Roundness is one of the most important geometric measures for circular objects in the process of mechanical assembly. The roundness problem is stated as follows: Given n points in the Euclidean plane, find a center of the concentric circles enclosing all given points between outer and inner circles, and minimizing the difference between the radii of the outer and inner circles. This problem can be considered as a kind of facility location problem. This article presents a new exact roundness algorithm whose time complexity is O(n2). The algorithm is based on a property of the union of the nearest-point Voronoi diagram and the farthest-point Voronoi diagram. Furthermore, it is shown that this roundness algorithm can be improved efficiently, by introducing the deletion of the unnecessary points, in practical applications. In addition, the computational experience of this revised algorithm is presented. [In Japanese.]
