C1 Hermite interpolation with simple planar PH curves by speed reparametrization

We introduce a new method of solving C1 Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t−c)2n+1+d. Next, we introduce a speed reparametrization. Finally, we show that, for C1 Hermite data, we can use PH curves of type K(t−c)2n+1+d or strongly regular PH quintics satisfying the G1 reduction of C1 data, and use these curves to solve the original C1 Hermite interpolation problem.