PURPOSE: To approximate an optional free curved surface with one C1-successive NURBS curved surface by referring to given permissible precision and match the border of the approximated NURBS curved surface with the border of the original free curved surface.

CONSTITUTION: A border curved surface is converted into an NURBS curve and two opposite border curves are equalized in degree. The NOT vectors of the border curves are merged to constitute meshes on a parameter space. An approximate curve on a curved surface is found by utilizing the meshes to constitute meshes of the curved surface, and mesh-by-mesh, approximation using one hyperbolic tertiary Bezier patch is performed to obtain C1 succession. The precision of the Bezier patch is checked; when the precision is higher than the permissible precision, the degree of the Bezier patch is adjusted and the original border curve is reflected on the border of the approximated Bezier patch, thereby making all approximated Bezier patches into one NURBS curved surface shown in the figure.