PRESCRIBING THE LENGTH OF RATIONAL BEZIER CURVES

Theorems and corresponding algorithms are presented which produce a ra tional Bezier curve of a specified are length subject to certain const raints. Extraneous inflection points are avoided. The problem is reduc ed to expressing the are length as a function of a single variable. A general theorem from a previous paper of the authors is used which giv es conditions under which the are length function is convex or strictl y convex. An algorithm to automatically choose the initial parameters for the secant method will produce a solution to this problem with per formance comparable to the Newton-Raphson method. Theory and algorithm s for rational parametric curves are presented. It is shown that in ce rtain cases rational parametric curves of degree three can be used whi le polynomials of bounded degree cannot.