NURBS approximation of surface/surface intersection curves

We use a combination of both symbolic and numerical techniques to construct a degree bounded C-continuous, rational B-spline -approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points we use the classical Newton power series factorizations to determine the distinct branches of the space intersection curve. Besides singular points we obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achieves C continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided.