Approximation- and alignment-problem in the field of coordinate measurement techniques are solved in most cases by using the L2-norm (Gaussian least squares sum) as the objective function. However, for an increasing number of applications the L2-norm leads to inaccurate results so that the Tschebyscheff-norm should be applied instead. These cases are for example the measurement of deviations in form and position, matching-tests or the computational fitting of measured points into tolerance-zones. This paper describes a universal algorithm for the approximation according to both the L2norm and T-norm. Additionally, two limits are calculated in between which the “true” value of the maximum deviation lies. Basic mathematics will be briefly explained and results obtained by measurements will be discussed.