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A planar or quadric surface can be fit to a segment of range data in a locally optimal sense by selecting the minimum eigensolution of a scatter matrix for that segment. We obtain a globally optimal fit by perturbing the local eigensystems with constraints reflecting relations among the corresponding primitives of a model. These pairwise relations define a view-invariant description of the model. For segments containing a few hundred pixels, the resulting perturbation is small enough to justify a linear treatment of the coupled system. From this globally optimal fit, we determine the pose of the object algebraically.