Drawing Parametric Curves Using Chebyshev Polynomials

Polynomial parametric curves are powerful and popular modeling tools in Computer Graphics and Computer Aided Design. There are two requirements that are placed on techniques for displaying these curves. In interactive applications, such as drawing and design, the need is for a fast display. In non interactive applications, such as typeset ting, the need is for accuracy (or at least the appearance of accuracy). Most techniques address one or the other of these conflicting requirements. We propose and demonstrate the use of Chebyshev basis functions for an adaptive curve drawing method which is both fast and accurate. The use of Chebyshev polynomials provide us with an inexpensive linearity measure which is useful in an recursive algorithm. Further applications of this approach include efficient boxing and the generation of smooth filtered curves.