A common problem encountered in coordinate measuring technology is fitting shaped elements according to their tolerances. This is important when comparing a measured part with its ideal model and is a virtual variation of mechanical gauging. Under normal circumstances, a Gaussian fit is the method of choice. However, in some cases, this is insufficient because the Gaussian method minimizes the sum of the least squares, i.e. no direct consideration is made about whether a real point is within its corresponding tolerance range. The department “Machine Vision and Signal Processing” has developed a 3D tolerance fit method to solve this problem. In the method, the following ideal geometries - each assigned a tolerance zone – are considered: plane, straight line and point. The tolerance zone means that a plane has two tolerance planes, with the original plane lying in the middle. As a result, a point together with its tolerance zone becomes a sphere and a straight line becomes a cylinder. Ideal geometries are derived, for example, from a CAD model. Each ideal geometry has corresponding measured points, which are generated via coordinate measurements from the real component. The 3D tolerance fit enables measured points to be optimally fitted into the tolerance zones of the ideal geometries. Here, ‘optimally’ means that each measured point lies in the best possible position within its corresponding ideal geometry. Thanks to this new 3D tolerance fit method, components can now be optimally gauged virtually. This has major advantages with regard to reproducibility and accuracy.