Abstract: An image processing apparatus for forming a modified image from an original image, in which addresses for the modified image are calculated, and corresponding addresses of the original image are calculated, both sets of calculations being performed in such a manner that a substantial amount of the data needed for the calculations is prestored in a look-up table or the like. In addition, the calculations are carried out in such a manner as to reduce the number of multiplications and divisions (versus additions) which must be performed, to increase calculation speed.

Abstract: The present invention provides a method of editing NC programs for a four-axis lathe for creating NC programs that make possible simultaneous machinining by two tool rests. In order to raise machining efficiency, the machining speed is adjusted between the NC programs edited for each tool rest or an adjustment is performed by altering machining sequences or by resetting them in such a manner that the machining sequences are executed simultaneously. This facilitates modification of machining speed, resetting of machining sequence, etc.