带形状参数的三次三角Bézier曲线

Cubic trigonometric Bézier curves with shape parameters

引入一种带2个形状参数1λ,2λ的三次三角Béz ier曲线,简称为CT-Béz ier曲线。它不仅具有三次Béz ier曲线许多常见的性质,而且利用1λ,2λ的不同取值能局部或整体调控曲线的形状,使两段CT-Béz ier曲线的C1及C2连接具有一定的灵活性。利用CT-Béz ier曲线能精确表示椭圆与抛物线弧。

A cubic trigonometric Bézier curve,which is called the CT-B6zier curve, with two shape parameters λ1 and λ2 is presented in this paper. The curve possesses most of the properties of the cubic Bézier cuve. By taking the different values of ,λ1 and λ2, the shape of the curve can be adjusted locally or totally, and two pieces of CT-Bézier curves can be connected with C1 or C2 continuity flexibly. The elliptic and parabolic arcs can be represented exactly by the CT-Bézier curve.