Time-Discrete Geodesics in the Space of Shells

Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation...

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Bibliographic Details
Published in:Computer graphics forum Vol. 31; no. 5; pp. 1755 - 1764
Main Authors: Heeren, B., Rumpf, M., Wardetzky, M., Wirth, B.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2012
Subjects:
Bending
Computation
Computational mathematics
Computer graphics
Deformation
Distortion
Evolution
Geodetics
I.3.5 [Computer Graphics]: Computational geometry and object modeling-Physically based modeling
Mathematical models
Shells
Studies
Thin walled shells
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation energy on top of membrane distortion terms in order to obtain a physically sound notion of distance between shells, which does not require additional smoothing. Our bending energy formulation depends on the so‐called relative Weingarten map, for which we provide a discrete analogue based on principles of discrete differential geometry. Our computational results emphasize the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.
Bibliography:ark:/67375/WNG-GJVBQ1NZ-2
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ArticleID:CGF3180
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03180.x