A new NURBS offset curves and surfaces algorithm based on different geometry shape

A new approach for computing NURBS offset curves and surfaces was proposed in this paper. First of all, the special NURBS curves and surfaces were recognized to be different with free form ones. The offsets of the special cases were precisely calculated according to their equations. The offset of free form NURBS curves and surfaces were solved using the following steps: (1) Decomposing the NURBS curve and surface into Bezier segments or surface patches; (2) Sampling Bezier segments or surface patches and removing duplicate points; (3) Interpolating the offset points and creating offset curve or surface; (4) Reducing the control points by removing all removable knots with a user defined tolerance. On the premise of keeping the shape of offset curves and surfaces, not only the degree of curve or surface could be freely controlled, but also less number of control points was needed and also duplicate knots were avoided. It was proved in practical engineering that the efficiency and precision were improved mush.