基于网格边的复杂曲面优化展开

Optimal flattening of complex surfaces based on mesh edges

提出了一种基于网格边的复杂曲面优化展开的新方法.该方法以曲面三角网格中各网格边的长度为优化变量,以展开前后网格边的长度误差为优化目标,以网格中各内部点均可展为约束条件,并用牛顿法和矩阵分块等方法对该优化问题进行求解,构造出与原始曲面边长误差最小的可展曲面.最后对构造出的可展曲面用基于中心三角片的"涟漪式"展开方法进行展开,从而实现复杂曲面的优化展开.数值实验结果表明,该方法具有稳定性好、收敛速度快、展开精度高、展开操作简单等优点,可以应用于各种复杂曲面的优化展开.

A novel optimal method based on mesh edges is presented for flattening complex surfaces. In the optimal flattening model, the edge-lengths of the original surface＇s mesh are selected as optimization variables, and the error of the edge-lengths between the original mesh and the flattened mesh is selected as objective function, and each internal point of the mesh being developable is se- lected as optimization constrain. By Newton＇s method and matrix blocking technologies, the optimization problem can be resolved and a developable surface, which has the minimum error of the edge- lengths, can be constructed. Finally, a ripple-style flattening method is used to flatten the developable surface, and the flattening result of the original surface is obtained. Numerical experimental resuits show that the method can flatten all kinds of complex surfaces stably, quickly and accurately, and the flattening operation can be finished more simply.