带形状参数的二次三角Bézier曲线

Quadratic Trigonometric Polynomial Bézier Curves with a Shape Parameter

给出了二次三角多项式Bézier曲线,基函数由一组带形状参数的二次三角多项式组成。由四个控制顶点生成的曲线具有与三次Bézier曲线类似的性质,但具有比三次Bézier曲线更好的逼近性。形状参数有明确几何意义:参数越大,曲线越逼近控制多边形。曲线可精确表示椭圆弧,还给出了两段三角多项式曲线的G2和C3连续的拼接条件。

Quadratic trigonometric polynomial Bézier curves with a shape parameter are presented in this paper. The trigonometric polynomial curves retain the main superiority of cubic Bézier curves. With the shape parameter, the trigonometric polynomial curves can be close to the cubic Bécurves or close to the given control polygon then the cubic Bécurves. Shape parameter has the property of geometry, the larger is the parameter, and the more approach is the curves to the control polygon. The curves can represent ellipse and circle precisely. The G2 and C3 -continuity condition of two-piece of trigonometric polynomial Bézier curves are also discussed.