基于离线插补的参数跟踪法的应用研究

提出面向曲线插补的参数跟踪法,以曲线的参数方程为基础,对其进行归一化处理,并推导出曲线参数方程的导数方程。以导数值预测参数跨步步长,实现参数的递增,完成曲线的插补。以圆弧、阿基米德螺旋线和摆线为例说明参数跟踪法的求解过程。推导圆弧、阿氏螺旋线和摆线的导数方程,并给出具体的插补案例。结合坐标系旋转的公式,以阿氏螺旋线为例说明任意角度旋转的标准曲线的插补方法,证明了参数跟踪法也适用于非标准曲线方程。详细说明参数跟踪法使用过程中的关键技术,即归一化处理增强插补方法的规范性;阐述参数导数方程出现的零点现象并通过设置跨零步长来处理;阐述参数步长异常情况和解决方法。

Application Research of Parameter Tracking Method Based on Off-line Interpolation

A parameter tracking method for curve interpolation was proposed. Based on the parameter equation of the curve, it was normalized and the derivative equation of the curve parameter equation was derived. Derivative values were used to predict the step size of the parameter to accomplish the increase of parameter, and the interpolation of the curve was completed. The arc, Archimedes spiral and cycloid were used as examples to illustrate the solution process of the parameter tracking method. Derivative equations of arc, Archimedes spiral and cycloid were derived, and specific interpolation cases were given. Combined with the formula of coordinate system rotation, the interpolation method of standard curve with arbitrary angle rotation was explained by taking Archimedes spiral as an example, and the parameter tracking method also applicable to non standard curve equations was proved. The key techniques in the use of the parameter tracking method were explained in detail, that was, the normalization processing enhanced the normalization of the interpolation method. The zero point phenomenon of the parametric derivative equation was described and solved by setting the cross zero step sizes.