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Splines in the Space of Shells
Author(s) -
Heeren Behrend,
Rumpf Martin,
Schröder Peter,
Wardetzky Max,
Wirth Benedikt
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12968
Subject(s) - interpolation (computer graphics) , mathematics , generalization , euclidean space , discretization , surface (topology) , acceleration , space (punctuation) , mathematical analysis , geometry , algorithm , computer science , artificial intelligence , motion (physics) , physics , classical mechanics , operating system
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.