This paper explains in detail a simulator that has been developed for graphic verification of five-axis Numerical Control (NC) machining. Exact parametric representations for the surfaces generated by common NC milling cutters during five-axis motions have been derived using the theory of envelopes as the mathematical basis. Parts of these surfaces form the boundary of the total swept volume generated. For each cutting motion, the swept volume of the cutter is determined and then subtracted from the stock. The Boolean subtraction is done in the image space at the pixel level, using a modified depth-buffer algorithm. A shaded image of the “as machined” part at the end of each cutting motion is then displayed for verification.

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