Abstract
The work presented in this paper derives from the design of a position sensing interferometer, in which circular fringe patterns are automatically analyzed by a computer vision system. Central to this process is a circle fitting problem in the sense of least Linfinity norm, also known as Chebichev or MinMax fit. The problem at hand can be formulated as follows: Given a set of points in the plane, find the pair of concentric circles with minimum radial gap enclosing all the points.
The solution to this problem is elegantly given by common computational geometry tools, indeed the center of such a circle is necessarily a vertex of the Nearest Point Voronoi Diagram (NVD), a vertex of the Farthest Point Voronoi Diagram (FVD), or an intersection of edges from both diagrams.
An algorithm for determining the Chebichev circular fit is presented and illustrated on the basis of that observation. Applications and potential extensions of this method to soft gauging and image metrology will also be discussed.
The Geodesic Farthest-Point Voronoi Diagram in a Simple Polygon
