两种带形状参数的三角曲线

Two kinds of trigonometric curves with shape parameters

定义了带形状参数的三次三角多项式曲线和三次三角样条曲线。前者具有与二次Bézier曲线类似的端点性质,但逼近性比二次Bézier曲线更好,且在拼接时能达到更高阶的连续性。而后者与二次B样条曲线类似,其每一段由相继的三个控制顶点生成。对于等距节点,在一般情况下曲线C2连续,在特殊条件下可达C3连续。

Two kinds of trigonometric curves with shape parameters are defined, they are trigonometric polynomial curves and cubic trigonometric spline curves. The former retains the main properties of the quadratic B6zier curve, and it is closer to the control polygon and can achieve higher order of continuity than the quadratic B6zier curve. The latter is similar to the quadratic B-spline curve, each piece of it is generated by three consecutive control points. For equidistant knots, the curves are C2 continuous, and they are C3 continuous under special conditions.