Form error is specified on the basis of an ideal geometric feature established from the actual measurements such that the maximum deviation from the ideal feature is the least possible value. The least squares method of establishing the ideal feature does not yield a minimum value. A few attempts have been made to establish the feature with a minimum value of error. In case of roundness evaluation modern instruments specify the error based on minimum deviation and ring-and plug-gauge circles. However the instrument manufacturers do not reveal the algorithms used. This paper deals with the methods of establishing the enveloping features for different geometric features namely straight line circle plane and cylinder. A non-linear optimization technique is followed to solve simple numerical examples. The values are compared with the values obtained by the least squares and minimum deviation methods. NOMENCLATURE ECF Enveloping crest feature EVF Enveloping valley feature e. Deviation of a point from assessment feature f Function to be minimized K Number of points in a section L Number of sections LSF Least squares feature 1 m Slope values (l'' for transformed values) o o 0 0 MDF Minimum deviation feature N Total number of points r. O. Polar coordinates of a point R. Radius of a circle/cylinder/ x. y. z. Cartesian coordinates of a point(x 1 1 1 1 1 1 for transformed values) x y z Estimated coordinates. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.