Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
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An intuitive approach to designing spatial C2 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" C2 cubic B---spline curve determined by the given control polygon is first computed, and the C2 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.