Abstract
In this paper, a method for constructing a class of quintic curves with rational offsets is presented. Although this class of planar curves does not include PH curves, such curves are widely applied in CAD because they have rational offsets. A complex variate model is employed to deduce the proposed method. The quintic OR curves are first classified into two classes according to the different factorization of their hodographs, and are then discussed. With the given $C^1$ Hermite data, the curves are determined by specifying a real parameter. This real parameter can be used to adjust the shape of the constructed curves, and affects the parameter values of the cusps.
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