卵形线

卵形线及其在直角坐标系中示意图

卵形线,是类似于椭圆,但是一头大,一头小,有一条对称轴且光滑封闭的平面曲线。卵形线的对称轴与大、小头的两个交点称为卵形线的大端点和小端点,记为Q、P。卵形线上到其对称轴距离最大的两点称为卵形线的对称端点,记为S、T。线段QP、ST分别称为卵形线的直径和对称直径.卵形线的直径与对称直径的交点称为卵形线的卵心,记为O,线段OP、OQ、OS(或OT)分别称为卵形线的长半径、短半径、对称半径,其长度分别记为a、b、c。长半径、短半径、对称半径称为卵形线的三个特征参数。

已知卵形线的长、短、对称半径a、b、c这三个特征参数,在平面直角坐标系中,以卵形线的对称轴作为x轴,x轴正向与卵形线小头方向一致,卵形线的卵心作为坐标系原点。以正数a、b、c(a > b)为长、短、对称半径的卵形线,在直角坐标系中示意图如图所示。

三次卵形线方程:

[1]

參考文獻

  1. ^ 李湘江. 卵圆方程研究. 图学学报. 2016, 37 (4): 467-470. 

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