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数字几何中的网格曲面重建及处理
Alternative TitleMesh Surface Reconstruction and Processing for Digital Geometry
南亮亮1,2
Department现代装备研究室
Thesis Advisor刘伟军
ClassificationTP391.7
Keyword数字几何处理 曲面重建 交互式变形 重新网格化 参数化
Call NumberTP391.7/N17/2009
Pages125页
Degree Discipline机械电子工程
Degree Name博士
2009-01-15
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract数字几何是图形学中三维物体的主要表示方法之一,相应的数字几何处理理论和技术是计算机图形学研究的热点,在曲面造型、工业制造以及影视娱乐等领域得到了广泛应用。近20年来,数字几何处理取得了很大的发展,特别是数字几何作为一种多媒体数据所取得的突破,使其有可能成为继数字音频、数字图像和数字视频之后的第四类多媒体数据。但是,目前针对数字几何的处理技术和能力非常有限,数字几何处理的理论还不够成熟,其应用范围还有待进一步扩展。围绕上述问题,本文对数字几何处理中的若干关键技术进行了深入的研究和探讨,主要研究内容和贡献如下: 1. 散乱点是数字几何数据的主要存在形式之一,这些通过测量得到的数据仅包含采样点的三维坐标,缺乏必要的拓扑信息。为便于后续数字几何处理,研究了散乱点集的网格曲面重建方法。提出了用于散乱点网格曲面增量重建的外接球准则,将二维Delaunay三角剖分的空外接圆性质扩展到三维空间,利用该准则实现了一种高效的重建方法。并对因散乱点密度分布不均或具有严重噪声等原因造成的拓扑错误和孔洞,也给出了改正和修补的方法。与已有方法相比,本文方法重建出的网格模型具有Delaunay性质(孔洞修补区域除外),同时算法的时间复杂度低,提高了散乱点网格曲面重建的效率。 2. 针对网格模型包含噪声、数据量存在冗余、拓扑规则性和几何规则性不高等缺陷,详细讨论了数字几何处理中的多种优化技术,主要包括光顺、精简、细分和重新网格化。其中,为了满足交互式变形编辑和数值分析对模型规则性的要求,重点研究了网格模型的重新网格化技术。提出了一种基于采样和松弛的重新网格化方法,主要分为采样、粒化、匀价、松弛和回映五个步骤,通过迭代完成。其中粒化过程对大的面片进行分割,对小的面片进行合并;匀价和松弛过程分别用来提高模型的拓扑规则性和几何规则性;模型的分辨率通过改变包围盒的分割数进行控制。算法还针对机械类零件模型,将模型的尖锐棱角作为特征对待,使其在重新网格化后得到保持。与已有基于参数化的方法相比,所提出的方法直接在网格模型上进行,避免了耗时的参数化过程,也无须对封闭模型进行分割,因此该方法效率高,具有良好的拓扑适应性。 3. 研究了网格模型的交互式变形编辑技术。给出了三角网格模型微分属性表示方法在微分几何学上的解释,并采用这种表示方法实现了网格模型的交互式变形编辑。提出了一种通过修改侧影轮廓改变模型三维几何形状的交互式编辑方法。与已有变形方法相比,本文的交互方式更加灵活。由于所采用的微分属性表示反映了曲面的内蕴几何属性,因此在变形过程中能够保持模型的几何细节。经过变形编辑的模型既可以用于快速原型制造,也可以作为通用CAD系统的输入进行更复杂的造型编辑。 4. 详细讨论了参数化中度量扭曲的产生,并对多种平面参数化方法进行了比较。针对拓扑圆盘类网格曲面,研究了参数化方法在运动机构轨迹规划和动画制作中的应用。提出了一种基于均值坐标映射的运动机构轨迹规划方法,并对封闭网格模型的整体运动轨迹规划进行了初步研究。该方法不仅适用于自由曲面类零件的数控加工,也可以用于激光熔覆、喷涂和抛光等场合,扩大了网格模型参数化技术的应用范围。提出了一种基于平面参数化的二维和三维网格之间渐变的方法,通过关键帧插值实现了简单的动画制作。 5. 设计并实现了一个数字几何处理原型软件。作为实验平台,该系统集成了本文所取得的全部研究成果,同时也包括了多种常用的数字几何处理算法。
Other AbstractDigital Geometry is one of the most popular representation methods for 3D geometric objects, and the corresponding processing technique, named Digital Geometry Processing (DGP), is a hotspot in Computer Graphics, which has wide applications in geometry modeling, manufacturing, entertainment, as well as many other areas. Although exciting progresses have been achieved in the last two decades, especially signal processing techniques that made Digital Geometry the fourth type of multimedia after sounds, images and videos, current processing tools have much limit and we still lack complete and systemic research focus on it. Also, its application areas need to be extended. This dissertation discusses and studies some key techniques, and aims to develop a software system for DGP. The main topics and contributions are: 1. Digital Geometry data exists in the form of either scattered points or meshes. Since scattered points obtained by scanning devices only contain 3D coordinates, it is hard to be processed. For the convenience of DGP, the topology should be reconstructed. We mainly focus on the reconstruction of triangular meshes from scattered points. A three-dimensional circum-sphere criterion is presented, which is an extension of the empty circum-circle property of 2D Delaunay Triangulation. Based on this criterion, we introduce a novel algorithm for surface reconstruction from scattered points. Also, holes and illegal triangles, especially for highly noised or non-uniform data set, are detected and then repaired, which significantly reduce the dependence on the quality of the input data. The most important feature of the algorithm is that good final meshes are obtained with Delaunay properties (excluding the borders of holes). Both experimental results and practical applications show that this method works well for arbitrary topology surface and compares favorably with respect to related approaches in terms of speed and flexibility. 2 Several mesh optimization techniques, such as denoising, simplification, subdivision and especially remeshing, have been investigated. The remeshing technique that we have paid more attentation to aims to satisfy the applications including interactive deformation and numerical simulation. A novel remeshing method, based on sampling and relaxation, is presented, which is used to improve the topological and geometric regularity of input mesh models. The whole algorithm contains five steps: sampling, granulating, degree equalizing, relaxation and remapping. Among the above five steps, the most important three are granulating, degree equalizing and relaxation that performed to split large facets and merge small ones, improve the whole topological regularity and gain better geometric regularity, respectively. Meshes with different resolutions can be obtained by changing the division of the bounding box of the original model. The algorithm also has a special treatment for models with sharp features, especially for mechanical parts. Compared with existing methods that always need expensive parameterization procedure and segmentation as pretreatment for closed models, our method performs remeshing directly on the mesh, which leads to high efficiency, and also flexibility for closed meshes with complicated topology. 3. We give an explanation of the differential based mesh representation that used for implementing our deformation algorithm, from the viewpoint of Differential Geometry. Finally, the interactive manner is enhanced with silhouette editing to achieve more powerful editing tools, which modifies the shape via manipulation of the silhouette of the region to be edited. Experimental results show that the method is straightforward and intuitive, and also efficient for interactive editing. The most important property is that the local details of the mesh are preserved. Mesh models obtained from the editing can be used as input for Rapid Prototyping and other CAD system for further modeling. 4. The metric distortion is discussed in detail for mesh parameterization, and several planar parameterization methods have been compared. Then kinematics path generation and mesh morphing is deeply investigated. A Mean Value Coordinate mapping based method for kinematics path generation on open meshes homeomorphic to discs is proposed. A primary global kinematics path for closed meshes is also obtained, which needs to be further studied and discussed, since the closed model can be cut into discs. Our method can be used not only for CNC machining, but also for laser cladding, plasma spray and polishing, which opens a new research area for mesh parameterization techniques in DGP. Finally, a key frame interpolation based animation algorithm is devised for mesh morphing between planar parametric domain and 3D meshes. 5. A software system for DGP has been designed and implemented. Being an experimental platform, it integrates all the algorithms proposed in this dissertation, and offers most of the commonly used and recent developed algorithms in this area.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/392
Collection智能产线与系统研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院研究生院
Recommended Citation
GB/T 7714
南亮亮. 数字几何中的网格曲面重建及处理[D]. 沈阳. 中国科学院沈阳自动化研究所,2009.
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