Exploring the Geometry of the Space of Shells
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Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley and Sons Ltd.
Abstract
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.
Description
@article{10.1111:cgf.12450,
journal = {Computer Graphics Forum},
title = {{Exploring the Geometry of the Space of Shells}},
author = {Heeren, Behrend and Rumpf, Martin and Schröder, Peter and Wardetzky, Max and Wirth, Benedikt},
year = {2014},
publisher = {The Eurographics Association and John Wiley and Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.12450}
}