与给定多边形相切的三次均匀B样条的扩展曲线

An Extension of the Cubic B-Spline Curve with Given Tangent Polygon

利用1个对称的调配函数,结合NURBS曲线中权的思想,在曲线控制顶点处引进调配参数,将三次均匀B样条曲线进行扩展,得到的新曲线比原来的曲线有更强的描述能力,并且包含了原曲线形式.讨论了扩展曲线的基表示及曲线的性质,调配参数可以用来控制曲线的局部形状,特别适用于自由曲线曲面的设计,在CAD/CAM中具有很好的应用前景.

By using the a symmetric blending function, combining with weight thought of the NURBS curve and introducting of blending parameters in the curve control points, the cubic uniform B-spline curve is extended, the new curve is a better description ability than the original curve, and contains the original curve. The basis representation and properties of the extension curve are stud- ied, the blending parameters can be used to control the local shape of the curve, especially suitable for the design of free curve and surface, it has good application prospects in CAD/CAM.