Rational Curves

Rational curves and splines are one of the building blocks of computer graphics and geometric modeling. Although a rational curve is more exible than its polynomial counterpart , many properties of polynomial curves are not applicable to it. For this reason it is very useful to know if a curve presented as a rational space curve has a polynomial parametrization. In this paper, we present an algorithm to decide if a polynomial parametrization exists, and to compute the parametrization. In algebraic geometry it is known that a rational algebraic curve is polynomially parametriz-able ii it has one place at innnity. This criterion has been used in earlier methods to test polynomial parametrizability of algebraic plane curves. The resulting algorithm is complicated and also requires that the parametric curves be implicitized. This causes problem for rational space curves. In this paper we give a simple condition which is both necessary and suucient for polynomial parametrizability of rational space curves. The calculation of the polynomial parametrization is simple, and involves only a rational reparametrization of the curve.