Apparatus for superimposing at least part of a 3D image of a person with a virtual surface, the apparatus comprising: one or several cameras for providing the 3D image of the person, wherein a relative coordinate system is set on the basis of a position of the one or several cameras, and a computing unit, which is configured to determine depth information from a plurality of voxels or vertices in the 3D image of the person and to generate a 3D grid structure of the person and to superimpose the virtual surface of the 3D grid structure, characterized by a position determiner, which is configured to determine an absolute position of a reference point of the person in an environment, three signal sources (32a, 32b, 32c) for attachment to the person, wherein each of the three signal sources is configured to emit a signal that differs from the signal of the respective other signal sources, three receivers (34a, 34b, 34c) for positioning at differing angles around the person, wherein the receivers are connected to the position determiner and receive the signals (36a, 36b, 36c), wherein the position determiner is configured to determine runtime information of the received signals (36a, 36b, 36c) from the signal sources (32a, 32b, 32c) to the receivers (34a, 34b, 34c) and to compute the absolute position and an orientation of the reference point of the person in the environment on the basis of the runtime information, wherein the computing unit is configured to - determine the depth information of the plurality of voxels or vertices in the 3D image of the person on the basis of the absolute position of the reference point, and - compare positions of the reference point in the absolute coordinate system and relative coordinate system in order to compute a position of each voxel or vertex in the 3D image, so that a position in the 3D image at which the virtual surface is oriented and the depth information of each voxel or vertex in the 3D image are known. one or several cameras for providing the 3D image of the person, wherein a relative coordinate system is set on the basis of a position of the one or several cameras, and a computing unit, which is configured to determine depth information from a plurality of voxels or vertices in the 3D image of the person and to generate a 3D grid structure of the person and to superimpose the virtual surface of the 3D grid structure, characterized by a position determiner, which is configured to determine an absolute position of a reference point of the person in an environment, three signal sources (32a, 32b, 32c) for attachment to the person, wherein each of the three signal sources is configured to emit a signal that differs from the signal of the respective other signal sources, three receivers (34a, 34b, 34c) for positioning at differing angles around the person, wherein the receivers are connected to the position determiner and receive the signals (36a, 36b, 36c), wherein the position determiner is configured to determine runtime information of the received signals (36a, 36b, 36c) from the signal sources (32a, 32b, 32c) to the receivers (34a, 34b, 34c) and to compute the absolute position and an orientation of the reference point of the person in the environment on the basis of the runtime information, wherein the computing unit is configured to - determine the depth information of the plurality of voxels or vertices in the 3D image of the person on the basis of the absolute position of the reference point, and - compare positions of the reference point in the absolute coordinate system and relative coordinate system in order to compute a position of each voxel or vertex in the 3D image, so that a position in the 3D image at which the virtual surface is oriented and the depth information of each voxel or vertex in the 3D image are known. - determine the depth information of the plurality of voxels or vertices in the 3D image of the person on the basis of the absolute position of the reference point, and - compare positions of the reference point in the absolute coordinate system and relative coordinate system in order to compute a position of each voxel or vertex in the 3D image, so that a position in the 3D image at which the virtual surface is oriented and the depth information of each voxel or vertex in the 3D image are known.