Introduction

This textbook addresses the challenges of fitting and interpolation on Riemannian manifoldsRiemannian manifold. Initially, it delves into developing techniques for fitting data on a general Euclidean space. A significant emphasis will be placed on a specific aspect involving Bézier curves and the de Casteljau algorithm. Our particular attention is on Bézier spline interpolations due to their simplicity, flexibility, and theoretical guarantees. Subsequently, the exploration extends to the generalization of the proposed Euclidean Bézier curve techniques to various examples of Riemannian manifolds. Such generalization involves an in-depth examination of the geometric properties of the Riemannian manifold.