三次Hermite插值曲线及曲面的构造与显示

摘  要

曲线曲面造型是计算机几何设计和计算机图形学的1项重要内容，主要研究在计算机图像系统的环境下对曲线曲面的表示、设计、显示和分析。作为它的1个重要组成部分，Hermite 插值曲线曲面以其特性不仅在几何造型系统中有着广泛的应用，而且在工程设计中也受到了人们的青睐。本文简要介绍了Hermite插值曲线与Conns曲面的定义和相关定理，阐述了如何构造Ferguson曲面及双3次Conns曲面，对3次Hermite插值曲线曲面的广泛应用也做了相应的举例说明。文章采用 MATLAB语言来绘制3次Hermite插值曲线及Coons曲面。matlab语言丰富的图形表现方法，极大的简化了3次Hermite曲线曲面的绘制过程，可以方便地、多样性地实现了可视化，这是其它语言所不能比拟的。

关 键 词:Hermite插值曲线；合成Ferguson曲线；Coons曲面；MATLAB语言；

Abstract

The curve surface modeling that is a important content in the computer aided geometric design and computer graphics, it chiefly researchs the expression, design, display and analysis of the curve and surface under the computer image system environment. The Hermite interpolation curve and surface , as the important component of the curve and surface modeling, that not only has wide application in the geometry modeling system, but also assist many people in the engineering design. This paper introduces the definition and correlative theery of Hermite interpolation curve and the Coons surface briefly, and elaborates how to structure the Ferguson surface and double cubic Coons surface, moreever, this paper also make some corresponding explanations and examples for the wide application of cubic Hermite interpolation curve and suface. This paper uses the MATLAB language to draw up cubic Hermite interpolation curve and Coons surface. There are richful performance methods of graphics in MATLAB language, this make the drowing process of cubic Hermite curve and surface very easy, and make the accomplishment of visualization conveniently, multiply. These points are useful advantages that other language don’t have.

Keywords:Hermite interpolation curve；Complex Ferguson curve;Coons surface;MATLAB language;

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