计算机辅助几何设计中的曲线光顺算法研究

【作者】 戴霞；

【导师】 叶正麟；

【作者基本信息】 西北工业大学 ， 应用数学， 2004， 硕士

【摘要】 随着在飞机、汽车、船舶以及家用电器等的计算机辅助几何设计(CAGD)中人们对产品外形光顺性要求的提高，曲线曲面的光顺性(fairness)研究现已成为了国内外研究的热点。本文针对目前曲线光顺算法存在的问题，提出了一种采用最小二乘法来拟合曲线型值点列的二阶导数曲线，然后通过两次积分来反求光顺曲线思想的曲线光顺算法，并给出了实际的算例来说明本文算法的优越性。本文的主要研究内容如下： 1．在综述几何造型原理的基础上，回顾几何造型技术的发展趋势和现状，并介绍了曲线曲面光顺技术的意义和发展前景。 2．介绍了光顺的基本原理和方法，在详细分析已有方法优缺点的基础了上，通过实际算例说明了目前曲线光顺算法存在的问题，并提出了解决的思路。 3．提出了一种针对小挠度曲线的逆向曲线光顺算法，该算法直接拟合曲线型值点列的二阶导数曲线，然后通过两次积分来反求出光顺后的曲线，并对该算法的误差分析、效果分析、光顺优化等问题进行了深入探讨。 4．通过对一些实际算例和工程中实际的曲线光顺问题进行的计算，显示了本文提出的曲线光顺算法的有效性和优越性。更多还原

【Abstract】 As a result of the require of CAGD in airplane, automobile shipping andelectrical appliance etc, fairing of curves and surfaces has become the hot subject in all over the world. This paper presents a new method for fairing of curves based on fitting the derivative of second order of curves. Several practicality examples has been given to show the advantage of this arithmetic. The main results in this paper are as following:1. Summarize the develop and actuality of CAGD. Introduce the meaning and foreground in fairing of curves and surfaces.2. Introduce the principle and method in fairing of curves and surfaces. Through the analyze to existing method of fairing of curves and surfaces, we point out the disadvantage in presently method in fairing.3. Presents a new method for fairing of curves which has a small flexibility based on fitting the derivative of second order of curves. We fit the derivative of second order of curves by a polynomial fitting, then find an indefinite integral of this polynomial to get a approach of curves. Otherwise, we discuss the analyze of the error and the optimize of fairing to this arithmetic.4. Give several examples which is got from the practicality engineering problem to show the validity and advantage of the arithmetic in this paper.更多还原