一种NURBS曲面形状修改的新方法

目的研究NURBS曲面形状修改问题。方法首先在各参数点处分别构造出一系列满足该点处几何约束的局部曲面,并由此构造总曲面。接着构造一张满足多余约束的插值多余曲面。最后利用Coons曲面的构造思想,得到最终的修改曲面。结果该方法使得修改后的曲面在多个参数点处满足用户给定的几何约束。结论运用该方法的思想,基于控制顶点变动的解决单参数点约束问题的方法都可以被推广并用来解决多参数点的约束问题。

Shape modification of NURBS surfaces

Aim To study a new approach for shape modification of NURBS surfaces.Methods Firstly,some new conceptions such as local surfaces,total surfaces,redundant constraints and redundant surfaces are introduced.Next,on every parametric point,a local surface satisfying geometric constraints is constructed.By means of these local surfaces,a total surface was constructed.Thirdly,a redundant surface satisfying the redundant constraints is interpolated. Finally,applying the idea of constructing Coons surfaces,the modified surface is gotten.Results The modified surface satisfies specified geometric constraints at a series of selected parametric points.Conclusion Applying the idea of the proposed method,control-point-based modification methods for modifying geometric constraints at a selected point can be extended to the case for modifying geometric constraints at a series of selected points.