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| 用于保特征四边形网格生成的Morse算法改进 |
| Improved Morse algorithm for Feature-Preserving Quadrilateral mesh generation |
| 投稿时间：2020-03-23 修订日期：2020-04-20 |
| DOI： |
| 中文关键词: Morse理论 迭代算法 特征约束 四边形网格 |
| 英文关键词: Morse theory iterative algorithm feature-preserving quadrilateral mesh |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 在Morse理论的基础上, 提出了迭代算法来计算特征函数, 通过优化可生成保特征的四边形网格. 本文算法首先在拉普拉斯矩阵中加入模型的曲率信息, 计算出的特征函数能够更加符合模型的几何特征; 其次, 我们提出了使用迭代的算法来求得特征函数, 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; 我们在迭代算法的过程中加入特征信息, 最终求得的特征函数可以很准确的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, 可以生成保特征的四边形网格. 本文提出的算法简单, 易于实现, 输入信息较少. |
| 英文摘要: |
| Based on the Morse theory, we propose an iterative algorithm to calculate the eigenfunction, and a fea-ture-preserving quadrilateral mesh is generated. Our approach can calculate eigenfunction is more in line with the characteristics of the model by adaption of the curvature term in the Laplacian operator. Then, we propose an iterative algorithm to calculate the eigenfunction, which is not only the eigenvector corre-sponding to the eigenvalue, but also any arbitrary value. This approach makes the selection of eigenfunc-tions more flexible. Prepare for the follow-up. We add feature information to the iterative algorithm. The resulting eigenfunction can accurately locate the critical point on the feature line. Our approach can gener-ate a feature-alignment Morse-Smale complex. By optimization, the final feature-preserving quadrilateral mesh is generated. Our algorithm is simple, easy to implement and less input. |
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