PURPOSE: To prevent a cutter from thrusting into a workpiece at an abrupt change point in the shape of a model without the model being damaged, by detecting an abrupt point in the model shape before a stylus reaches the abrupt point, so that the control of deceleration is carried out.

CONSTITUTION: Light from a spot light source 13 impinges upon a light receiving element 18 through lenses 14, 15 and a half mirror 16 and as well so that the light receiving element 19 through a half-mirror 17 so that the light receiving elements 18, 19 issue signals (a, b). A differential amplifier 20 computes the difference between the signals (a, b), and delivers the value of the difference to a speed signal generator circuit 21. A speed control unit 22 drives a motor 24 at a speed corresponding to a signal from the circuit 21 to move the lens 15 to a position where the signals (a, b) are made equal together. A processing device 26 detects the position of the lens 15 at predetermined time intervals by means of a positional detector 25 to calculate the moving amount of a lens 15. If the moving amount is larger than a predetermined moving amount so that there is judged an abrupt change point in a model, a profile control section 10 issues a decelerating signal (d), and after machining at a decelerated speed, the processing device 26 removes the signal (d).