Out-Of-Roundness Problem Revisited

The Out-Of-Roundness measurement of a circular profile undertakes different schemes depending on the type of center specified. The most common standard recommended by the American National Standards Institute (ANSI) is the Minimum Radial Separation center. In conjunction to that, we introduce another standard called the Minimum Area Difference center. Although the two centers are different in characteristics, the approach to finding both centers shares many commonalities. In this report, we present an O(nlogn + k) time algorithm to compute the Minimum, Radial Separation center, and the Minimum Area Difference center of a simple polygon G, where n is the number of vertices of G, and k is O(n sup 2), a parameter defined in the text.