Speaker
Description
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 admit rational offset curves, which are useful in computer-aided design and manufacturing. 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 key 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, making PH curves useful in robotics as well. In the talk we give an overview of various PH construction algorithms and methods, supported by numerical examples that illustrate their efficiency, present some recent developments and future challenges.
