Abstract: Boundary representation model composed of multiple B-spline surfaces reconstructed from point cloud suffers from various local shape imperfections inevitably caused by noise in the point data and the reverse modeling strategies. A beautification technique is proposed to remove the local shape irregularities of such a model. Based on the topologies of the B-rep model, the basic patterns of local beautification are classified firstly. The shape beautification is compared with the traditional surface fairing according to the pattern classification. Then, the mathematical model of the beautification is given after analyzing acceptable shape optimization criteria and their intrinsic characteristics of differential geometry. Finally, the local irregularities on the model regions are identified by using shape interrogation methods. As the beautifying variables, each control point associated with the regions is modified solely subject to the tolerance constraints and/or G0 continuity constraints. Simultaneously, an optimization method is used to preserve an approximated G1 continuity in the local regions. Consequently, the shape is improved without destroying the model topologies. The practical examples reveal the value of the local beautification technique in reverse engineering.

Key words: Computer aided geometric design, Freeform surface, Reverse engineering, Shape improvement