自由曲面的局部美化技术

Local Beautification Technique for Freeform Surfaces

针对反求工程中由多张B-样条曲面构成的边界表示模型在局部区域会出现的形状不规则性的问题,提出利用局部美化技术来消除这种外形的不规则性的方法。首先根据边界表示模型的拓扑给出局部美化的模式,并阐述曲面光顺与模型局部美化之间的区别和联系。然后,通过分析可接受的形状优化准则及其局部微分几何特性,给出局部美化的数学模型。最后,在利用形状分析方法构造局部形状不规则性区域的方法后,借鉴离散的非线性优化方法来保证形状修改的局部性和保持模型的拓扑。给出应用实例揭示了局部美化技术在反求工程中的意义。

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 G^0 continuity constraints. Simultaneously, an optimization method is used to preserve an approximated G^1 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.