2014 • Conference Paper
Piecewise-Bézier C¹ interpolation on Riemannian manifolds with application to 2D shape morphing
Authors:
Gousenbourger, Pierre-Yves,
Samir, Chafik,
Absil, Pierre-Antoine
Published in:
ICPR2014
We present a new framework to fit a path to a given finite set of data points on a Riemannian manifold. The path takes the form of a continuously-differentiable concatenation of Riemannian Bézier segments. The selection of the control points that define the Bézier segments is partly guided by the differentiability requirement and by a minimal mean squared acceleration objective. We illustrate our approach on specific manifolds: the Euclidean plane (for sanity check), the sphere (as a first nonlinear illustration), the special orthogonal group (with rigid body motion applications), and the shape manifold (with 2D shape morphing applications).