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数学图形(1.49)Nephroid曲线
昨天IPhone6在国内发售了，我就顺手发布个关于肾的图形。Nephroid中文意思是肾形的。但是这种曲线它看上去却不像个肾，当你看到它时，你觉得它像什么就是什么吧。
The name nephroid (meaning ‘kidney shaped‘) was used for the two-cusped epicycloid by Proctor in 1878. The nephroid is the epicycloid formed by a circle of radius a rolling externally on a fixed circle of radius 2a.The nephroid has length 24a and area 12π2.
其数学公式为：
x = a(3cos(t) - cos(3t))
y = a(3sin(t) - sin(3t))
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脚本代码：
#http://www-gap.dcs.st-and.ac.uk/~history/Curves/Nephroid.htmlvertices = 2000t = from 0 to (2*PI)a = 2x = a*(3*cos(t) - cos(3*t))y = a*(3*sin(t) - sin(3*t))
变异的Nephroid曲线：
#http://xahlee.info/SpecialPlaneCurves_dir/Nephroid_dir/nephroid.htmlvertices = 200t = from (0) to (50*PI)x = 3*cos[t]-cos[3*t]y = 3*sin[t]-sin[3*t]
将Nephroid曲线绕x轴旋转：
vertices = D1:100 D2:100u = from 0 to (PI) D1v = from 0 to (2*PI) D2a = 2x = a*(3*cos(u) - cos(3*u))n = a*(3*sin(u) - sin(3*u))y = n*cos(v)z = n*sin(v)
将Nephroid曲线绕Y轴旋转：
vertices = D1:100 D2:100u = from (-PI/2) to (PI/2) D1v = from 0 to (2*PI) D2a = 2n = a*(3*cos(u) - cos(3*u))y = a*(3*sin(u) - sin(3*u))x = n*cos(v)z = n*sin(v)
数学图形(1.49)Nephroid曲线
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