Title: Pythagorean-hodograph curves

 

Abstract:

Polynomial Pythagorean-hodograph curves (PH curves) have been introduced in 1990 by Farouki and Sakkalis. They are characterized by the property that their parametric speed, i.e., the derivative of the arc length with respect to the curve parameter, is a polynomial function. Polynomial PH curves form an important class of parametric polynomial curves for which the arc length can be computed exactly and their offsets (parallel curves) are rational curves. This makes them very useful in many practical applications, e.g. in CAD/CAM systems, robotics, animation, NC machining, spatial path planning based on rotation-minimizing frames, etc.