A machine-implemented circle-generation method calculates a sequence of coordinates (x.sub.n, y.sub.n) of points approximating a circle or circular arc according to the iterative formula: ##EQU1## or an approximation thereto. This formula is suitable for high-speed computation and approximates a true circle extremely closely. When rounded off to integer coordinates, the starting and ending points of a full circle coincide.
Digital sinusoidal waves are generated using a method based on an error measuring algorithm used to generate a synthesized circle. X and Y waves are generated step-wise to follow the contour of a reference circle in the x-y plane by computing the mean square error at each step and using the error value to calculate the next values of X and Y. The digital sine waves are converted to three-phase, pulse width modulated signals. Direct current power is inverted to three phase power to operate a motor under the control of the PWM signals. The controller permits control of voltage, voltage-frequency ratio, boost voltage, and acceleration-deceleration.
