In a copy control device wherein a model (6) and a workpiece moved relatively with a tracer head (4) and a tool in an X-Y plane, measured distance values to the surface of the model, which are detected by first and second non-contact detectors (5a, 5b) obliquely mounted on the tracer head (4) rotatable about a Z axis are periodically sampled to obtain the coordinate values of measured points on the surface of the model, a normal vector (Nn) on the surface of the model is calculated from three coordinate values out of four measured points (P1n-1, P1n, P2n-1, P2n) successively obtained by the both detectors, and the tracer head is rotated so as to move along a projection (N1n) of the normal vector (Nn) on the X-Y plane, so that measuring axes of the detectors are controlled to be approximately vertical to the surface of the model. After two points are selected from four measured points, such a point is selected out of the remaining two measuring two points as a third point that satisfies a condition that a point of intersection between a perpendicular from such a point to a straight line passing through the previously selected two points and the above-mentioned straight line is interposed between the previously selected two points, and that satisfies a condition that the length of the above mentioned perpendicular is larger than a predetermined value.