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Some three dimensional scene analysis programs pair data surface patches (eg as extracted from range data) to model surface patch features. From the correspondences, a variety of rotation and translation constraints on the model instance can be deduced, depending on the assumptions behind the correspondences. This paper elaborates some of the constraints and their associated assumptions for planar, cylin-drical, conical and generic surface patches. For example, if one knows that a planar model patch must overlap a planar data patch, then this constrains the alignment of the model surface normal and the possible translations of the model patch. The con-straints are expressed algebraically for patches that are: nearby, touch, contained, or registered. The constraints are used to estimate object position, given a single patch correspondence. Examples of their use and evaluation are given.