基于方向场与模式的四边形网格生成算法

发布时间：2018-07-12 17:26

本文选题：四边形网格生成 + 方向场　；参考：《清华大学》2016年硕士论文

【摘要】：四边形网格在几何造型、纹理映射、有限元模拟仿真、计算机动画以及建筑学等领域都有着大量广泛的应用。相比于传统的三角形网格,四边形网格拥有很多优良的特性,如天然地具有张量积性质,其网格面片能够非常自然地与矩形纹理保持一致对齐,而且可以直观地捕获模型的几何特征与语义特征。因此,四边形网格生成算法已经成为了当今国内外研究的热点内容。然而,如何生成符合用户设计意图、奇异点少且分布良好的各向异性高质量四边形网格模型仍然是一个开放性的问题,其主要困难在于:1)在不同的应用领域中,用户对四边形网格质量的控制需求往往不尽相同。而这些控制需求常常又是相互制约,甚至相互矛盾的。2)当今主流的全自动生成算法缺乏对奇异点的控制,而用户辅助的生成算法又对用户的手工建模能力提出了过高的要求。因此,如何结合这两类四边形网格生成算法的各自优势是一项很大的挑战。于是,针对目前四边形网格生成算法存在的这些问题,本文提出了相应的解决方案:1)提出了一种基于方向场的可控四边形网格生成算法。本文在前人的基础上提高了用户的可控性:通过引入测地线技术和三维草绘技术,允许用户对方向场的方向进行自由直观的控制,同时为了处理用户在控制方向场时产生的冲突和误差,本文提出了相应的解决方向约束冲突以及修正用户交互不精确性问题的处理方案,进而扩展优化了正交场的光滑能量函数,使其能够插值生成用户可控的全局光滑正交场,从而能够控制决定最终四边形网格的网格边方向、以及奇异点分布。2)提出了一种基于模式的用户辅助四边形网格生成算法。针对前人方法中拓扑模式种类过少的问题,本文提出了一种面片松弛分解操作,通过面流塌缩处理可将原始输入的多边形面片进行分解化简,然后根据大量简化的面片,设计出了多种更加复杂的拓扑模式,进而再通过面片填补操作便能够生成拓扑结构更加丰富的四边形网格,即扩展了四边形网格生成的解空间。3)结合全自动生成算法与用户辅助生成算法的各自优势,本文将上述两种算法进行了整合,设计开发出了一套完整的四边形网格生成与编辑系统,可以快速方便地生成符合用户需求、且具有各向异性的高质量四边形网格模型。
[Abstract]:Quadrilateral mesh is widely used in geometry modeling, texture mapping, finite element simulation, computer animation and architecture. Compared with traditional triangular meshes, quadrilateral meshes have many excellent properties, such as natural tensor product properties, and their meshes are naturally aligned with rectangular textures. Moreover, the geometric and semantic features of the model can be captured intuitively. Therefore, quadrilateral mesh generation algorithm has become a hot topic at home and abroad. However, how to generate anisotropic high quality quadrilateral mesh models with few singular points and good distribution is still an open problem. The main difficulty is that: 1) in different application fields. Users' requirements for quadrilateral mesh quality control are often different. However, these control requirements are often restricted to each other, or even contradictory. 2) nowadays, the mainstream automatic generation algorithms lack the control of singularity points, and the user-aided generation algorithms require too much on the manual modeling ability of users. Therefore, how to combine the advantages of these two quadrilateral mesh generation algorithms is a great challenge. Therefore, aiming at these problems existing in the current quadrilateral mesh generation algorithm, this paper proposes a corresponding solution: 1) A controllable quadrilateral mesh generation algorithm based on directional field is proposed. This paper improves the controllability of users on the basis of predecessors: by introducing geodesic technology and 3D sketching technology, the user is allowed to control freely and intuitively in the direction of the field. At the same time, in order to deal with the conflicts and errors caused by the user in controlling the direction field, this paper proposes a corresponding solution to the direction constraint conflict and to correct the inaccuracy of user interaction. Furthermore, the smooth energy function of orthogonal field is optimized, which can interpolate and generate the globally smooth orthogonal field which is controllable by the user, so that the edge direction of the final quadrilateral grid can be controlled. And singular point distribution .2) A user-aided quadrilateral mesh generation algorithm based on patterns is proposed. In order to solve the problem of too few topological patterns in previous methods, a relaxation decomposition operation is proposed in this paper, in which the original input polygonal surface slices can be decomposed and simplified by surface flow collapse processing, and then according to a large number of simplified facets, A variety of more complex topology patterns are designed, and then the quadrilateral mesh with more abundant topology can be generated by the patch filling operation. That is, the solution space of quadrilateral mesh generation is expanded. 3) combining the advantages of automatic generation algorithm and user-aided generation algorithm, the two algorithms are integrated in this paper. A complete quadrilateral mesh generation and editing system is designed and developed. The quadrilateral mesh model with high quality and anisotropy can be generated quickly and conveniently.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.7

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