Abstract: Optimal localization of free-form shaped parts is a key issue in precision inspection. Aiming at the problems on estimate of the initial transformation and the calculation of closest points, an effective and exact localization method is presented. First, this method establishes the corresponding relationships between two free-form surfaces with constraints of angle and distance by means of the surface features of the Gaussian curvature and the mean curvature. Then the rough localization is realized. Using the robust arithmetic for multivariate Bernstein-form polynomials, a novel algorithm to calculate closest point is proposed. An improved iterative algorithm is used in the exact adjustment of localization to ensure the global optimization. Experiment results demonstrate the feasibility of the proposed method.

Key words: Closest points, Exact localization, Precision inspection, Rough localization