Methods for digitizing complex surfaces of dental objects such as impressions of dental surfaces and shapes. While an impression mold is being scanned by translation along a known trajectory, typically in a plane, the line of sight of a distance probe is directed toward successive positions on the surface of the impression mold, such as by a periodic series of reflecting surfaces characterized by normal vectors at distinct non-orthogonal angles with respect to their axis of symmetry. One or more reference objects are scanned using the same translation and mirror positioning systems. Gathered coordinate data are processed to apply angular corrections and combined to form a single distortion-corrected image of the impression mold. An apparatus and methods are provided for measuring both sides of a dental object separately, and then registering the two sides relative to each other in a digital representation of the object.