Interpolation on manifolds using Bézier functions
(2016) “International Traveling Workshop on Interactions Between Sparse Models and Technology” — Location: Aalborg, Denmark (24.August.2016)
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- Abstract
- Given a set of data points lying on a smooth manifold, we present methods to interpolate those with piecewise Bézier splines. The spline is composed of Bézier curves (resp. surfaces) patched together such that the spline is continuous and differentiable at any point of its domain. The spline is optimized such that its mean square acceleration is minimized when the manifold is the Euclidean space. We show examples on the sphere S2 and on the special orthogonal group SO(3).
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Gousenbourger, P.-Y., Absil, P.-A., Wirth, B., & Jacques, L. (2016). Interpolation on manifolds using Bézier functions. Proceedings of the third “international Traveling Workshop on Interactions between Sparse models and Technology” iTWIST′16. Published. “International Traveling Workshop on Interactions Between Sparse Models and Technology”, Aalborg, Denmark. https://hdl.handle.net/2078.5/181419 (Original work published 2016)