Kuen Surface应该又是一个以数学家名字命名的曲面.
本文将展示几种Kuen Surface的生成算法和切图,其中有的是标准的,有的只是相似.使用自己定义语法的脚本代码生成数学图形.相关软件参见:数学图形可视化工具,该软件免费开源.QQ交流群: 367752815
公式1
#http://jalape.no/math/kuentxt vertices = D1:100 D2:100 u = from (-4.5) to (4.5) D1 v = from (PI*0.01) to (PI*0.99) D2 x=2*(cos(u)+u*sin(u))*sin(v)/(1+u*u*sin(v)*sin(v)) z=2*(sin(u)-u*cos(u))*sin(v)/(1+u*u*sin(v)*sin(v)) y=log(tan(v/2))+2*cos(v)/(1+u*u*sin(v)*sin(v))
公式2
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#http://www.mathcurve.com/surfaces/kuen/kuen.shtml vertices = D1:100 D2:100 u = from (-4.5) to (4.5) D1 v = from (PI*0.01) to (PI*0.99) D2 x=2*(cos(u)+u*sin(u))*sin(v)/(1+u*u*sin(v)) z=2*(sin(u)-u*cos(u))*sin(v)/(1+u*u*sin(v)) y=ln(tan(v/2))+2*cos(v)/(1+u*u*sin(v))
公式3
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#http://www.mathcurve.com/surfaces/kuen/kuen.shtml vertices = D1:100 D2:100 u = from (-4.5) to (4.5) D1 v = from (-PI*1.5) to (PI*1.5) D2 t = u*u+ch(v)*ch(v) x=2*(cos(u)+u*sin(u))*ch(v)/t z=2*(sin(u)-u*cos(u))*ch(v)/t y=v - sh(2*v)/t
公式4
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#http://mathworld.wolfram.com/KuenSurface.html vertices = D1:100 D2:100 u = from (-PI*1.6) to (PI*1.6) D1 v = from (PI*0.01) to (PI*0.99) D2 a = sin(u) b = cos(u) c = sin(v) d = cos(v) t = 1 + u*u*c*c x = 2*(b + u*a)*c/t z = 2*(a + u*b)*c/t y = ln[tan(v/2)] + 2*d/t y = limit(y, -50, 50)
数学图形之Kuen Surface,布布扣,bubuko.com
原文：http://www.cnblogs.com/WhyEngine/p/3899623.html