Abstract: Presents a new kind of linear and circular interpolation method in a coordinate plane, .the interpolation precision of which can reach 0.5 of a pulse equivalent, while interpolation precision of the method in common use can only attain 1 pulse equivalent. In addition less amount of data needs to be handled .with this method and the speed of interpolation is higher. Thus it is of practical value in improving precision and speed of controllers, especially in common level numerical control systems. Besides interpolation methods for quadratic curves in general are dealt with, giving similarly precision of 0.5 pulse equivalent