On G1 and G2 Hermite interpolation by spatial Algebraic-Trigonometric Pythagorean Hodograph curves with polynomial parametric speed

In this paper we focus on the class of Algebraic-Trigonometric Pythagorean Hodograph curves (ATPH for short) that is characterized by a purely polynomial parametric speed. Within such a class of ATPH curves, we first construct interpolants to spatial G1 Hermite data equipped with curvature values. With respect to the solutions proposed in [24], the G1 Hermite ATPH interpolants we here propose are characterized by C0- and C1-continuous curvature plots. Secondly, we investigate the existence of ATPH interpolants to spatial G2 Hermite data and show that solutions exist under some restrictions on the Hermite input data.