Apparatus (300; 400; 500; 700) for three-dimensional measurement of an object , comprising: a positioning unit (310; 716; 722) that is configured to receive, from a camera, image information (312; 710) showing intersections of a line whose position is to be determined with a plurality of at least three lines of predetermined or known position that are arranged at or on a carrier member that is configured to carry the measurement object and that lie in one plane and that are not all parallel to one another, and to determine a position of the line based on the received image information; wherein the positioning unit (310; 716, 722) is configured to define a coordinate origin (p 0 ) of a coordinate system allocated to the line whose position is to be determined and a unit section (s) of the coordinate system allocated to the line whose position is to be determined and to determine a plurality of parameters (k i ) that describe intersections between the line whose position is to be determined and the lines of the plurality of lines of predetermined or known position; wherein the positioning unit (310; 716, 722) is configured to determine the parameters (k i ) such that the parameters or amounts of the parameters describe distances of the intersections from the coordinate origin (p 0 ) of the coordinate system allocated to the line whose position is to be determined; wherein the positioning unit (310; 716, 722) is configured to determine a position of the coordinate origin (p 0 ) of the coordinate system allocated to the line whose position is to be determined in a coordinate system allocated to a carrier member carrying the lines of predetermined or known position or with respect to which the lines of predetermined or known position are imaged in a stationary manner. a positioning unit (310; 716; 722) that is configured to receive, from a camera, image information (312; 710) showing intersections of a line whose position is to be determined with a plurality of at least three lines of predetermined or known position that are arranged at or on a carrier member that is configured to carry the measurement object and that lie in one plane and that are not all parallel to one another, and to determine a position of the line based on the received image information; wherein the positioning unit (310; 716, 722) is configured to define a coordinate origin (p 0 ) of a coordinate system allocated to the line whose position is to be determined and a unit section (s) of the coordinate system allocated to the line whose position is to be determined and to determine a plurality of parameters (k i ) that describe intersections between the line whose position is to be determined and the lines of the plurality of lines of predetermined or known position; wherein the positioning unit (310; 716, 722) is configured to determine the parameters (k i ) such that the parameters or amounts of the parameters describe distances of the intersections from the coordinate origin (p 0 ) of the coordinate system allocated to the line whose position is to be determined; wherein the positioning unit (310; 716, 722) is configured to determine a position of the coordinate origin (p 0 ) of the coordinate system allocated to the line whose position is to be determined in a coordinate system allocated to a carrier member carrying the lines of predetermined or known position or with respect to which the lines of predetermined or known position are imaged in a stationary manner. <EOS>