Adaptive gregory patch approximation to z-map data

A method is proposed for Gregory surface approximation to 3D array data poi nts. Surface approximation is the process of constructing a compact represe ntation to model an object surface based on a fairly large number of measur ed 3D data points. Based an 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 app roximated. The method has been implemented using piecewise bicubic Gregory patches with G(I) continuity. An advantage of this approach is that the ref inement is essentially local, reducing the computational requirements that permit the processing of a large number of data points. This method, combin ed with the inverse offsetting method can be used to obtain an offset surfa ce without self-interference. The offset surface can be used to generate ga uging-free CL tool paths far machining compound surfaces on milling machine s.