Chebyshev approximation to data by geometric elements

Abstract

An algorithm is presented and proved correct, for the efficient approximation of finite point sets in ℝ² and ℝ³ by geometric elements such as circles, spheres and cylinders. It is shown that the approximation criterion used, viz. minimising the maximum orthogonal deviation, is best modelled mathematically through the concept of aparallel body. This notion, besides being a valuable tool for form assessment in metrology, contributes to approximation theory by introducing a new kind of approximation, here called “geometric” or “orthogonal”. This approach is closely related to but different from Chebyshev approximation.