Visualization of moving objects using dual quaternion curves

Abstract

The interpolation of some positions (= point + orientation) of a moving object is examined with help of dual quaternion curves. In order to apply the powerful methods of computer-aided geometric design, an interpolating motion whose trajectories are rational Bézier curves is constructed. The interpolation problem is discussed from a mechanical and a geometrical viewpoint. A representation formula for rational motions of fixed order is presented. Finally, the construction of rational spline motions is outlined. Dual quaternions prove to be very useful in computer graphics. © 1994.