Abstract: Parametric shape recognition is achieved through a decomposition of shapes into a hierarchy of subshapes ordered by their decreasing restrictions. Instances of each of the subshapes are individually located in the design shape and then reconstructed to form an instance of the entire shape. The basis for the hierarchy of subshapes can be specified by the designer or based on the default parameter relations that come from architectural and engineering knowledge. The levels of the hierarchy are defined so that the most constrained lines of a shape are those lines that the designer intended exactly. These most constrained lines have specified parametric relations to other line segments and those relations, if altered, will compromise the designer's intentions. Conversely, the lowest level of the hierarchy, which contains the least constrained line segments, only implies a specific connectivity between line segments, necessitating a vaster search.