Fine tuning of rational b-splines motions

This paper presents two algorithms for ne-tuning rationalspatial motions suitable for Computer Aided Design. The rationalmotions are represented by rational B-spline curves in aprojective dual three-space known as the Image Space of SpatialKinematics. The problem of ne-tuning of rational motions isstudied as that of ne-tuning the corresponding rational curvesin the Image Space called the image curves. The path-smoothingalgorithm automatically detects and smoothes out the third ordergeometric discontinuities in the path of a cubic rational Bsplineimage curve. The speed-smoothing algorithm uses a quinticrational spline image curve to obtain a second-order geometricapproximation of the path of a cubic rational B-spline imagecurve while allowing specication of the speed and the rate ofchange of speed at the key points to obtain a near constant kineticenergy parametrization. The notion of kinetic energy isused in the paper as a natural way of combining the rotationaland translational speed of a spatial motion. The results have applicationsin trajectory generation in robotics, planing of cameramovement, spatial navigation in visualization and virtual reality systems, as well as mechanical system simulation.