The problem of part definition, description, and decomposition is central to the shape recognition systems. We present an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface (bi-quadrics) and volumetric (superquadrics) primitives, without a priori domain knowledge or stored models. Surface segmentation is performed by a novel local-to-global iterative regression approach of searching for the best piecewise description of the data in terms of bi-quadric models. Region adjacency information, surface discontinuities, and global shape properties are extracted and used to guide the volumetric segmentation. Superquadric models are recovered by a global-to- local residual-driven procedure, which recursively segments the scene to derive the part- structure. A set of acceptance criteria provide the objective evaluation of intermediate descriptions, and decide whether to terminate the procedure, or selectively refine the segmentation, or generate negative volume description. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of part-models by shrinking the global model. We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation, object manipulation, qualitative vision, and active vision.