圆弧-线段一阶混合曲线及其插补算法

一阶混合曲线具有多种几何元素的特征,其中也包含线段和圆弧。首先推导了由两个几何元素组合的一阶混合曲线参数表达式,同时证明了线段和圆弧混合可以形成摆线、两个圆弧混合可以形成椭圆,并对线段和圆弧、圆弧和圆弧混合曲线表达式进行了归一化处理。然后提出了面向一阶混合曲线加工的插补合成法,对在线插补合成法和离线插补合成法的运算流程分别进行了说明,其中离线插补合成法的数据格式采用了字节流形式。最后用曲线插补实例验证了插补合成法的可靠性,结果证明运用插补合成法对一阶混合曲线进行插补运算具有过程清晰和运算简洁等特点。

Arc-line First-order Blending Curve and Its Interpolation Algorithm

The first-order blending curve has the characteristics of many geometric elements,including line and arcs.Firstly,the parameter expression of the first-order blending curve composed of two geometric elements is derived,and it is proved that the line and arc blending can form a cycloid,the two arc blending can form an ellipse,and the line-arc and the arc-arc blending curve expressions are normalized.Then an interpolation synthesis method for first-order mixed curve processing is proposed,and the operation flow of the online interpolation synthesis method and the offline interpolation synthesis method are explained respectively,and the data format of the offline interpolation synthesis method uses a byte-flow-string form.Finally,the reliability of the interpolation synthesis method is verified by the example of curve interpolation.The results prove that the interpolation operation of the first-order mixed curve with the interpolation synthesis method has the characteristics of clear process and simple operation.