Time-Discrete Geodesics in the Space of Shells
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Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
Abstract
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.
Description
@article{10.1111:j.1467-8659.2012.03180.x,
journal = {Computer Graphics Forum},
title = {{Time-Discrete Geodesics in the Space of Shells}},
author = {Heeren, Behrend and Rumpf, Martin and Wardetzky, Max and Wirth, Benedikt},
year = {2012},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2012.03180.x}
}