FURUHATA Hitoshi
Department of Mathematics
Hokkaido University

アファイン曲面論の計算

トムゼン曲面を中心にして 


heltoenn[c_][u_,v_]:={
(1+c)^(-1)(u + c*(1-c^2)^(-1/2) Sin[(1-c^2)^(1/2)*u]*Cosh[(1-c^2)^(1/2)*v] ),
(1+c)^(-1)(c*v + (1-c^2)^(-1/2) Cos[(1-c^2)^(1/2)*u]*Sinh[(1-c^2)^(1/2)*v] ),
(1+c)^(-1)( Sin[(1-c^2)^(1/2)*u]*Sinh[(1-c^2)^(1/2)*v])}

ParametricPlot3D[Evaluate[heltoenn[*][u,v]],{u,-1,1}, {v,-1,1}, 
PlotPoints->{40,20}]]

(Enneper surface)
↑

c=-0.9
c=-0.8
c=-0.7
c=-0.6
c=-0.5
c=-0.4
c=-0.3
c=-0.2
c=-0.1
c= 0.0
(helicoid)
c=+0.1
c=+0.2
c=+0.3
c=+0.4
c=+0.5
c=+0.6
c=+0.7
c=+0.8
c=+0.9

↓
(plane)

[Top] [Back]