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Generalized Metric Energies for Continuous Shape Deformation

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8177))

Abstract

High quality deformations of planar and volumetric domains are central to many computer graphics related problems like modeling, character animation, and non-rigid registration. Besides common “as-rigid-as-possible” approaches the class of nearly-isometric deformations is highly relevant to solve this kind of problems. Recent continuous deformation approaches try to find planar first order nearly-isometric deformations by integrating along approximate Killing vector fields (AKVFs). In this work we derive a generalized metric energy for deformation vector fields that has close-to-isometric AKVFs as a special case and additionally supports close-to-length-preserving, close-to-conformal as well as close-to-equiareal deformations. Like AKVF-based deformations we minimize nonlinear energies to first order using efficient linear optimizations. Our energy formulation supports nonhomogeneous as well as anisotropic behavior and we show that it is applicable to both planar and volumetric domains. We apply energy specific regularization to achieve smoothness and provide a GPU implementation for interactivity. We compare our approach to AKVF-based deformations for the planar case and demonstrate the effectiveness of our method for the 2d and 3d case.

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Author information

Authors and Affiliations

  1. Visual Computing Group, University of Magdeburg, Germany

    Janick Martinez Esturo, Christian Rössl & Holger Theisel

  2. Max Planck Institute for Computer Science, Saarland University, Germany

    Janick Martinez Esturo

Authors
  1. Janick Martinez Esturo
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  2. Christian Rössl
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  3. Holger Theisel
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Martinez Esturo, J., Rössl, C., Theisel, H. (2014). Generalized Metric Energies for Continuous Shape Deformation. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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