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.html

vertices = 2000

t = from 0 to (2*PI)

a = 2

x = 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.html

vertices = 200
t = 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 D2:100

u = from 0 to (PI) D1
v = from 0 to (2*PI) D2

a = 2

x = 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 D2:100

u = from (-PI/2) to (PI/2) D1
v = from 0 to (2*PI) D2

a = 2

n = a*(3*cos(u) - cos(3*u))

y = a*(3*sin(u) - sin(3*u))

x = n*cos(v)
z = n*sin(v)