空间曲面参数化及其应用

发布时间：2018-09-19 07:52

【摘要】：参数化在科学和工程的各个领域都有着广泛的应用,包括离散数据的拟合,样条曲面的重新参数化以及对CAD模型的修复。最初参数化方法的发展过程中主要驱动力是计算机图形学中使用的纹理映射,以提高多边形模型的视觉质量。后来,由于快速发展的三维扫描技术以及由此带来的日益复杂的三角剖分的高效压缩方法的需求,其它应用如表面逼近和重新网格化对参数化将来的发展有很大影响。曲面参数化可以看成一个曲面到适当参数区域的一个映射。构建一个参数化主要要用到计算机图形学、图论、线性代数以及数值分析的知识,本文具体地创建空间曲面三角剖分的全局参数化,它就是一个曲面三角剖分,它是由邻点构建凸组合得到的线性或非线性方程组的解。本文给出一些使得曲面逼近在视觉上更光滑的参数化方法。本文在熟练掌握计算机图形学以及图论的基础上,首先对空间曲线进行参数化,主要应用均匀法和弦长法;其次对空间非封闭曲面参数化,这里非封闭曲面是指带有外边界的单连通空间曲面;再次对封闭曲面参数化,其主要方法是在保留三角结构的基础上将所有顶点投影到单位球面上,通过球面几何知识可以列出非线性方程组并求解;最后对两个相容的空间曲面建立分片的仿射变换以实现源图像和目标图像的渐变过渡。
[Abstract]:Parameterization is widely used in various fields of science and engineering, including the fitting of discrete data, the reparameterization of spline surface and the restoration of CAD model. The main driving force in the development of parametric methods is texture mapping used in computer graphics to improve the visual quality of polygon models. Later, due to the rapid development of 3D scanning technology and the resulting demand of increasingly complex triangulation efficient compression methods, other applications such as surface approximation and re-meshing have a great impact on the future development of parameterization. Surface parameterization can be regarded as a mapping from a surface to an appropriate parametric region. In order to construct a parameterization, we mainly use the knowledge of computer graphics, graph theory, linear algebra and numerical analysis. In this paper, we create the global parameterization of triangulation of space surface, which is a triangulation of surface. It is the solution of linear or nonlinear equations obtained by convex combination of adjacent points. In this paper, we give some parameterization methods which make the surface approximation more visually smooth. On the basis of mastering computer graphics and graph theory, this paper first parameterizes the space curve, mainly applies the uniform method and the chord length method, and then parameterizes the space unclosed surface. Here unclosed surfaces are simply connected space surfaces with outer boundaries. The main method for parameterization of closed surfaces is to project all vertices onto the unit sphere on the basis of preserving the triangular structure. Through the knowledge of spherical geometry, the nonlinear equations can be set up and solved. Finally, the piecewise affine transformation of two compatible space surfaces is established to realize the gradual transition between the source image and the target image.
【学位授予单位】：中国石油大学(北京)
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.7

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