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The machining of three dimensional objects that embody complex surfaces such as aircraft contours or ship propellers challenges the machine tool numerical control programmer. In industries where automated manufacturing is playing an increasingly important role, product designs often call for physical surfaces that cannot be represented analytically by simple mathematical expressions. An aircraft fuselage or an automobile body, for example, may be conceived in clay, but eventually it is produced in aluminum or steel by methods that demand a numerical representation of the surfaces. With the growth of numerical control, the need has increased to devise analytical techniques for the description of these surfaces, particularly for the application of the techniques to the Automatic Programmed Tool (APT) numerical control processor.1 In fact, the application of APT, the most powerful and widely used numerical control parts programming language to more sophisticated and complex machining requirements, has emphasized the need for a more advanced numerically controlled sculptured surface technology. By sculptured surface is meant the mathematical description of a conceptualized physical surface that requires a process similar to sculpturing to produce.
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