Tube Representation of Trajectories Using Spline Functions

Abstract

The tube representation of three dimensional trajectories using 4th order B-splines and quintic splines is presented. Lines or curves have been used to display trajectories such as streamline, electric force line, and various trajectories of moving objects. A still picture, depicted by using this tube models, is able to express a shape of the trajectory, velocity, acceleration, and various attributes in a three dimensional manner, because a tube has a finite volume and it can assign local variables such as size, tortuosity, color, and texture. This representation is useful to analyze various object motions comprehensively.