带形状参数的五次三角Bézier曲线

Quintic Trigonometric Bézier Curve with Shape Parameter

构造了带一个形状参数的五次三角多项式基函数,由此定义了带形状参数的五次三角Bézier曲线,它具有Bézier曲线的几何特性、端点性、对称性等.通过改变形状参数α的取值,可对曲线的形状进行调控.当形状参数α越大,曲线越逼近控制多边形.该曲线还可表示为椭圆弧、抛物线弧等,给出了2段曲线达到C1、C2连续的条件及其在曲线设计中的应用实例.

In this paper, a set of quintic trigonometric polynomial function with shape parameter is constructed, and the quintic trigonometric Bezier curve with shape parameter is defined. The new curve holds many geometrical characteristics of Bezier curve, such as endpoint and symmetry. The shape of the curve can be adjusted through changing the value of the shape parameter. The larger the shape parameter is, the closer the curve approaches the control polygon. The curve can also be represented as elliptic arc and parabola arc, etc. Theand continuity conditions of two pieces of curves as well as their application in curve design are also discussed.