Characterization and Coordination of Point-line Trajectories

Abstract

A point-line refers to a rigid combination of a directed line and an endpoint along the line. To trace a point-line trajectory, one must control not only the trajectory of the endpoint (the directrix) but also the direction of the point-line (the indicatrix). This paper addresses three issues on point-line trajectories. First of all, by considering the relationship between the point trajectory and the corresponding point-line direction, it offers the complete characterization of point-line trajectories. It presents the coordination of the point-line axis with a free point trajectory and also with a point trajectory constrained on a free form surface. The issue of maintaining an invariant orientation relationship between the point-line axis and the point trajectory is also addressed.