基于三点形状可调的二次三角Bzier曲线

Quadratic Trigonometric Bézier Curves Based on Three-Points Shape Parameters

给出了二次三角多项式形式的Bzier曲线,基函数由一组带形状参数的二次三角多项式组成。由三个控制顶点生成的曲线具有与二次Bzier曲线类似的性质,但具有比二次Bzier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 Bezier curves with a shape parameter are presented in this paper. The trigonometric polynomial curves retain the main superiority of the quadratic Bezier curves. With the shape parameters, the trigonometric polynomial curves can approach more to the quadratic Bezier curves or to the given control polygon than the quadratic Bezier curves. Shape parameters have the property of geometry, the larger is the parameter, the more the curves approach to the control polygon. The curves represent ellipse and circle precisely. The G^2 and C^3-continuity condition of two-piece trigonometric polynomial Bezier curves are also discussed.