This paper presents a unified framework for best-fitting of complex rigid surface to measured 3-D coordinate data by adjusting its location (position/orientation). For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its properties are investigated, especially, its increment with respect to the differential motion of the surface, up to the second order, is derived. On this basis, localization and profile error evaluation of complex surface are formulated as a nonlinear least-squares problem and nonlinear constrained optimization problem respectively, and sequential approximation algorithms are developed to solve them. The two algorithms have the advantages of implementational simplicity, computational efficiency and robustness. Also strategies for estimating initial solution and compensating probe radius are presented. Examples confirm the validity of the proposed approach.
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