Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 9, Issue 4, Pages 1788-1828Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1057978
Keywords
composite Bezier surface; Riemannian manifold; differentiability conditions; bending energy
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Funding
- Alfried Krupp Prize for Young University Teachers - Alfried Krupp von Bohlen und Halbach-Stiftung
- Deutsche Forschungsgemeinschaft (DFG)
- Cells-in-Motion Cluster of Excellence [EXC1003 - CiM]
- University of Muunster, Germany
- Interuniversity Attraction Poles Programme
- Belgian Science Policy Office
- Belgian FNRS [FRFC 2.4585.12]
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We generalize the notion of Bezier surfaces and surface splines to Riemannian manifolds. To this end we put forward and compare three possible alternative definitions of Bezier surfaces. We furthermore investigate how to achieve C-0 - and C-1 - continuity of Bezier surface splines. Unlike in Euclidean space and for one-dimensional Bezier splines on manifolds, C-1-continuity cannot be ensured by simple conditions on the Bezier control points: it requires an adaptation of the Bezier spline evaluation scheme. Finally, we propose an algorithm to optimize the Bezier control points given a set of points to be interpolated by a Bezier surface spline. We show computational examples on the sphere, the special orthogonal group, and two Riemannian shape spaces.
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