In curved surface machining it is customary to represent and to generate the surface as a sequence of short linearly interpolated moves. Experimental measurements of such stop-start motion shows that full cutting speed is achieved typically for only ten percent of the machining time; the remaining time is spent in accelerating, decelerating, or pausing between instructions. An algorithm is presented which uses a recursive approach to maximize the number of circularly interpolated moves for surface generation. A reduction in machining time of up to 5:1 is demonstrated using this approach.