1. A non-contact object scanning system, including: a support structure for maintaining an object completely within a predetermined viewing volume for exposure to radiant energy for surface scanning, wherein the support structure, at least within and proximate the viewing volume, is formed of a material substantially nonreflective of the radiant energy and further is adapted to allow passage of the radiant energy therethrough; a scanning apparatus comprising a radiant energy source located outside of the viewing volume to direct the radiant energy onto the object maintained in the viewing volume, and a radiant energy sensor adapted to detect the radiant energy reflected by an exterior surface of the object visible from outside the viewing volume; a controller operatively associated with the scanning apparatus to automatically step the scanning apparatus through a sequence of scans of the object maintained in the viewing volume, wherein each of the scans comprises directing the radiant energy onto a selected segment of the exterior surface associated with the scan, and detecting the radiant energy reflected by the associated segment to generate a surface data set representing a three-dimensional shape of the associated segment, wherein the sequence of scans consists essentially of direct scans of first selected segments disposed to receive the radiant energy directly from the radiant energy source, and indirect scans of second selected segments disposed to receive the radiant energy via passage of the radiant energy through the support structure, and the first segments and second segments in combination comprise substantially the entire visible exterior surface; and an information processor coupled to receive the surface data sets associated with the scans of the sequence, and adapted to merge and align the surface data sets into a selected three dimensional coordinate space to generate in said space a three dimensional representation of an entire continuous exterior shape of the object.