毕业设计（论文）具有插值和拟合两特性的曲线曲面的构造.docVIP

摘 要 本文构造了具有插值和拟合两特性曲线曲面，用一种模型实现从逼近到插值的转换，方法是在多项式空间上构造了含两个参数的调配函数，如果参数在一定的取值范围内，得出均匀三次B样条的基函数，进而构造一个插值函数，最后利用线性组合的方法，构造出具有插值和拟合两特性的多项式。由于曲线形状和端点性质密切相关，因此对所构造的多项式进行求导，进而得出满足构造条件的端点性质，由条件知曲线具有连续性。在此方法构造的情况下B样条曲线具有良好的保形性和连续性，这些综合因素就使得曲线在形状变化的过程中始终可以较好地保持控制多边形的特征。构造曲面则采用张量积方法将曲线推广至曲面，由于使用的是张量积方法，本文中的曲线和曲面具有类似的性质，最后给出了曲线曲面实例，实例显示了本文研究的构造方法在造型设计中是有效的。 关键词：B样条曲线曲面；线性组合；分段组合；形状参数；插值拟合 Abstract In this paper, we have constructed a class of the curve which has properties of interpolation and approximation, and use a model to realize the transformation from approximation to interpolation. The method is to construct a blending function with two parameters in the polynomial space. If the parameters are in a certain range, we obtain a basis function of the cubic B-spline, and then construct an interpolation function. Finally, we use the method of linear combination to construct the polynomial with interpolation and approximation. Because of the relationship between the shape of the curve and the endpoints property of the curve, the constructed polynomial is derived, and then the endpoints properties which meet with the construction condition are obtained and the curve meet with continuous. In the case of this method, the B-spline curve has good shape-preserving and continuity, and these synthetic factors make it possible to keep the control polygon better in the process of shape change. In this paper, the curve and surface are similar to each other. Finally, an example of the curve and surface is given. The examples show the construction method of the research in this paper. In this paper, we use the tensor product method to extend the curve to the surface. The method is effective in the design. Key words: B-spline curve and surface; linear combination; piecewise combination; shape parameter; interpolation and approximation. 目录 摘 要 I Abstract II 目录 III 第一章 绪 论 1 1.1计算机图形学应用研究 1 1.2曲线与曲面应用研究 1 1.3本论文主要研究内容 2 第二章 B样条以及曲线曲面的基础理论 3 2.1样条曲线定义 3 2.2 B样条曲线的定义： 3 2.2.1 B样条曲线的方程式： 3 2.2.