Method for determining a position and orientation of an object using a profilometer

A method comprising:

• capturing, using a profilometer, cartesian coordinates for each of three measurement points on a profilometer-detected profile line of a measurement body having a defined spatial relationship to an object;
• calculating, using the coordinates and known measurement body geometric values, a sequence of three rotations of the measurement body about 1) a measurement body z-axis, 2) an intermediate y-axis resulting from the z-axis rotation, and 3) a profilometer-defined x-axis;
• calculating, using the coordinates, the geometric values, and the above-calculated three rotations, a set of three translational displacements of the measurement body relative to the respective profilometer-defined x-, y-, and z-axes;
• and
• determining a position of the object using the defined spatial relationship.

A method comprising:

• capturing, using a profilometer, cartesian coordinates of three points on a measurement body relative to a profilometer-defined frame-of-reference;
• calculating, using the coordinates and geometric values of the measurement body, three sequential rotations of the measurement body to transfer each point of the measurement body into a reference frame-of-reference;
• and
• calculating, using the coordinates, the geometric values, and the three rotations, three translation displacements of the measurement body relative to the frame-of-reference.