Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
A method for computing rational motions of a rigid body is presented. The method is based on the construction of spatial quintic Pythagorean-hodograph (PH) spline curves interpolating \(G^1\) Hermite motion data, i.e. initial/final points and rotations at the given points. The orientation of the rigid body coincides with the Euler-Rodrigues frame. The Euler-Rodriques frame is rational by construction and always non-singular at inflection points. The resulted PH curve is expressed with three free parameters used to control the length of the curve (or to provide a \(C^1\) interpolant) and to guarantee that the Euler-Rodrigues frame is as close as possible to the corresponding rotation minimizing frame. The presented method can be applied in computer animation, robot manipulation, construction of a smooth camera motion, spatial path planning in manufacturing and in many other areas where the motion of a rigid body along curved paths is considered.
spatial quintic Pythagorean-hodograph spline curves
scientific article; zbMATH DE number 6107058