绕一角点的Bézier三角曲面片的光滑拼接

Smooth Connection of Triangular Bézier Patches with a Common Vertex

为了降低绕一角点的Bézier三角曲面片光滑拼接的难度,根据曲面光滑拼接的几何特征和相容性条件构造了插值数据应满足的方程组,利用方程组有解的条件得到绕一角点的多项式曲面片G1,G2和高斯曲率连续拼接的方法;然后利用重心坐标和直角坐标的关系将多项式曲面片转化为Bézier三角曲面片,得到相应的绕一角点的Bézier三角曲面片光滑拼接的方法.对于G1,G2和高斯曲率连续拼接,曲面的次数分别为3次,5次和4次.实例结果表明,采用文中方法所得曲面的次数低、易于修改,且该方法快捷、形状局部可调性强.

In order to simplify the problem of smoothing connection of triangular Bezier patches around a common vertex, a system of equations about the interpolating data is obtained according to the geometric feature of smoothing connection and consistence conditions. According to the conditions that the system has solutions, the methods for constructing polynomial surfaces with a common vertex and with G1, G2 and Gaussian curvature continuity are presented respectively. Then we get the methods for smoothing connection of triangular Bezier patches with a common vertex by transforming polynomial surfaces to triangular Bezier patches. The resulting polynomial surfaces have lower degree and can be adjusted easily, their degrees are 3, 5 and 4 for G1 , G2 and Gaussian curvature continuity respectively. The examples show that the methods are efficient and flexible for local shape adjustment.