基于能量法的G2连续的曲面过渡

提出一种基于能量法的G2连续过渡面的构造方法,着重分析过渡曲面能量优化模型的建立,边界约束、法矢方向一致约束以及主曲率相等约束的表达和处理。将过渡曲面的能量优化模型转化为非线性等式约束的二次数学规划问题,并运用Lagrange乘子法求解过渡曲面的能量优化模型。最后给出了应用该方法生成G2连续过渡曲面的几个实例。

Generating Blending Surface with G2 Connectivity Based on Energy Optimization Method

This paper at first analyzes several methods about generating blending surface, and points out the advantages of blending surface with G2 connectivity over with C2 connectivity. Then it puts forward a new modeling method about generating blending surface with G2 connectivity based on energy optimization. It stresses foundation of energy optimization model of deformable blending surface. It also details the expressing and processing of boundary constraints and G2 connectivity constraints (normal vector direction constraints and main curvature constrains) between the blending surface and original surfaces, through which the energy optimization model of deformable blending surface is converted into the quadratic mathematical programming problem with nonlinear equality constraints. After then, It introduces the progress of solving the energy optimization model using the Lagrange multiplier method which suits for the quadratic mathematical programming. At last, it gives several examples of generating blending surface with G2 connectivity applying this method.