Abstract: Although the curve with shape parameters has become one of the most popular topics in the
curve modeling, but the values of shape parameters are always given as intervals, while in practice,
the optimal parameter values is often needed to ensure that the curves have good fairness and
smoothness. According to this problem, firstly, a automatic mathematical model which is based on the
fairing criterion is established to obtain the optimal parameters, and then the concrete steps of genetic
algorithm is given to solve the model. At the last, two classes of curves are used as examples to
illustrate the effectiveness of our methods.

Key words: parameter curve, shape parameter, optimal value of parameter, fairness and smoothness;
genetic algorithm