Algebraic-Trigonometric Pythagorean-Hodograph curves and their use for Hermite interpolation

In this article we define a new class of Pythagorean-Hodograph curves built-upon a sixdimensional mixed algebraic-trigonometric space, we show their fundamental properties and compare them with their well-known quintic polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve different application problems, such as interpolating C Hermite data and constructing spirals as G transition elements between a line segment and a circle, as well as between a pair of external circles.