Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
The Mathematical Basis of the UNISURF CAD System
The Mathematical Basis of the UNISURF CAD System
Computer Aided Geometric Design
A two-step algorithm of smooth spline generation on Riemannian manifolds
Journal of Computational and Applied Mathematics
Constructing spherical curves by interpolation
Advances in Engineering Software
On parametric smoothness of generalised B-spline curves
Computer Aided Geometric Design
Bézier curves and C2 interpolation in Riemannian manifolds
Journal of Approximation Theory
On the Geometry of Rolling and Interpolation Curves on Sn, SOn, and Grassmann Manifolds
Journal of Dynamical and Control Systems
International Journal of Systems Science - The Seventh Portuguese Conference on Automatic Control (Controlo'2006)
Elastic Morphing of 2D and 3D Objects on a Shape Manifold
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Computer Aided Geometric Design
On parametric smoothness of generalised B-spline curves
Computer Aided Geometric Design
Higher-order smoothing splines versus least squares problems on Riemannian manifolds
Journal of Dynamical and Control Systems
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Motion detection with pyramid structure of background model for intelligent surveillance systems
Engineering Applications of Artificial Intelligence
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We examine the De Casteljau algorithm in the context of Riemannian symmetric spaces. This algorithm, whose classical form is used to generate interpolating polynomials in {\Bbb R}^n, was also generalized to arbitrary Riemannian manifolds by others. However, the implementation of the generalized algorithm is difficult since detailed structure, such as boundary value expressions, has not been available. Lie groups are the most simple symmetric spaces, and for these spaces we develop expressions for the first and second order derivatives of curves of arbitrary order obtained from the algorithm. As an application of this theory we consider the problem of implementing the generalized De Casteljau algorithm on an m-dimensional sphere. We are able to fully develop the algorithm for cubic splines with Hermite boundary conditions and more general boundary conditions for arbitrary m.