Recognizing and fitting shape primitives from underlying 3D models are key components of many computer graphics and computer vision applications. Although a vast number of structural recovery methods are available, they usually fail to identify blending surfaces, which corresponds to small transitional regions among relatively large primary patches. To address this issue, we present a novel approach for automatic segmentation and surface fitting with accurate geometric parameters from 3D models, especially mechanical parts. Overall, we formulate the structural segmentation as a Markov random field (MRF) labeling problem. In contrast to existing techniques, we first propose a new clustering algorithm to build superfacets by incorporating 3D local geometric information. This algorithm extracts the general quadric and rolling-ball blending regions, and improves the robustness of further segmentation. Next, we apply a specially designed MRF framework to efficiently partition the original model into different meaningful patches of known surface types by defining the multilabel energy function on the superfacets. Furthermore, we present an iterative optimization algorithm based on skeleton extraction to fit rolling-ball blending patches by recovering the parameters of the rolling center trajectories and ball radius. Experiments on different complex models demonstrate the effectiveness and robustness of the proposed method, and the superiority of our method is also verified through comparisons with state-of-the-art approaches. We further apply our algorithm in applications such as mesh editing by changing the radius of the rolling balls.