网格模型姿态迁移与拓扑优化

发布时间：2018-01-05 19:17

本文关键词：网格模型姿态迁移与拓扑优化　出处：《华南理工大学》2016年博士论文　论文类型：学位论文

【摘要】：三维模型的形状编辑与拓扑优化是数字几何处理的重要内容.通过形状编辑技术可以使得用户更方便地创建各种各样的新形状与新姿态,而网格剖分质量对模型编辑与操纵等数字几何处理有直接影响.基于样例的网格建模技术为模型重用提供了一种重要途径.作为基于样例的网格建模技术,变形迁移利用参考网格模型不同姿态之间的变形来驱动源网格模型进行形变.不同于变形迁移,姿态迁移仅输入参考模型的一个姿态,由于对姿态的定义比较困难,这使得研究连接关系不同的网格模型之间的姿态迁移具有挑战性.由于四边形网格结构的特殊性,使得四边形网格的优化比较困难,四边形网格质量受螺旋条带结构的影响.本文对这两方面的内容展开研究,具体内容及主要贡献如下：1)特征保持的谱姿态迁移.网格模型的拉普拉斯矩阵的低频成分编码网格模型的粗略姿态,而网格的拉普拉斯坐标保持模型细节特征,我们把这两者统一到一个框架中,提出了一个细节保持的谱姿态迁移方法,并定义相应的非线性优化能量.由于求解该非线性优化问题导致一个稠密线性系统,我们集成了基于广义重心坐标的子空间技术,这不仅能大大降低解空间的规模,而且由于一定程度上减少了变形的自由度而使得解的稳定性得到保证.2)分层谱姿态迁移策略.三维模型姿态具有多尺度性质,利用模型的低频系数只能处理模型的大尺度姿态,而无法顾及中尺度姿态或局部区域的姿态,导致姿态迁移不充分.我们把参考姿态看成是一个分层结构,利用模型分割技术把原本不是大尺度的姿态,即中小尺度姿态,转化成局部区域的大尺度姿态.然后,对这些局部区域的姿态应用同样的姿态迁移方法.通过分层姿态迁移能够把参考模型的不同尺度的姿态逐步地迁移到源模型上,获得令人满意的姿态迁移效果.3)四边形网格中螺旋条带生成算法.四边形网格的拓扑的正则性受螺旋条带结构的影响,而螺旋条带跟四边形网格中的不规则点密切相关.我们系统地分析了四边形网格中不规则顶点与螺旋条带的关系以及不规则顶点对螺旋条带走向的影响,给出了四边形网格中基于原网格的螺旋条带生成算法,并应用于四边形网格模型的拓扑优化.通过修改螺旋条带的拓扑结构可以减少四边形网格的奇异顶点个数从而提高网格质量.
[Abstract]:Shape editing and topology optimization of 3D model is an important part of digital geometry processing. Editing technology can make it easier for users to create a variety of new shapes and new attitude through the mesh shape, and the quality of model editing and manipulation of digital geometry processing has a direct impact. Provides an important way for grid modeling technology sample the model is based on reuse. As the grid modeling technology based on the sample deformation transfer with deformation between different attitude reference mesh model to drive the source mesh model deformation. Different from the deformation of migration, migration only a gesture input attitude reference model, the definition of the attitude is more difficult, which makes the Research on grid connection between model the relationship between different attitude transfer challenging. Because of the particularity of quadrilateral mesh structure, the optimization of the quadrilateral mesh is difficult , quadrilateral mesh quality is influenced by the spiral strip structure. This paper studies the content of these two aspects, the specific contents and main contributions are as follows: 1) the migration characteristics. Keep spectrum attitude attitude rough grid model Laplasse matrix encoding the low-frequency components of the grid model, and Laplasse coordinates keep the details of feature model. We put the two into a unified framework, put forward a method of attitude transfer spectral detail preserving, and define the corresponding energy. Because of the nonlinear optimization to solve this nonlinear optimization problem leads to a dense linear system, we integrated the generalized barycentric coordinates based on subspace, which can not only reduce the solution space the scale, and to some extent reduce the deformation due to the degree of freedom and the stability of solution is guaranteed.2) hierarchical spectrum migration strategy. Attitude attitude with 3D model A multiscale nature, using the model of the low frequency coefficient model can only deal with large scale attitude, and can not take into account the mesoscale attitude or local attitude, attitude to migration is not sufficient. We put the reference attitude as a hierarchical structure, this is not the original segmentation technology of large scale attitude by the model, namely small scale attitude into a large scale, the local attitude. Then, on these areas pose the same attitude application migration method. Through the hierarchical attitude to migration reference model of different scale attitude gradually migrate to the source model, obtain satisfactory attitude transfer effect.3) quadrilateral mesh generation algorithm of spiral strip the topological quadrilateral mesh regularity influenced by spiral strip structure, and spiral bands with irregular quadrilateral grid points are closely related. We systematically analyzed four Influence of the shape of irregular grid boundary vertices and spiral bands and irregular vertices of spiral bands to, given the original spiral grid based quadrilateral mesh generation algorithm with, and the application of topology optimization in quadrilateral mesh model. By modifying the spiral strip topology can reduce the number of singular the vertices of quadrilateral mesh so as to improve the quality of the grid.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.7

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