摘要
PH曲线是一类特殊的多项式参数曲线,其最显著的优点是弧长函数为多项式,其等距线可由兼容于CAD系统的有理多项式曲线表示。鉴于此,基于三次DP曲线,从平面PH曲线的定义出发,给出了三次DP曲线为PH曲线时其控制多边形满足的充分必要条件,得到了关于控制多边形的边长和夹角的几何特征条件,给出DP-PH曲线的定义。通过DP-PH控制多边形几何特征条件,给出可以先通过构造控制多边形进而构造出三次DP-PH曲线的几何构造方法。进一步分析了DP曲线和DP-PH曲线的误差。
The PH curve is a special kind of polynomial parameter curve. The most significant advantage is that the arc length function is a polynomial. And the equidistant line can be represented by a rational polynomial curve, which is compatible with the CAD system. Based on the DP curve, a necessary and sufficient condition for a cubic plane DP curve to be a PH curve is obtained. The geometrical characteristics of the edge length and the angle of the control polygon are obtained and the definition of the DP-PH curve is obtained. The geometric feature condition of polygon is controlled by DP-PH. We describe the construction of a control polygon for a cubic DP-PH curve from geometric construction method, based on the procedure for a DP curve. Then the errors between DP curve and DP-PH curve are analyzed.
出处
《应用数学进展》
2019年第12期1986-1992,共7页
Advances in Applied Mathematics
基金
国家自然科学基金(61702244,61502217)
辽宁省教育厅项目(901132)。
