均匀CB样条曲线曲面的扩展

Extensions of uniform CB-spline curves and surfaces

运用积分定义的方式,构造了带多形状参数的均匀CB样条曲线曲面,随着基函数次数的升高,形状参数的范围可以扩展,具体讨论了3～9次时形状参数的取值范围。它们包含均匀CB样条曲线曲面为其特例且具有均匀CB样条曲线曲面的主要性质。改变形状参数的值,能整体或局部调控曲线曲面的形状,比均匀CB样条具有更强的造型能力,在CAD/CAM中具有很好的应用前景。

Uniform CB-spline curves and surfaces with multiple shape parameters are constructed by an interal approach. With the elevation of the basis function degree, feasible range of shape parameter value is extended. The feasible range of shape parameter value is topically discussed from the thirth degree to the ninth degree. They include the uniform CB-spline curves and surfaces and combine the main properties of uniform CB-spline curves and surfaces. The shape of the curves and surfaces can be adjusted entirely or locally by changing the values of the shape parameters. Their shape-control capability is shown to be much better than uniform CB-spline. They are useful in some applications of CAD/CAM.