The measurement of form and profile errors of mechanical parts involves the
fitting of continuous surfaces, curves or lines to a set of coordinate poi
nts returned by inspection instrumentation. For circularity, both ASME (Y14
.5M-1994 [1995]) and ISO (1R 1001, 1983) prescribe the fitting of a pair of
concentric circles with minimum radial separation to a set of discrete coo
rdinate points sampled around the periphery of a surface of revolution at a
plane perpendicular to the axis of revolution. This criterion is often ref
erred to as the minimax or minimum zone criterion. The contribution of this
paper is to provide a refinement to the basic results of both Ventura and
Yeralan and Etesami and Qiao as an improved path to the optimum solution to
the minimax roundness problem. The proposed solution applies the Voronoi d
iagram approach to the P2(k) problem to show that the optimum solution can
only reside at a particular type of vertex of the MAX region. This particul
ar type of vertex corresponds to one of the possible type (ii) solutions of
Ventura and Yeralan's P2(k) problem. In other words, Etesami and Qiao's ap
proach need not examine all vertices of the MAX region and Ventura and Yera
lan's P2(k) solution need not examine any type (i) solutions. This results
in a substantial saving in time required to identify the optimum solution a
nd would be useful for applications that return a large number of points su
ch as dedicated roundness testers, axis of rotation analysers or telescopic
ball bars.