Bézier curves and C2 interpolation in Riemannian Symmetric Spaces

Chafik Samir (1) , Ines Adouani

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

We consider the problem of interpolating a finite set of observations at given time instant. In this paper, we introduce a new method to compute the optimal intermediate control points that define a C 2 interpolating Bézier curve. We prove this concept for interpolating data points belonging to a Riemannian symmetric spaces. The main property of the proposed method is that the control points minimize the mean square acceleration. Moreover, potential applications of fitting smooth paths on Riemannian manifold include applications in robotics, animations, graphics, and medical studies.

Domaines: Intelligence artificielle [cs.AI]; Optimisation et contrôle [math.OC]; Statistiques [math.ST]

Chafik Samir, Ines Adouani. Bézier curves and C2 interpolation in Riemannian Symmetric Spaces. 4th International Conference on Geometric Science of Information, Aug 2019, Toulouse, France. ⟨10.1007/978-3-030-26980-7_61⟩. ⟨hal-02289874⟩