Exploring the Geometry of the Space of Shells

We prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time‐ and space‐discrete geodesic calculus. In particular we show how to...

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Bibliographic Details
Published inComputer graphics forum Vol. 33; no. 5; pp. 247 - 256
Main Authors Heeren, B., Rumpf, M., Schröder, P., Wardetzky, M., Wirth, B.
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.08.2014
Subjects
Analysis
Animation
Calculus
Categories and Subject Descriptors (according to ACM CCS)
Computer animation
Computer graphics
Deformation
Elastic deformation
Extrapolation
Foundations
I.3.5 [Computer Graphics]: Computational geometry and object modeling-Physically based modeling
Mathematical analysis
Rigid-body dynamics
Shells
Studies
Transport
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Summary:We prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time‐ and space‐discrete geodesic calculus. In particular we show how to shoot geodesics with prescribed initial data, and we give a construction for parallel transport in shell space. This enables, for example, natural extrapolation of paths in shell space and transfer of large nonlinear deformations from one shell to another with applications in animation, geometric, and physical modeling. Finally, we examine some aspects of curvature on shell space.
Bibliography:ark:/67375/WNG-WFDZRJ9Z-C
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ArticleID:CGF12450
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12450