RICAM Colloquium - Marjeta Knez - On Pythagorean-hodograph curves and their applications
Polynomial Pythagorean-hodograph (PH) curves, characterized by the property that their unit tangent is rational, have many important features for practical applications. Planar PH curves are important since they posses rational offset curves. Spatial PH curves are especially interesting because their construction from a quaternion preimage curve allows one to equip the curve with a rational orthonormal adapted frame which makes these curves an efficient tool for motion design applications. Another advantage of the polynomial PH curve is that its arc length function is also a polynomial. This property significantly simplifies the computation of PH curves with prescribed length and allows simple real-time interpolator algorithms, which makes PH curves useful in robotics as well. In the talk we give an overview of different PH construction algorithms and methods together with numerical examples to illustrate their efficiency, present some recent developments and future challenges.