This paper proposes a new approach to scan path planning for automated inspection of manufactured parts with an industrial robot based on the control of the overlap between 2 successive scanning paths. The novelty lies in the use of the least-squares conformal map, which stretches a 3D surface on a 2D plane. Equidistant paths calculated in the 2D space are transformed into equidistant paths in the 3D space. Controlling the overlap can maximize the coverage region on the scanned part. On the other hand, digitizing quality is ensured by managing the sensor configuration relatively to the part with respect to quality criteria. The approach is implemented with success for a laser-plane scanner mounted on an industrial robot.