MATLAT下B样条曲线曲面的绘制

摘要

B样条曲线曲面是1种非常重要的工业产品几何定义，在计算机辅助几何设计（CAGD）类软件中应用较为普遍；本文选用的开发工具维MATLAB，它是集数值计算、符号计算和图形可视化3大基本功能于1体的，功能强大、操作简单的语言，是国际公认的优秀数学应用软件之1。文章首先对于B样条曲线曲面的'定义、性质及分类进行简单介绍和分析，结合其图形进1步将释义具体化，以令读者加深对B样条曲线曲面概念的理解。其次利用MATLAB语言的特性，利用样条工具箱的函数调用来完成B样条曲线曲面的绘制，从而极大地简化了对B样条曲线定义的概括，轻松实现其绘制的过程。另外，对于B样条曲线曲面的广泛应用也有举例简要说明，以升华本文的研究目的和研究意义。

关键词
计算机辅助几何设计（CAGD）；MATLAB；B样条曲线；B样条曲面；

Abstract

B-spline curves&surfaces are very important geometric definitions on industrial productions, and are so wild used in CADC software; This paper choose MATLAB as the exploring tool, thus it has various skills which consisted with three important functions, and easy to operate. Because of these features, MATLAB become one of the worlds most popular software that wildly used in many fields, such as mathematics. The paper first gives a simple description on B-spline curves&surfaces as follows, their definition, character and classification, together with several graphs and examples in order to strengthen readers comprehension on B-spline curves&surfaces. Second, it indicates the distinction of MATLAB, using function in spline tools to draw B-spline curves&surfaces, in this circumstance, the definition of B-spline curves&surfaces, as well as the drawing procedure would be simplified greatly. By the way, the paper also give brief illustrations on how B-spline curves&surfaces so widely used in daily life, as a result, sublimate the purpose and significance on B-spline curves&surfaces.

Keywords
CAGD; MATLAB; B-Spline curves; B-spline sufaces