Splines in the Space of Shells
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...
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| Veröffentlicht in: | Computer graphics forum 2016-08, Vol.35 (5), p.111-120 |
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| container_title | Computer graphics forum |
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| creator | Heeren, Behrend Rumpf, Martin Schröder, Peter Wardetzky, Max Wirth, Benedikt |
| description | 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. |
| doi_str_mv | 10.1111/cgf.12968 |
| format | Article |
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| ispartof | Computer graphics forum, 2016-08, Vol.35 (5), p.111-120 |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete; Business Source Complete |
| subjects | Acceleration Analysis Categories and Subject Descriptors (according to ACM CCS) Computational efficiency Data points Derivatives Distortion Euclidean geometry Euclidean space I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Image processing systems Interpolation Splines Studies Topological manifolds |
| title | Splines in the Space of Shells |
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