【作者】 范宜艳；

【导师】 王仲； 邾继贵；

【作者基本信息】 天津大学 ， 测试计量技术及仪器， 2004， 硕士

【摘要】 本文对基于 NURBS 的曲线曲面重构技术进行了研究。由于非均匀有理 B 样条(NURBS)可以精确表示解析形状自由曲线曲面,国际标准组织(ISO)于 1991 年把 NURBS 作为表示工业产品几何形状的工业标准。本文采用了 NURBS 理论对数据点阵进行曲面插值，获得 NURBS 参数曲面方程，开发了基于 NURBS 的曲面重构系统，为工业自动化生产提供标准接口。 论文中主要研究内容如下： 1、通过对曲面重构基本原理及其方法的深入分析，发现 Bézier 曲线曲面，B-spline 曲线曲面重构方法均有各自的局限性，进而提出采用 NURBS 方法作为系统软件曲线曲面重构的基本方法。 2、介绍了 NURBS 曲线曲面重构的相关基础理论；研究了由一组数据点直接重构 NURBS 曲线和曲面的基本算法。详细论述了 NURBS 曲线曲面插值的步骤：数据点的参数化，节点矢量的确定，求取 NURBS 基函数Ni ，反算控制顶 ,p点从而求出曲面。 3、详细介绍了测量三维数据的获取过程。针对液晶图像的特点，依次经过图像平滑、二值化和形态学技术对图像进行处理，并提出基于相关技术的液晶编码技术，获得了物体的三维空间点阵。 4、设计了基于 NURBS 的自由曲面重构系统。通过对 NURBS 曲线曲面重构的基本算法的研究，利用可视化技术的优势，采用面向对象技术，结合数据库操作，开发了一个基于微机 Microsoft Windows 系统的 NURBS 曲面重构的软件NURBSsuf 系统。该软件按面向对象思想设计，可以显示具有真实感的三维图形，具有丰富的人机交互功能。在这个软件的基础上，可以添加更改自己的算法，而无需考虑三维显示、文件 I/O、交互操作等细节问题。更多还原

【Abstract】 The technique of curve and surface reconstruction based on NURBS theory isstudied in this thesis. Since its rich geometric properties allow it to represent bothanalytic shapes and free-form curves and surfaces, ISO defined non-uniform rationalB-splines(NURBS) as industry standard for representing geometry in 1991. Thesepoints define a surface equation based on NURBS theory. It supplies interface toindustry manufacture. The main works of this thesis are summarized as follows: 1. Analyzing the basal theory and method of surface reconstruction, we find thedeficiency of Bézier and B-spline method and take NURBS as the essential method ofthe surface reconstruction. 2. The correlative thoery of NURBS curve and surface reconstruction isintroduced. We present methods to interpolate NURBS curve and surface.It includesthe parameteral of data points, confirming of knot vectors, computing basis functionand control points. 3. The metrical process of the data is introduced. A special image processingsoftware is programmed according to the characteristic of LCD image and thecoding method based on morphological technology is presented. The coordinates ofthese points are calculated. 4. The system of free-form surface reconstruction based on NURBS method isdesigned. A NURBS curve and surface reconstruction software based on MicrosoftWindows is developed. It adapts Object Based Programming(OBP) conception anddatabase manipulation and has lots of interactive function. The reconstruction usingNURBS method supplies standard interface for industry manufacture.更多还原