Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Generating curves and swept surfaces by blended circles
Computer Aided Geometric Design
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
The De Casteljau Algorithm on Lie Groups and Spheres
Journal of Dynamical and Control Systems
Elastic Morphing of 2D and 3D Objects on a Shape Manifold
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
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This paper presents a simple geometric algorithm to generate splines of arbitrary degree of smoothness in Euclidean spaces. Unlike other existing methods, this simple geometric algorithm does not require a recursive procedure and, consequently, introduces a significant reduction in calculation time. The algorithm is then extended to other complete Riemannian manifolds, namely to matrix Lie groups and spheres.