Adaptive Gregory Patch Approximation to Z-Map Data

A method is proposed for Gregory surface approximation to 3D array data points. Surface approximation is the process of constructing a compact representation to model an object surface based on a fairly large number of measured 3D data points. Based on an adaptive subdivision technique, the proposed method begins with a rough initialisation of the surface and progressively refines it in successive steps in the regions where the data is poorly approximated. The method has been implemented using piecewise bicubic Gregory patches with G 1 continuity. An advantage of this approach is that the refinement is essentially local, reducing the computational requirements that permit the processing of a large number of data points This method, combined with the inverse offsetting method, can be used to obtain an offset surface without self-interference. The offset surface can be used to generate gouging-free CL tool paths for machining compound surfaces on milling machines.