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Element Quality Refinement in 2D Mesh Generation and Surface Remeshing
Khan Dawar
Thesis AdvisorXiaopeng Zhang
Degree Grantor中国科学院研究生院
Place of Conferral北京
KeywordMesh Generation Triangulation Obtuse Triangles Mesh Quality
Finite element mesh generation has numerous applications such as modelling, animation, simulation and many other computer graphics applications. Unfortunately these meshes are usually generated in a raw form containing low-quality elements - especially when the mesh generation process is error-prone such as automated mesh generation. It is difficult to use such raw meshes in downstream applications directly. Therefore a remeshing process is demanded at this stage to improve the mesh quality. Existing methods often fail to efficiently remove low-quality  elements especially in regions with sharp features or application with  special quality requirements. 
In this thesis, we first present a novel method for elimination of obtuse triangles and small angle triangles from a 2D mesh. A pre-processing of Centroidal Voronoi Tessellation (CVT) is applied first. Consecutively the process of point’s insertions, point’s removal and mesh smoothing and optimization are applied in a loop till the generation of a high quality 2D mesh with elimination of all obtuse angles.  In experimental study, a complete comparison with the state-of-the-art methods is carried out for the analysis of the results.  The results show that our method performs well over the state-of-the-art methods in terms of maximal and minimal angle improvement and other mesh quality refinements. Our method removes all obtuse angles and generates a well-shaped mesh. 
We also present a user-guided surface remeshing method which is based on a prior robust mesh segmentation.  Mesh segmentation is initiated with an existing tool called live-wire which allows real-time user interaction. The mesh is further refined with local mesh operations.  Unlike live-wire, our method segments the input mesh with a minor (negligible) change in the input mesh. After segmentation, a segment wise surface remeshing is applied. We proposed a segment-based surface remeshing approach which uses local region operators to generate a considerably high-quality mesh with sharp feature preservation.   Experimental results reveal that our methods for mesh segmentation as well as surface remeshing perform well that that of the previous methods.     
Finally, we proposed a mesh refinement method for molecular surface meshes. The molecular sruface remeshing has additional challenges such as complex mesh and very tiny or zero degree angles. The proposed method uses local operators for the refinement of molecular surface meshes. A cut and fill strategy is used to remove small angle triangles with their local neighbourhoods; creating holes in the input mesh. The holes are carefully filled again and the newly filled regions are smoothed  locally for minimal angle improvement and other quality refinement. In experimental study, we compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over  state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method for molecular surface remeshing showed satisfactory results in terms of the ratio of regular vertices and  the preservation of area and volume
Other Abstract
有限元网格生成具有许多的应用,如建模、动画、仿真和许多其它计算机图形学应用。然而,这些网格通常由原始数据生成,包含了许多低质量的元素,特别是自动网格生成方法十分容易出错。由于这种原始网格在下游中难以直接应用,所以需要重新网格化过程来提高网格质量并消除低质量的元素,如小角度、大(钝)角度、短边、冗余顶点和自相交的三角形。现有方法往往无法有效地去除低质量元素,特别是在具有尖锐特征的区域或具有特殊质量要求的应用中 .
在本论文中,我们首次提出了一种消除钝角三角形和小角度的二维网格生成方法。我们的方法从Centroidal Voronoi Tessellation(CVT)的预处理开始,之后迭代地进行点插入、点删除、网格平滑和优化步骤直到生成无钝角三角形的网格。在实验中,我们与现有先进的方法作了充分的比较,结果表明,我们的方法在最大角、最小角等网格质量上比现有方法表现的更好。我们的方法生成了没有钝角三角形的高质量三角化网格。  
最后,我们提出了分子表面网格的网格优化方法。因为复杂的结构和和小或零角度,分子表面重新网格化具有更多的挑战。所提出的方法使用局部算子优化分子表面网格结构,利用切割消除了局部邻域中的小角度三角形并产生空洞,之后通过填充策略填补空洞并进行平滑操作以提高小角度和其他质量。在实验中,我们与目前先进的四种方法进行了对比,发现我们的方法在最小角度,长短边比,规则顶点和其他网格质量测量参数方面比先前的方法有明显的提高。 此外,我们的分子表面重新网格化方法在规则顶点比率和面积体积的保持方面表现出满意的结果。 
Subject AreaComputer Graphics
Document Type学位论文
AffiliationInstitute of Automation, Chinese Academy of Sciences
First Author AffilicationInstitute of Automation, Chinese Academy of Sciences
Recommended Citation
GB/T 7714
Khan Dawar. Element Quality Refinement in 2D Mesh Generation and Surface Remeshing[D]. 北京. 中国科学院研究生院,2018.
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