Electro-optical system for determining the position and orientation of a movable portion, the system comprising a fixed portion which comprises projection means and which has a projection centre and a movable portion, the fixed portion being fixedly connected to a virtual image plane (Pi), the movable portion being fixedly connected to at least two linear electro-optical devices (A'B', C'G'), the projection means projecting into a zone which comprises the electro-optical devices (A'B', C'G'), at least two beam networks, whose intersection with the image plane (Pi) defines at least two networks of non-parallel straight lines, each of the networks of straight lines comprising at least three parallel segments, each of the electro-optical devices (A'B', C'G') being intercepted at least at two triplets of locations, characterised in that, since the two electro-optical devices (A'B', C'G') are coplanar and their direction intersects, the orientation and the position of the movable portion is determined in accordance with vanishing points (E, F) in the image plane (Pi) of the two straight lines which comprise the first electro-optical device (A'B') and the second electro-optical device (C'G'), respectively, calculation means allowing, on the basis of the intersection locations of the beams at the electro-optical devices (A'B', C'G'), the determination of the positions: • of the projections (A, I, B) on the image plane (Pi) of the first triplet of locations (A', I', B') comprising the ends and the centre of the first device, on the basis of the preservation of double ratios according to a central projection in the plane of the first device and in the image plane (Pi), the respective projections being intersection locations, with the image plane (Pi), of a bundle of straight lines originating from the centre of projection and extending through the first triplet (A', B', I') of locations, • of the projections (C, J, G) on the image plane (Pi) of the second triplet of locations (C', J', G') comprising the ends and the centre of the second device (C'G') on the basis of the preservation of double ratios in accordance with a central projection in the plane of the second device and in the image plane (Pi), the respective projections being intersection locations with the image plane (Pi) of a bundle of straight lines originating from the centre of projection and extending through the second triplet (C' J' G') of locations, and • of the positions in the image plane (Pi) of a first vanishing point of a straight line which comprises the first device (A'B') and a second vanishing point of a straight line which comprises the second device (C'G') based on the fact that a bundle of four straight lines which originate from the centre of projection and which extend through the projections (A, I, B) on the image plane (Pi) of the first triplet of locations (A' I' B') and through the first vanishing point, and a bundle of four straight lines originating from the centre of projection and extending through the projections (A' I' B') on the image plane (Pi) of the second triplet of locations (C' I' G') and through the second vanishing point are harmonic bundles. • of the projections (A, I, B) on the image plane (Pi) of the first triplet of locations (A', I', B') comprising the ends and the centre of the first device, on the basis of the preservation of double ratios according to a central projection in the plane of the first device and in the image plane (Pi), the respective projections being intersection locations, with the image plane (Pi), of a bundle of straight lines originating from the centre of projection and extending through the first triplet (A', B', I') of locations, • of the projections (C, J, G) on the image plane (Pi) of the second triplet of locations (C', J', G') comprising the ends and the centre of the second device (C'G') on the basis of the preservation of double ratios in accordance with a central projection in the plane of the second device and in the image plane (Pi), the respective projections being intersection locations with the image plane (Pi) of a bundle of straight lines originating from the centre of projection and extending through the second triplet (C' J' G') of locations, and • of the positions in the image plane (Pi) of a first vanishing point of a straight line which comprises the first device (A'B') and a second vanishing point of a straight line which comprises the second device (C'G') based on the fact that a bundle of four straight lines which originate from the centre of projection and which extend through the projections (A, I, B) on the image plane (Pi) of the first triplet of locations (A' I' B') and through the first vanishing point, and a bundle of four straight lines originating from the centre of projection and extending through the projections (A' I' B') on the image plane (Pi) of the second triplet of locations (C' I' G') and through the second vanishing point are harmonic bundles.