On polynomial approximation of circular arcs and helices
On polynomial approximation of circular arcs and helices
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DOI：
10.1016/j.camwa.2011.12.036
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发表时间：
2012-04
期刊：
影响因子：
--
通讯作者：
Lizheng Lu
中科院分区：
文献类型：
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作者：
Lizheng Lu
提出了一种用两点泰勒展开式表示三角函数的圆弧和螺旋线多项式逼近的简单方法。我们用一种有效的方法得到了逼近问题的（2n+1）次多项式，这种方法可以很方便地通过增加新的项来增加多项式的次数.近似误差的上限是可用的，因此我们可以获得最低阶多项式曲线，该曲线可以在任何用户指定的误差容限内近似圆弧或螺旋段。
We present a simple method for polynomial approximation of circular arcs and helices by expressing the trigonometric functions using the two-point Taylor expansion. We obtain the degree-(2n+1) polynomial for the approximation problem in an efficient way, which is very convenient to increase the degree of polynomial by adding new terms. An upper bound on the approximation error is available, so that we can obtain the lowest degree polynomial curve that can approximate a circular arc or helix segment within any user-prescribed error tolerance.