arrangement for the intra - operative determination of the spatial position and angular position of a joint replacement implant , especially a hip socket or shoulder socket or an associated stem implant , or a vertebral replacement implant , especially a lumbar or cervical vertebral implant , using a computer tomography method , having : a computer tomography modeling device for generating and storing a three - dimensional image of a joint region or vertebral region to be provided with the joint replacement implant , an optical coordinate - measuring arrangement for providing real position coordinates of defined real or virtual points of the joint region or vertebral region and / or position reference vectors between such points within the joint region or vertebral region or from those points to joint - function - relevant points on an extremity outside the joint region or vertebral region , the coordinate - measuring arrangement comprising a stereocamera or stereocamera arrangement for the spatial recording of transducer signals , at least one multipoint transducer , which comprises a group of measurement points rigidly connected to one another , and an evaluation unit for evaluating sets of measurement point coordinates supplied by the multipoint transducer and recorded by the stereocamera , and a matching - processing unit for real position matching of the image to the actual current spatial position of the joint region or vertebral region with reference to the real position coordinates of the defined points , the matching - processing unit being configured for calculating transformation parameters with minimalization of the normal spacings .