Time-Discrete Geodesics in the Space of Shells

Authors:
B. Heeren;M. Rumpf;M. Wardetzky;B. Wirth
Affiliations:
Institute for Numerical Simulation, University of Bonn, Germany;Institute for Numerical Simulation, University of Bonn, Germany;Institute of Num. and Appl. Math, University of Göttingen, Germany;Courant Institute, New York University, USA
Venue:
Computer Graphics Forum
Year:
2012

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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. © 2012 Wiley Periodicals, Inc.