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 (4109a, 4109b, 4109c, 4110a, 4110b, 4110c) of a line whose position is to be determined with a plurality of at least three lines (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) 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 (4109a, 4109b, 4109c, 4110a, 4110b, 4110c) between the line whose position is to be determined and the lines (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) 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 (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) 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 (4109a, 4109b, 4109c, 4110a, 4110b, 4110c) of a line whose position is to be determined with a plurality of at least three lines (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) 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 (4109a, 4109b, 4109c, 4110a, 4110b, 4110c) between the line whose position is to be determined and the lines (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) 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 (4106, 4107a, 4107b, 4107c, 4108a, 4108b, 4108c) of predetermined or known position or with respect to which the lines of predetermined or known position are imaged in a stationary manner.