3种带形状参数的二次三角样条曲线

Three kinds of quadratic trigonometric spline curves with shape parameter

构造了3种带参数的三角样条基,基于这3组基定义了3种三角样条曲线。与二次B样条曲线类似,这3种曲线的每一段都由相继的3个控制顶点生成。这3种曲线具有许多与二次B样条曲线类似的性质,但它们的连续性都比二次B样条曲线更好。对于等距节点,在一般情况下,这3种曲线都整体C2连续,在特殊条件下它们都可达C3连续。另外,这3种曲线都具有比二次B样条曲线更好的对控制多边形的逼近性。

Three kinds of trigonometric spline bases are constructed in this paper. Based on these bases, three kinds of trigonometric spline curves are defined. As each piece of these trigonometric spline curves is generated by three consecutive control points, these curves retain many properties of the quadratic B-spline curve, but they have higher order of continuity than the quadratic B-spline curve. For equidistant knots, these curves are C2 continuous, and they are Ca continuous under special conditions. Besides, these curves are closer to the control polygon than the quadratic B-spline curve.