In the construction and analysis of a planar Pythagorean–hodograph (PH) quintic curve r(t), t∈[0,1] using the complex representation, it is convenient to invoke a translation/rotation/scaling transformation so r(t) is in canonical form with r(0)=0, r(1)=1 and possesses just two complex degrees of freedom. By choosing two of the five control–polygon legs of a quintic PH curve as these free complex parameters, the remaining three control–polygon legs can be expressed in terms of them and the roots of a quadratic or quartic equation. Consequently, depending on the chosen two control–polygon legs, there exist either two or four distinct quintic PH curves that are consistent with them. A comprehensive analysis of all possible pairs of chosen control polygon legs is developed, and examples are provided to illustrate this control–polygon paradigm for the construction of planar quintic PH curves.
Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints
2023-01-01
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
DDC: | 629 |
Cooperative Trajectory Generation Using Pythagorean Hodograph Bézier Curves
Online Contents | 2016
|Appendix B: Pythagorean Hodograph
Wiley | 2010
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