复杂自由曲面模型的局部协调设计技术

Local consistent mending technique for complex freeform surface model

综合应用自由曲面模型的全局美化技术和基于离散边界约束条件及裁剪B样条曲面模型的任意边域曲面填充方法,提出了一种新的针对复杂自由曲面模型的局部协调设计技术.利用可微流形的无穷小变形技术,实现紧公差约束下对点云逼近的多张B样条曲面的全局美化,保证了N边汇交曲面相邻边界处收敛的G1光滑拼接,并改善了模型的整体形状.构造包含汇交点的局部区域来裁剪N边汇交曲面,并基于边界条件的离散化处理和裁剪B样条曲面模型重构局部区域,使得局部重构曲面(即协调曲面)与裁剪汇交曲面之间满足近似G1连续,同时光滑地逼近于局部区域的特征趋势.应用实例表明,该局部协调设计技术能够较好地实现复杂曲面造型和反求工程建模中模型的整体G1连续性和保形性,并且为进一步研究基于局部协调设计的拓扑还原技术奠定了坚实可靠的基础.

A new local consistent mending scheme for complex freeform surface model was proposed,by the combined use of global beautification technique for freeform surface model and N-sided hole filling method, which was based on discretization of boundary conditions and trimmed B-spline surface model. Firstly, the infinitesimal deformation technique of differentiable manifold was used to beautify the multiple surfaces approximated to point cloud subject to tight error globally, which could generate convergent G^1 smooth B-spline surfaces and improve the shape of the model. Secondly, the local region containing N-patch corner was clipped off the original multiple surfaces,and then the trimmed area based on discretization of boundary conditions and the trimmed B-spline surface model was reconstructed to satisfy the approximate G^1 continuity with adjacent surfaces while reflecting the feature trend of the original surface. Practical applications illustrate that the presented local consistent mending technique can achieve the global G^1 continuity and the shape preserving in the complex surface modeling and reverse engineering, as well as provide a stable and reliable basis for further research on topology recovery technique.