Mathematical analysis on affine maps for 2D shape interpolation

Shizuo Kaji, S. Hirose, S. Sakata, Yoshihiro Mizoguchi, K. Anjyo

    Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
    Title of host publicationComputer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012
    EditorsDieter W. Fellner
    PublisherAssociation for Computing Machinery, Inc
    Pages71-76
    Number of pages6
    ISBN (Electronic)9783905674378
    Publication statusPublished - Jul 29 2012
    Event11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012 - Lausanne, Switzerland
    Duration: Jul 29 2012Jul 31 2012

    Other

    Other11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
    CountrySwitzerland
    CityLausanne
    Period7/29/127/31/12

    All Science Journal Classification (ASJC) codes

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

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  • Cite this

    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). Association for Computing Machinery, Inc.