example25[a_, b_][u_,v_] :={ u, v, u^(-a) v^(-b)}

ParametricPlot3D[Evaluate[example25[1,1][u,v]],{u,1/500,5},{v,1/500,5}]

ParametricPlot3D[ Evaluate[example25[-1/2, -1/2 + 1/100][u, v]], {u, 1/500, 5}, {v, 1/500, 5}

example26[a_, b_][u_, v_] := {u, v, (u^2 + v^2)^b Exp[-a ArcTan[u/v]]}

ParametricPlot3D[Evaluate[example26[1,-1+1/10][u,v]],{u,-1,1},{v,1/10,3}]

example27[a_,b_][u_,v_]:={u,v,-u(a Log[u]+b Log[v])}

ParametricPlot3D[ Evaluate[example27[-1, -1/2 - 1/1000][u, v]], {u, 1/100, 2}, {v, 1/100, 5}]

example29[u_,v_] :={ Exp[2v], 2^(1/2) u Exp[2v], 2(u^2+v) Exp[2v]}

ParametricPlot3D[Evaluate[example29[u,v]],{u,-2,4},{v,-2,1}]

fujie[u_, v_] := {(1/2) u^(-1) Exp[- 2u -2 v], (1/2) u^(-1) Exp[ -2 u +2 v], (1/2)(2 - u^(-1))}

fujih[x_, y_] := {x^(-1) Exp[-x] Cos[y], x^(-1) Exp[-x] Sin[y], 1 - x^(-1)}

ParametricPlot3D[Evaluate[fujie[u, v]], {u, 0.01, 2}, {v, -1.00, 2}]

中心写像の像は平面上にあります：

ParametricPlot3D[Evaluate[fujih[x, y]], {x, 0.05, Pi}, {y, -Pi, Pi}]

ParametricPlot[fujihpro[t] // Evaluate, {t, 0.05, Pi}, AspectRatio -> 1] 1]

中心写像の像は平面上にあります：

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