Structural invariance of spatial Pythagorean hodographs
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
Spatial pythagorean hodograph quintics and the approximation of pipe surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Design of C2 spatial pythagorean-hodograph quintic spline curves by control polygons
Proceedings of the 7th international conference on Curves and Surfaces
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Dealing with Pythagorean Hodograph quintic Hermite interpolation in the space, we deepen the analysis of the so-called CC criterion proposed in Farouki et al. (2008) for fixing the two free angular parameters characterizing the set of possible solutions, which remarkably influence the shape of the chosen interpolant. Such criterion is easy to implement, guarantees the reproduction of the standard cubic Hermite interpolant when it is a PH curve and usually allows the selection of interpolants with good shape. Here we first rigorously prove that the PH interpolant it selects doesn@?t depend on the unit pure vector chosen for representing its hodograph in quaternion form. Then we evaluate the corresponding interpolation scheme from a theoretical point of view, proving with the help of symbolic computation that it has fourth approximation order. A selection of experiments related to the spline implementation of the method confirms our analysis.