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 = t = from to (*PI) a = x = a*(*cos(t) - cos(*t)) y = a*(*sin(t) - sin(*t))
变异的Nephroid曲线:
#http://xahlee.info/SpecialPlaneCurves_dir/Nephroid_dir/nephroid.html vertices =
t = from () to (*PI) x = *cos[t]-cos[*t]
y = *sin[t]-sin[*t]
将Nephroid曲线绕x轴旋转:
vertices = D1: D2: u = from to (PI) D1
v = from to (*PI) D2 a = x = a*(*cos(u) - cos(*u)) n = a*(*sin(u) - sin(*u)) y = n*cos(v)
z = n*sin(v)
将Nephroid曲线绕Y轴旋转:
vertices = D1: D2: u = from (-PI/) to (PI/) D1
v = from to (*PI) D2 a = n = a*(*cos(u) - cos(*u)) y = a*(*sin(u) - sin(*u)) x = n*cos(v)
z = n*sin(v)