This paper addresses the problem of generating smooth trajectories between an initial and a
final position and orientation in space. The main idea is to define a functional depending on …

Functional data analysis (FDA) is a fast-growing area of research and development in
statistics. While most FDA literature imposes the classical L 2 Hilbert structure on function …

Abstract We examine the De Casteljau algorithm in the context of Riemannian symmetric
spaces. This algorithm, whose classical form is used to generate interpolating polynomials …

This article presents a new mathematical framework to perform statistical analysis on time-
indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of …

We investigate higher-order geometric k-splines for template matching on Lie groups. This is
motivated by the need to apply diffeomorphic template matching to a series of images, eg, in …

Abstract Given data points p 0,…, p N on a closed submanifold M of ℝ n and time instants 0=
t 0< t 1<⋅⋅⋅< t N= 1, we consider the problem of finding a curve γ on M that best …

This paper develops a method for generating smooth trajectories for a moving rigid body
with specified boundary conditions. Our method involves two key steps: 1) the generation of …

We present a procedure to generate smooth interpolating curves on submanifolds, which
are given in closed form in terms of the coordinates of the embedding space. In contrast to …

In a connected Riemannian manifold, generalised Bézier curves are C∞ curves defined by
a generalisation, in which line segments are replaced by minimal geodesics, of the classical …

This paper studies variational collision avoidance problems for multiagent systems on
complete Riemannian manifolds. That is, we minimize an energy functional, among a set of …