Algebraic-trigonometric Pythagorean-hodograph curves and their use for Hermite interpolation
Résumé
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 C 1 Hermite data and constructing spirals as G 2 transition elements between a line segment and a circle, as well as between a pair of external circles.
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