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学校代号 10532 学号 S1124W116 分类号 TP391 密级普通工程硕士学位论文基于 OpenGL 的三维模型简化算法的研究与实现学位申请人姓名张非凡培养单位信息科学与工程学院导师姓名及职称常炳国副教授王祥宗高级工程师学科专业软件工程研究方向计算机图形学论文提交日期 2015 年 4 月 30 日

学校代号：10532 号：S1124W116 级：普通学密湖南大学工程硕士学位论文基于 OpenGL 的三维模型简化算法的研究与实现学位申请人姓名：张非凡导师姓名及职称：常炳国副教授王祥宗高级工程师培养单位：信息科学与工程学院专业名称：软件工程论文提交日期：2015 年 4 月 30 日论文答辩日期：2015 年 5 月 30 日答辩委员会主席：杨贯中教授

Research and Implementation on Simplified Scheme of Three-dimensional Model Based on OpenGL by ZHANG Feifan B.E. (Hunan University) 2011 A thesis submitted in partial satisfaction of the Requirements for the degree of Master of Engineering in Software Engineering in the Graduate School of Hunan University Supervisor Associate Professor CHANG Bingguo Senior Engineer WANG Xiangzong May, 2015

工程硕士学位论文学位论文原创性声明和学位论文版权使用授权书湖南大学学位论文原创性声明本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。除了文中特别加以标注引用的内容外，本论文不包含任何其他个人或集体已经发表或撰写的成果作品。对本文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明。本人完全意识到本声明的法律后果由本人承担。作者签名：日期：年月日学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅。本人授权湖南大学可以将本学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文。本学位论文属于 1、保密□，在______年解密后适用本授权书。 2、不保密□。（请在以上相应方框内打“√”）作者签名：导师签名：日期：年月日日期：年月日 I

基于 OpenGL 的三维模型简化算法的研究与实现摘要大型数据的可视化及实时显示已在诸多领域得到广泛的运用，如虚拟现实技术、三维动画、游戏制作等，三维实体显示技术已成为领域研究热点。随着三维建模及数据获取等相关技术的发展、以及为了提高模拟显示的效果，三维模型变得越来越复杂精细，这些模型的三角网格数据往往包含数十万或数百万个面片，有的甚至达到了上亿。这种三维模型复杂、数据量大的特点使得模型存储难、传输难、绘制难，也给人机交互带来了巨大的挑战。采用模型简化算法对网格模型进行简化并保留其相关的几何特征具有十分重要的意义。论文首先对模型简化方法进行了有意义的探索，研究了几何元素删除法、顶点聚类法、采样法、自适应细分法这四类基本模型简化算法特点。在此基础上本文进一步研究了 QEM 边折叠算法。为了解决 QEM 边折叠算法在对模型高度简化时无法保留三维模型细节特征的缺陷，本文提出了一种基于法向量误差和体积误差的边折叠算法。该算法采用蝶形插值细分法计算边折叠后新顶点的空间位置，根据新顶点的空间位置计算边折叠时简化网格的顶点法向量和模型体积误差并建立折叠序列，成功在模型的高曲率区和低曲率区实现对网格模型的简化。因此本文算法既考虑到了简化模型的体积变化，又能够很好地反映网格局部曲面的几何变化。接着算法通过实现渐进网格方法，实现了对网格模型的动态简化。最后本论文在 Visual Studio 2010 平台上，结合 OpenGL 开发了一个三维模型简化软件，并把改进前后的算法集成到了该软件当中进行对比，并对本文算法的简化效果进行验证。该软件可以处理 PLY 格式的模型文件，并实现了简单的人机交互和渲染等功能。实验结果表明，开发的基于 OpenGL 的三维模型简化软件能够成功导入并简化 PLY 格式的三维模型文件，并且相较于 QEM 边折叠算法，改进后的边折叠算法显示效果更好，模型的几何形状和细节特征得到较好的维持。该软件达到预期研究目的，且运行良好。关键词：网格简化；边折叠；法向量；体积误差 II

工程硕士学位论文 Abstract Currently, large-scale data’s visualization and real-time display have been widely used in many areas, such as virtual reality, video games and movies. Three-dimensional solid display technology has become a hot area of research . With the development of three-dimensional modeling and data acquisition and other related technologies , and in order to improve the effect of the analog display, three-dimensional model becomes more complex. The triangular mesh data for these models often contain hundreds of thousands or millions of facets, some models even reached millions. The features of this three-dimensional model is complex and larger amount of data. This makes the model becomes difficult to store, difficult to transport, difficult to draw, and it also create huge challenges for Human–Machine Interaction. So how to simplify the mesh model and retain the geometric features is very important. This thesis simplified start a meaningful exploration of Model Simplification, and study the characteristics of four basic model simplification algorithm s for geometric element decimation, vertex clustering method, sampling method and adaptive refinements. On this basis, this paper further studied the QEM edge collapse algorithm. The QEM edge collapse algorithm can't retain the minutiae of three-dimensional model when the model is highly simplified. In order to solve this defect, an edge collapse simplification algorithm based on normal and volume error is presented in this paper. The algorithm calculates the spatial location of the new vertex after edge collapse by the butterfly-shaped interpolating subdivision, and then computes the vertex normal and volume error of the simplified grid in edge co llapse according to the spatial location of the new vertex and establishes a folding sequence, and at last carries out the operation of edge collapse of the mesh model in the folding sequence, then the mesh model is simplified in the high curvature and low curvature region. This algorithm not only takes into account the volume changes of the simplified model, but also can well reflect the changes in the geometry of local surface meshes. Then the algorithm can dynamically simply the mesh model by implementing progressive mesh method. Meanwhile, upon Visual Studio 2010 platform, developed a model to model simplification software combined with the excellent three-dimensional graphics library OpenGL, and two algorithms deletion into the software. This software can handle models which are PLY file format, and has a simple human-computer interaction and rendering functions. III

基于 OpenGL 的三维模型简化算法的研究与实现 Experimental results show that the model-simplified software we develop based on OpenGL can success import PLY files, and compared to the QEM edge collapse algorithm, the improved edge collapse algorithm is better display the original algorit hm, the geometry of the model get a better maintained. This model-simplified software achieves our research purpose and running perfect. Key Words: Mesh simplification; edge collapse; Normal; Volume Error IV

工程硕士学位论文目录学位论文原创性声明和学位论文版权使用授权书 ................................................... I 摘要 ........................................................................................................................ II Abstract .................................................................................................................... III 目录 ........................................................................................................................ V 插图索引 ................................................................................................................. VII 插表索引 ................................................................................................................ VIII 第 1 章绪论 ..........................................................................................................1 1.1 研究背景及意义 .......................................................................................... 1 1.2 国内外研究的发展及现状 .......................................................................... 2 1.3 本文所做的主要工作 .................................................................................. 6 1.4 本文的章节安排 .......................................................................................... 6 第 2 章边折叠网格模型简化算法 ...........................................................................8 2.1 三角网格模型 .............................................................................................. 8 2.1.1 三角网格的几何性质 ........................................................................... 8 2.1.2 三角面片的法向量 ............................................................................... 9 2.1.3 网格模型的数学描述 ......................................................................... 11 2.2 边折叠简化算法 ........................................................................................ 11 2.2.1 边折叠算法概述 ................................................................................. 11 2.2.2 QEM 边折叠代价 ................................................................................ 13 2.2.3 新顶点的位置 ..................................................................................... 14 2.2.4 算法步骤 ............................................................................................. 15 2.2.5 实验结果 ............................................................................................. 15 2.3 本章小结 ................................................................................................... 16 第 3 章边折叠模型简化算法研究 ......................................................................... 17 3.1 三维模型动态简化的要求 ........................................................................ 17 3.2 改进的边折叠算法 .................................................................................... 18 3.2.1 法向量变化误差 ................................................................................. 19 3.2.2 体积变化误差 ..................................................................................... 20 3.2.3 新顶点的位置 ..................................................................................... 21 3.2.4 狭长三角形的控制 ............................................................................. 22 3.3 渐进网格 ................................................................................................... 22 3.3.1 渐进网格原理 ..................................................................................... 23 V

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基于OpenGL的三维模型简化算法的研究与实现.pdf

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