REFERENCE SOFTWARE FOR FINDING CHEBYSHEV BEST-FIT GEOMETRIC ELEMENTS

This paper summarizes work carried out in a project supported by the E uropean Communities' Bureau of Reference (BCR) to develop reference so ftware for finding best-fit geometric elements, under specified criter ia, to coordinate data. The geometric elements considered are the line , plane, circle, sphere, cylinder, and cone, The criteria for determin ing the elements are, generally, minimum zone (MZ) and, where appropri ate, minimum circumscribed (MC) and maximum inscribed (MI). The softwa re developed implements methods founded on optimization, theory Two ap proaches are described: the first implements mathematical programming methods that exploit the particular structure of the problems consider ed and provide a unified approach to their solution; the second, appli cable to the MZ and, where appropriate, MC problems for the line [in t wo-dimensions (2-D)] plane, circle (in 2-D) and sphere, implements a c ombinatorial method that returns all global solutions.