OPTIMAL PARAMETERIZATIONS

The problem of exercising the freedoms of reparameterization of polyno mial or rational curve segments to achieve a ''parametric flow'' close st to the unit-speed or are-length representation is addressed. A quan titative measure of ''closeness'' to are-length parameterization is fo rmulated and, according to this measure, the problem of identifying th e optimum rational reparameterization of a degree n polynomial curve i s shown to be analytically reducible to the determination of the uniqu e real root on (0, 1) of a quadratic equation. Examples indicate that, in practice, the algorithm can produce significantly more uniform par ameter variation across the extent of typical Bezier curves. The gener alization of the method to reparameterization of rational curves is mo re difficult, however, and does not admit generic reduction to a polyn omial equation in even the simplest context (the conics).