Approximating shapes using parameterised curves

Often in computer-aided engineering the problem arises of finding mathematically simple approximations to given curve shapes. This can be done using parameterized curves and for ease of computation the co-ordinate functions should be polynomials of low degree in the parameter. This paper describes a method for improving the accuracy of a rough approximation of this form. Not only is the change in the co-ordinate functions dealt with, but also the possibility of altering the parameterization itself is investigated.