FINE TUNING OF RATIONAL B-SPLINES MOTIONS

摘要

This paper presents two algorithms for fne-tuning rationalrnspatial motions suitable for Computer Aided Design. The rationalrnmotions are represented by rational B-spline curves in arnprojective dual three-space known as the Image Space of SpatialrnKinematics. The problem of fne-tuning of rational motions isrnstudied as that of fne-tuning the corresponding rational curvesrnin the Image Space called the image curves. The path-smoothingrnalgorithm automatically detects and smoothes out the third orderrngeometric discontinuities in the path of a cubic rational Bsplinernimage curve. The speed-smoothing algorithm uses a quinticrnrational spline image curve to obtain a second-order geometricrnapproximation of the path of a cubic rational B-spline imagerncurve while allowing specifcation of the speed and the rate ofrnchange of speed at the key points to obtain a near constant kineticrnenergy parametrization. The notion of kinetic energy isrnused in the paper as a natural way of combining the rotationalrnand translational speed of a spatial motion. The results have applicationsrnin trajectory generation in robotics, planing of camerarnmovement, spatial navigation in visualization and virtual realityrnsystems, as well as mechanical system simulation.