毕业设计（论文）基于三角Bézier曲线的过渡曲线曲面的构造.doc

摘 要 在计算机几何设计中，如何构造过渡曲线一直是一个非常重要的研究课题，国内外学者对这个课题进行了大量的探讨和研究。 作者首先给出了两类不同的Bézier曲线基函数，分别是多项式基函数和三角基函数。然后根据所给出的不同基函数提出了带形状参数的两种不同Bézier曲线的构造方法。在选取控制顶点的时候发现，当两条Bézier曲线具有相同的控制点且满足某些条件时，此时这两条Bézier 曲线具有一定的拟连续性。但是当控制顶点的选取无关时(即没有相同的控制顶点)，这时需要一条过渡曲线来连接两条Bézier曲线，当两条Bézier曲线和过渡曲线之间满足一定的拟连续性时，这条过渡曲线中的调配函数以及控制顶点的选取是至关重要的，这是本文的研究重点。本文给出了两类形状不同的过渡曲线(C型和S型)的例子来加深理解。最后，通过对过渡曲线的研究，上升到对过渡曲面如何构造的探讨，针对过渡曲面的研究，其调配函数的选取和过渡曲面的构造与过渡曲线中的方法基本是一致的，只是从二维空间上升到三维空间而已。通过选取不同的调配函数，得出三种不同的过渡曲面分别满足拟连续性。 关键词：形状参数；过渡曲线；过渡曲面；连续性 Abstract In the computer geometric design, how to construct the transition curve has always been a very important research topic, scholars at home and abroad have done a lot of research on this subject. First, two classes of Bézier curve basis functions are given by the author, they are polynomial basis functions and trigonometric basis functions. Two different Bézier curves with shape parameters are proposed by the given basis functions. When the control vertices are selected, it is found that the two Bézier curves have the same control points and satisfy certain conditions, the two Bézier curves have certain continuity at this point. However, when the selection of the control vertices is irrelevant (without the same control vertices), then a transition curve is required to connect two Bézier curves. When the two Bézier curves and the transition curves satisfy a certain quasi-continuity, the selection of the blending function and the control vertices in this transition curve is of vital importance, which is the focus of this paper. This paper gives two examples of different transition curves (C and S) with different shapes to understand. Finally, through the study of the transition curve, the discussion of how to construct the transition surface is discussed. For the study of the transition surface, the selection of the modulation function and the construction of the transition surface are basically the same as those in the transition curve. Space rose to three-dimensional