Approximate Proper Reparametrization of Rational Curves

Properness of a parameterization is a basic property of rational parametric curves and it has been well studied when the coefficients of the parameterization are rational.However,such coefficients in engineering and CAGD are often represented with float numbers with errors.This work gives an algorithm to simplify the rational curves in this situation.After the approximate proper index is defined,it is computed by solving the semi-algebra system.The greatest common divisor is obtained according to the computing process of approximate proper index.Finally,the approximate proper reparameterization is obtained by the least squares method.