Efficient approximation and optimization algorithms for computational metrology

Abstract

We give efficient algorithms for solving several geometric problems in computational metrology, focusing on the fundamental issues of {open_quotes}flatness{close_quotes} and {open_quotes}roundness.{close_quotes} Specifically, we give approximate and exact algorithms for 2- and 3-dimensional roundness primitives, deriving results that improve previous approaches in several respects, including problem definition, running time, underlying computational model, and dimensionality of the input. We also study methods for determining the width of a d-dimensional point set, which corresponds to the metrology notion of {open_quotes}flatness,{close_quotes} giving an approximation method that can serve as a fast exact-computation filter for this metrology primitive. Finally, we report on experimental results derived from implementation and testing, particularly in 3-space, of our approximation algorithms, including several heuristics designed to significantly speed-up the computations in practice.