Quantitative modeling of free-from curves and surfaces

In order to explore the new method for the curve and surface modeling, this paper introduced a new concept by the wavelet technique which is called the average wavelet smoothness rate (AWSR) of curves and surfaces. Based on the AWSR, a quantitative optimization modeling method of the NURBS curve and surface has been presented. Different from the traditional energy function in the optimization process, this method uses the AWSR as the objective function. Meanwhile, it can evaluate the smoothness of the results of the optimization modeling quantitatively using the value of the objective function. The experimental results are given to demonstrate the effectiveness and efficiency of this approach.