Rational Bézier Line-Symmetric Motions

Abstract

This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Bézier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Bézier line-symmetric motion is reduced to that of designing a rational Bézier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Bézier line-symmetric motion whose basic surface is a hyperboloid.