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数学图形之Kuen Surface

2024-07-16 12:22:54   219人阅读

 

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/kuentxtvertices = D1:100 D2:100u = from  (-4.5) to (4.5) D1v = from (PI*0.01) to (PI*0.99) D2x=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

.

#http://www.mathcurve.com/surfaces/kuen/kuen.shtmlvertices = D1:100 D2:100u = from  (-4.5) to (4.5) D1v = from (PI*0.01) to (PI*0.99) D2x=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

. 

#http://www.mathcurve.com/surfaces/kuen/kuen.shtmlvertices = D1:100 D2:100u = from  (-4.5) to (4.5) D1v = from (-PI*1.5) to (PI*1.5) D2t = u*u+ch(v)*ch(v)x=2*(cos(u)+u*sin(u))*ch(v)/tz=2*(sin(u)-u*cos(u))*ch(v)/ty=v - sh(2*v)/t

公式4

x=(2(cosu+usinu)sinv)/(1+u^2sin^2v)
(1)
=(2sqrt(1+u^2)cos(u-tan^(-1)u)sinv)/(1+u^2sin^2v)
(2)
y=(2(sinu-ucosu)sinv)/(1+u^2sin^2v)
(3)
=(2sqrt(1+u^2)sin(u-tan^(-1)u)sinv)/(1+u^2sin^2v)
(4)
z=ln[tan(1/2v)]+(2cosv)/(1+u^2sin^2v)
#http://mathworld.wolfram.com/KuenSurface.htmlvertices = D1:100 D2:100u = from  (-PI*1.6) to (PI*1.6) D1v = from (PI*0.01) to (PI*0.99) D2a = sin(u)b = cos(u)c = sin(v)d = cos(v)t = 1 + u*u*c*cx = 2*(b + u*a)*c/tz = 2*(a + u*b)*c/ty = ln[tan(v/2)] + 2*d/ty = limit(y, -50, 50)

 


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