affine maps for 2D shape interpolation. in DW Fellner (ed.), Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. 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 Fellner DW, editor, Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012. Association for Computing Machinery, Inc. 2012. p. 71-76. (Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012).

Kaji, S. ; Hirose, S. ; 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. editor / Dieter W. Fellner. Association for Computing Machinery, Inc, 2012. pp. 71-76 (Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012).

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