Splines in the Space of Shells
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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Cubic splines in Euclidean space minimize the mean squared acceleration among all curves interpolating a given set of data points. We extend this observation to the Riemannian manifold of discrete shells in which the associated metric measures both bending and membrane distortion. Our generalization replaces the acceleration with the covariant derivative of the velocity. We introduce an effective time-discretization for this novel paradigm for navigating shell space. Further transferring this concept to the space of triangular surface descriptors-edge lengths, dihedral angles, and triangle areas-results in a simplified interpolation method with high computational efficiency.
Description
@article{10.1111:cgf.12968,
journal = {Computer Graphics Forum},
title = {{Splines in the Space of Shells}},
author = {Heeren, Behrend and Rumpf, Martin and Schröder, Peter and Wardetzky, Max and Wirth, Benedikt},
year = {2016},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.12968}
}