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 six-dimensional 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 C1 Hermite data and constructing spirals as G2 transition elements between a line segment and a circle, as well as between a pair of external circles