Cool toroidal segment figure for the book.  toroidFig1.eps

<<peeters` ;
peeters`setGitDir[ "../project/figures/GAelectrodynamics" ]

<< GA30`;

j = Bivector[1,3,2] ;
i = Bivector[1,1,3];
e1 = Vector[1,1] ;
e2 = Vector[1,2];
e3 = Vector[1,3];

cis[t_, i_] := Cos[t] + i Sin[t];
(cis[-t/2, j]**(rho e1 ** cis[phi, i] + r e3)**cis[t/2, j]
)

{u1,u2,u3} = UnitVector[3,#]&/@Range[3];
toroid[t_,phi_,r_,rho_]:=rho Cos[phi] u1 + (r+rho Sin[phi]) Sin[t]u2+Cos[t] (r+rho Sin[phi]) u3;


Module[{o,r, rho, tt, pp, pt},
r = 2.5;
rho = 1;
o={0,0,0};
tt = Pi/5;
pp = 1.2 Pi/4;
pt[x_, l_] := (l) (u3 Cos[x] + u2 Sin[x]);
Show[
ParametricPlot3D[toroid[u,v,r, rho],{u,0,2 Pi/6},{v,0,2 Pi}, Ticks -> None,
PlotStyle->Directive[Opacity[0.5]], PlotRange -> {{-3,1.5},{0,3},{0,4}},Boxed->False,Axes->False],
ParametricPlot3D[toroid[0,v,r, rho],{v,0,2 Pi},PlotStyle->{Red// Darker}],
ParametricPlot3D[toroid[tt,v,r, rho],{v,0,2 Pi},PlotStyle->{Red// Darker}],
Graphics3D[{
Black,
Thick,
Arrow[Tube[{o,u1}]],
Arrow[Tube[{o,u2}]],
Arrow[Tube[{o,u3}]],
Text[Subscript["e"// bold, 1], 1.1 u1],
Text[Subscript["e"// bold, 2],1.1 u2],
Text[Subscript["e"// bold, 3],1.1 u3],
Green// Darker,
Thick,
Purple,
Line[{o,(r) u3}],
Line[{o,pt[tt, r-rho]}],
Arrow[Tube[{r u3,(r) u3 +  rho(u1 Cos[pp] + u3 Sin[pp])}]],
Black,
Text["θ", pt[tt/2, (r - rho)/3]],
Line[{r u3,(r) u3 + u1 rho}],
Text["ϕ",(r) u3 +  (rho/3)(u1 Cos[pp/2] + u3 Sin[pp/2])]
} ]
]
]

p1 = ;

peeters`exportForLatex["toroidFig1", p1]