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TORUS CUT
Backgraund figure by Horibe Kazunori

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a = 3;
b = 6;
c = Sqrt[b^2 - a^2];

fx[s_, t_] := (a*Cos[t] + b)Cos[s];
fy[s_, t_] := (a*Cos[t] + b)Sin[s];
fz[s_, t_] := a Sin[t];

fxx[s_, t_] := (c*fx[s, t] + a*fz[s, t])/b;
fyy[s_, t_] := fy[s, t];
fzz[s_, t_] := (-a*fx[s, t] + c*fz[s, t])/b;

Do[
ParametricPlot3D[{fxx[s, t], fyy[s, t], fzz[s, t]},
{t, 0, 2Pi},{s, -Pi, Pi },
PlotRange -> {{-(a + b + 1), a + b + 1}, {-(a + b + 1), a + b + 1}, {-(a + b + 1) + i, i}},
Axes -> False, PlotPoints -> {51, 71},
ViewPoint -> {0.934, -1.725, 2.757},
DisplayFunction -> $DisplayFunction],
{i, b, -b, -1}]

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