【作者】 杨雅迪；

【导师】 秦新强；

【作者基本信息】 西安理工大学 ， 计算数学， 2009， 硕士

【摘要】 自由曲线和曲面在飞机、汽车、船舶、家电外形设计和反求工程中有着广泛的应用。在CAGD中,经常用参数曲线曲面来插值、逼近、拟合测量得到的数据点。然而,由于计算和测量数据都不可避免的存在误差,由这些数据设计得到的曲线曲面一般都需要进行光顺处理。因此曲线曲面的光顺处理成为CAGD中一个非常重要的研究课题,受到人们的普遍重视。但是由于光顺处理的复杂性,直到现在,此问题还没有得到彻底的解决,对它的研究仍在进行之中。C-曲线作为一种新颖的曲线造型方法,它不仅能够处理自由形式的曲线,而且能够精确地表示一些常规二次曲线。因此研究C-曲线有着很重要的理论和应用价值。本文针对目前C-曲线光顺算法存在的问题,提出了一种光顺C-曲线的新算法,该算法的基本思想是：通过调整控制参数α和控制顶点使得曲线的能量最小,得到最优的光顺逼近曲线。通过最小二乘法和非线性泛函极小值的优化计算,对平面数据点进行光顺逼近,达到光顺的目的,并给出了数值算例来说明本文算法的有效性。本文的主要研究内容如下：1.介绍了曲线曲面光顺技术和C-曲线曲面理论的研究意义和发展概况；2.介绍了C-曲线的定义和性质以及光顺的概念、光顺准则和一些经典光顺法；3.提出了一种新的曲线光顺准则,将其分别应用于C-Bezier曲线和C-B样条曲线,构造了光顺算法；4.给出了由数据拟合的C-Bezier曲线和C-B样条曲线光顺的实例,通过对数值算例的计算,显示了本文提出的算法的可行性和有效性。更多还原

【Abstract】 Free-form curves and surfaces are widely used in airplane, automobile, shipping and electrical appliance shape design and inverse design in engineering. In CAGD, parametric curves and surfaces are usually applied to interpolate, approximate and fit the giving data. Nevertheless, as error exists due to measuring and calculating data, it is necessary to do fairing operations on the curves and surfaces obtained by these data, thus to get the aesthetic curves and surfaces. So the fairing of curves and surfaces is becoming one of the most important tasks in CAGD, and great importance is attached to it. But fairing process is so complicated that until now it is not completely resolved and the research for it is going on. Serving as a new method of curve/surface modeling, C-curves not only can deal with free form curves and surfaces, but also can present conic exactly. So the research of C-curves has the important value of theory and application. A new method of fairing C-curves is given in this paper in view of some disadvantages of fairing of C-curves at present.The mean idea is:fairing of C-curves is fulfilled by adjusting the value of parameter a and control points to reduce the implied energy. By using the technique of least square approximation and non-linear functional minimization, the data points of plane can be faired approximately. The examples of C-curves fairing show the efficiency of our method.The main results in this paper are as following:1. The meaning and general situation in fairing of curves and surfaces and the theories of C-curves and C-surfaces are introduced;2. The definition and property of C-curves, and the concept of fairing, fairness indicators and some classical fairing methods are introduced;3. A new fairness indicator of curves is put forward, and it is applied to C-Bezier curve and C-B spline curve, the fairing algorithm are constructed; 4. The examples of C-Bezier curve and C-B spline curve fairing are given. The validity and efficiency of the algorithm in this paper are shown by calculating these examples.更多还原