The objective of this thesis is to develop a methodology to calculate the size of a cylindrical profile accurately per ANSI standards. The ANSI Y 14.5.1M-1994 standard defines the size of a cylinder as the size of the largest ball rolling on a spine such that all points on the surface of the cylinder are external to it, or the size of the smallest ball rolling on a spine such that all points on the surface of the cylinder are internal to it.
Current methods of size evaluation reduce the complexity of the spine and model it as a straight line. A novel methodology to evaluate the control points of the spine modeled as a Bezier curve or an Open Uniform B-Spline curve of a pre-specified degree based on points collected on the surface of the cylinder has been developed in this thesis. This provides a quantitative measure of the size of the cylinder in accordance with ANSI standards. The formulations to evaluate the maximum inscribing spine and the minimum circumscribing spine are presented as multi-level optimization problems. The outer level optimization is used to identify the optimal set of control points for the spline representing the path of the rolling ball. The inner level optimization is used to find the nearest point on the curve corresponding to every point in the dataset.
The optimization formulation has been used to calculate the true size of cylinders for several published, simulated and real datasets. These results have been compared to traditional estimates for size of a cylinder, such as the maximum inscribed, minimum circumscribed and least squares cylinders. The results indicate that the method presented in this research conforms better to the ANSI standards as compared to the traditional methods. Further analysis is presented to observe the effect of sample size on the results of the algorithm. It is observed that with an increase in the sample size, the difference between the results of the presented algorithm and the traditional methods increases with the presented method providing more accurate estimates of the size of the cylinder.