Computing the Parameters of Points on Nurbs Curves and Surfaces via Moving Affine Frame Method

The numerical instability in computing the parameters of the points on Nurbs curves/surfaces is a fatal disadvantage of Nurbs methods. In this paper, the authors introduce the moving affine frame (MAF) method for intersection calculation of parametric curves and surfaces. Based on the principle of a MAF method, a new method for computing the parameters of the points on Nurbs curves and surfaces is presented. The numerical stability and the efficiency of the method are better than all traditional iterative methods. The new method has been applied to the commercial 3D CAD system GEMS5.0.