1. A sensing device for detecting a three-dimensional spatial shape of a body, comprising a sensing arrangement ( 28 ) which sensing arrangement comprises: a sensing end ( 32 ) for scanning a spatial shape to be scanned of a body; a camera ( 30 ); a connecting device ( 34 ) for rigidly connecting the camera ( 30 ) with the sensing end ( 32 ), wherein the rigid connection establishes a spatial position between the camera ( 30 ) and the sensing end ( 32 ), the camera ( 30 ) being arranged such that it can detect a surface ( 12 ) which is provided with marks ( 22 ) suitable to be automatically photogrammetrically evaluated and on which the body to be scanned has been placed, while the sensing end ( 32 ) scans different points of the spatial shape to be scanned of the body; and the sensing device further comprising: a photogrammetric evaluation program for a computing unit ( 18 ), the computing unit being configured such that image signals generated by the camera ( 30 ) can be routed to the computing unit ( 18 ) and the photogrammetric evaluation program can calculate the 3D coordinates of the spatial shape to be scanned by the sensing end ( 32 ) from the sequence of recorded and transmitted image sections by automatically photogrammetrically evaluating the captured marks ( 22 ) in the recorded and transmitted image sections and by determining a position of the camera ( 30 ) from the known exact space coordinates of the marks ( 22 ), the photogrammetric evaluation program being configured to determine a position of the sensing end ( 32 ) scanning different points of the spatial shape from the determined position of the camera ( 30 ) and the spatial position of the sensing end ( 32 ) with respect to the camera ( 30 ).