【作者】 吴庆阳；

【导师】 杨忠福；

【作者基本信息】 四川大学 ， 机械设计及理论， 2003， 硕士

【摘要】 近年来随着激光和结构光等三维数据采样技术和硬件设备的日益完善，随着计算机图形显示对于真实性、实时性和交互性要求的日益增强，随着CAD＼CAM或者其它快速成型技术的需求，三角形网格生成与简化成为三维重建这一研究领域的热点之一。三角形网格生成与简化的基本思想是对从三维测量得到的离散数据或造型软件的输出结果进行处理，形成规范和通用的数据格式，去除冗余信息而又保证模型的准确度，以利于图形显示的实时性、数据存储的经济性和数据传输的快速性。本文在总结了国内外一些经典的由海量离散数据点进行曲面重建的算法和一些三角形网格简化算法的基础上，结合我们使用现有的三维测量仪器的进行采集所得到数据的特点，提出了一种新的曲面重建算法和简化算法。使用这些算法计算速度快，得到的三角形网格的图象质量高，完全可以满足我们的要求。具体的研究结果如下：1．提出了一种基于动态圆的散乱数据点的三角网格生成算法。该算法适用范围广，计算效率高，生成的曲面的效果好。它可以直接处理来源于光学测量系统或者其他的一些三维测量系统的数据，而不用经过去除杂点的数据预处理过程；输出三角形网格的解析度可以由用户通过设置一些参数来进行控制；这个算法还可以处理一些来自于点云的点所带的除了(x，y，z)坐标以外的一些信息，比如说颜色信息(RGB)等；此外我们还提供了几种可以实现的纹理映射(texture mapping)的思路。2．本文给出一种简化三角形网格表示的三维模型的算法，算法采用以曲面的曲率的二阶导数为简化条件并以边折叠为基本简化方式，在简化的过程中，三角形简化与否取决于该三角形所处的平面以及周围三角形平面的曲率变化的大小，所以输出三角形的解析度可以随着物体表面的梯度的变化而变 化的大小，所以输出三角形的解析度可以随着物体表面的梯度的变化而变 化。在新顶点生成时，引入了二次误差的概念，新顶点的坐标就是当二次 误差取最小值时的坐标。这个简化算法可以用于简化各种曲面，如非封闭 曲面，简单封闭曲面，多连通封闭曲面。3.使用OpenGL技术对处理前后的三维模型进行显示，可以直接在屏幕上观 察到三维模型经过处理后得到的结果，并且可以对图形进行放大、缩小、 平移、旋转等基本操作，完全可以满足我们对图形显示的要求。4.输出格式很容易转化成现在计算机图形学软件所使用的.VRML文件格式， 从而使我们的数据可以直接输出到因特网或应用于其他的一些三维造型软 件，从而使我们数据可以在更广泛的领域得到应用。更多还原

【Abstract】 With the recent development of 3D data collection technologies and hardware facilities (e.g. laser and structured light), the higher requirements of authenticity, real time and interaction of computer graphic visualization, the demands of CAD, CAM and other quick molding technologies, the technology of triangle mesh generation and simplification have become one of the hotspots in the field of 3D reconstruction. The basic thought of triangle mesh generation and simplification is to process disperse data points obtained by 3D measurement or the output results from molding software to generate data in a standard and common format, wipe off the redundant information while at the same time by keeping the accuracy of the model to guarantee the real-time graphic visualization, the efficient of data storage and quickness of data transmissionThis thesis sums up some classical algorithms of surface reconstruction with vast disperse data and several simplification algorithms of triangle mesh. Based on these algorithms and the features of the data obtained by our 3D measurement instrument, a new surface construction and simplification algorithm is presented in this thesis. Using these algorithms, the programs are efficient and the obtained graphics of triangle mesh are of good quality, which meet our requirements quite well. The detailed results of the research are listed below:1. Presents an algorithm of triangle mesh generation of disperse data points based on dynamic circles. This algorithm is efficient, and the obtained cured surface is of good quality. It processes these data that gathered from the optical measurement system or other 3D measuring apparatus directly without thepreprocessing of wiping off noise points. User can define the resolution of the exported triangle mesh through setting a few parameters. It still can process other information of the points of cloud except for the x, y, z coordinates, such as color information (RGB). Besides, several feasible ideas of texture mapping are presented in this paper.2. Presents an algorithm of 3D model represented in simplified triangle mesh. This algorithm adopts the 2nd derivative of the curvature of the curved surface as the condition of simplification and the edge contraction as the basic simplification manner. The concept of quadric error is introduced in the generation of a new vertex.3. The results of the numerical experiments are visualized using OpenGL. The real-time processing results of three dimensions can be viewed on the screen. And the model can be zoomed , panned and rotated.4. It is easily to export three-dimensional geometry with a mapped texture into .VRML format. So we can directly export these data into Internet and use the data in other software, and extend the range of application.更多还原