Mathematical graphics-kuen Surface

 

Kuen surface should be a surface named after a mathematician.
This article will show several Kuen Surface generation algorithms and cut graphs, some of which are standard and some are similar. use the script code of the custom syntax to generate a mathematical image. for related software, see: Mathematical graphics visualization tool. This software is free and open-source. QQ chat group: 367752815

Formula 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)) 

Formula 2

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#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)) 

Formula 3

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#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

Formula 4

			(1)
			(2)
			(3)
			(4)

#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)