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We derive a variational model to fit a composite B\'ezier curve to a set ofdata points on a Riemannian manifold. The resulting curve is obtained in such away that its mean squared acceleration is minimal in addition to remainingclose the data points. We approximate the acceleration by discretizing thesquared second order derivative along the curve. We derive a closed-form,numerically stable and efficient algorithm to compute the gradient of aB\'ezier curve on manifolds with respect to its control points, expressed as aconcatenation of so-called adjoint Jacobi fields. Several examples illustratethe capabilites and validity of this approach both for interpolation andapproximation. The examples also illustrate that the approach outperformsprevious works tackling this problem.

A variational model for data fitting on manifolds by minimizing the acceleration of a B\'ezier curve