基于曲率参数的β样条插值

A New Method for β-splines Interpolation based on the Curvature Coefficient

提出了一种基于曲率参数的边界条件构造法。与目前常用的其它几种边界条件构造法相比，它不要求己知端点的切矢，而且克服了重顶点法构造边界条件时端点曲率为零等缺点，同时通过调整引入的曲率参数Ｋ，可自由改变曲线的端部形状使之合乎设计要求。该方法可用于汽车车身、船体型线以及飞机外壳等曲面外形的计算机辅助设计中。

his paper presents a new method based on the Curvature Coefficient toconstruct end conditions. Compared with other ordinary methods of end conditionconstruction, this method does not require to know the derivatives of curve ends, andit surmounts many shortcomings such as zero curvature at curve ends in multivertex.In addition, by adjusting the curvature coefficient, it can freely modify the curve endsto satisfy designer's demands. This method can be used in CAD of engineering objectssuch as car bodies, ship hulls and aircraft shells.