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。
The technique of curve and surface reconstruction based on NURBS theory is
studied in this thesis. Since its rich geometric properties allow it to represent both
analytic shapes and free-form curves and surfaces, ISO defined non-uniform rational
B-splines(NURBS) as industry standard for representing geometry in 1991. These
points define a surface equation based on NURBS theory. It supplies interface to
industry manufacture.
The main works of this thesis are summarized as follows:
1. Analyzing the basal theory and method of surface reconstruction, we find the
deficiency of Bézier and B-spline method and take NURBS as the essential method of
the surface reconstruction.
2. The correlative thoery of NURBS curve and surface reconstruction is
introduced. We present methods to interpolate NURBS curve and surface.It includes
the parameteral of data points, confirming of knot vectors, computing basis function
and control points.
3. The metrical process of the data is introduced. A special image processing
software is programmed according to the characteristic of LCD image and the
coding method based on morphological technology is presented. The coordinates of
these points are calculated.
4. The system of free-form surface reconstruction based on NURBS method is
designed. A NURBS curve and surface reconstruction software based on Microsoft
Windows is developed. It adapts Object Based Programming(OBP) conception and
database manipulation and has lots of interactive function. The reconstruction using
NURBS method supplies standard interface for industry manufacture.
引文
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