The construction of spatial C2 PH quintic interpolating splines is reduced, by means of the quaternion representation of Choi et al. [2], to solving a system of quadratic equations in quaternion un- knowns, with three degrees of freedom in each subinterval. A strategy to fix these free parameters is proposed. With this choice, a solution of the quadratic system can be efficiently computed to within machine precision by means of a few iterations of a Newton–like method. The quality of the resulting PH spline depends strongly upon the starting approximation. To guide this choice, we use first–order PH Hermite interpolants with derivatives from the “ordinary” cubic spline [10]. Examples from an implementation of the method are presented.
Spatial C^2 PH quintic splines / FAROUKI R.; MANNI C.; A. SESTINI. - STAMPA. - (2003), pp. 147-156. (Intervento presentato al convegno Fifth. International Conference on Curves and Surfaces tenutosi a Saint Malo, Francia nel 27 Giugno-3 Luglio 2002).
Spatial C^2 PH quintic splines
SESTINI, ALESSANDRA
2003
Abstract
The construction of spatial C2 PH quintic interpolating splines is reduced, by means of the quaternion representation of Choi et al. [2], to solving a system of quadratic equations in quaternion un- knowns, with three degrees of freedom in each subinterval. A strategy to fix these free parameters is proposed. With this choice, a solution of the quadratic system can be efficiently computed to within machine precision by means of a few iterations of a Newton–like method. The quality of the resulting PH spline depends strongly upon the starting approximation. To guide this choice, we use first–order PH Hermite interpolants with derivatives from the “ordinary” cubic spline [10]. Examples from an implementation of the method are presented.
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