用于保特征四边形网格生成的改进Morse算法

Improved Morse algorithm for feature-preserving quadrilateral mesh generation

在Morse理论的基础上,采用迭代算法来计算特征函数,通过优化生成保特征的四边形网格.首先,在拉普拉斯矩阵中加入模型的曲率信息,计算出的特征函数更加符合模型的几何特征;其次,使用迭代算法求得特征函数,可以求解任意数值的特征函数,不仅限于特征值,使得特征函数的选取更加具有灵活性,为后续做铺垫;最后,在迭代算法的过程中加入特征线信息,最终求得的特征函数可以很准确地将临界点定位在特征线上,这样可以生成沿特征线的Morse-Smale复形,通过优化生成保特征的四边形网格.所提算法简单,易于实现,输入信息较少.

Based on the Morse theory,an iterative algorithm is proposed to calculate the eigenfunction,and a feature-preserving quadrilateral mesh is generated by optimization.Firstly,the calculated eigenfunction is more in line with the geometric characteristics of the model by addition of the curvature term in the Laplacian matrix.Then,the eigenfunction calculated by iterative algorithm is not only the eigenvector corresponding to the eigenvalue,but also any arbitrary value.This approach makes the selection of eigenfunctions more flexible for the follow-up.Finally,the feature line information is added to the iterative algorithm,so the resulting eigenfunction can accurately locate the critical point on the feature line,then generate a feature-alignment Morse-Smale complex.By optimization,the final feature-preserving quadrilateral mesh is generated.The proposed algorithm is simple,easy to implement and less input.