基于DP曲线构建PH样条
Construction of PH Splines Based on DP Curves
DOI: 10.12677/AAM.2019.812228, PDF,    国家自然科学基金支持
作者: 段娇娇, 程晓旭, 张 娜, 李尚蔚, 彭兴璇：辽宁师范大学数学学院，辽宁 大连
关键词: PH曲线；DP曲线；DP-PH曲线；几何特征；PH Curve； DP Curve； DP-PH Curve； Geometrical Feature
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。
Abstract: 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.
文章引用：段娇娇, 程晓旭, 张娜, 李尚蔚, 彭兴璇. 基于DP曲线构建PH样条[J]. 应用数学进展, 2019, 8(12): 1986-1992. https://doi.org/10.12677/AAM.2019.812228

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