Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
A metric for parametric approximation
Proceedings of the international conference on Curves and surfaces in geometric design
The NURBS book
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
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
A general framework for high-accuracy parametric interpolation
Mathematics of Computation
Geometric Hermite Interpolation---
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
Construction of low degree rational motions
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geometric interpolation by rational spline motions is presented and two particularly important cases are analyzed, i.e., geometrically continuous quartic rational motions and second order geometrically continuous rational spline motions of degree six. In both cases sufficient conditions on the given Hermite data are found which guarantee the uniqueness of the solution. If the given data do not fulfill the solvability conditions, a method to perturb them slightly is described. Numerical examples are presented which confirm the theoretical results and provide evidence that the obtained motions have nice shapes.