An intuitive approach to designing spatial C 2 Pythagorean–hodograph (PH) quintic spline curves, based on given control polygons, is presented. Although PH curves can always be represented in Bézier or B–spline form, changes to their control polygons will usually compromise their PH nature. To circumvent this problem, an approach similar to that developed in [13] for the planar case is adopted. Namely, the “ordinary” C 2 cubic B–spline curve determined by the given control polygon is first computed, and the C 2 PH spline associated with that control polygon is defined so as to interpolate the nodal points of the cubic B–spline, with analogous end conditions. The construction of spatial PH spline curves is more challenging than the planar case, because of the residual degrees of freedom it entails. Two strategies for fixing these free parameters are presented, based on optimizing shape measures for the PH spline curves
Farouki, R., Manni, C., Pelosi, F., Sampoli, M. (2012). Design of C 2 spatial Pythagorean-hodograph quintic spline curves by control polygons. In J. Boissonnat, P. Chenin, A. Cohen, C. Gout, T. Lyche, M. Mazure, et al. (a cura di), Curves and surfaces: 7th International Conference, Avignon, France, June 24 - 30, 2010: revised selected papers (pp. 253-269). Springer [10.1007/978-3-642-27413-8_16].
Design of C 2 spatial Pythagorean-hodograph quintic spline curves by control polygons
MANNI, CARLA;PELOSI, FRANCESCA;
2012-01-01
Abstract
An intuitive approach to designing spatial C 2 Pythagorean–hodograph (PH) quintic spline curves, based on given control polygons, is presented. Although PH curves can always be represented in Bézier or B–spline form, changes to their control polygons will usually compromise their PH nature. To circumvent this problem, an approach similar to that developed in [13] for the planar case is adopted. Namely, the “ordinary” C 2 cubic B–spline curve determined by the given control polygon is first computed, and the C 2 PH spline associated with that control polygon is defined so as to interpolate the nodal points of the cubic B–spline, with analogous end conditions. The construction of spatial PH spline curves is more challenging than the planar case, because of the residual degrees of freedom it entails. Two strategies for fixing these free parameters are presented, based on optimizing shape measures for the PH spline curvesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
