Methods and devices are disclosed, by use of which an external fiducial element positioned in the mouth serves as a geometrical constraint on oral arch geometry. In some embodiments, the fiducial element is an oral insert which reaches to a plurality of oral arch regions to present surface details which are in well-defined distance and/or angular relationships to one another. These spatial relationships optionally comprise a spatial frame of reference which serves to constrain reconstruction of the geometry of one or both of the oral arches, for example reconstruction from a collection of digitally registered, partially-overlapping scans made along the oral arch.