%% 
%%  The LaTeX Graphics Companion, 2ed (first printing May 2007)
%% 
%%  Example 7-5-6 on page 510.
%% 
%%  Copyright (C) 2007 Michel Goossens, Frank Mittelbach, Denis Roegel, Sebastian Rahtz, Herbert Vo\ss 
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 

\documentclass{ttctexa}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{348.0pt}
\StartShownPreambleCommands
\usepackage[all,arc,knot]{xy}
\StopShownPreambleCommands
\begin{document}
\[ \xy 0;/r.18pc/:
 (20,2)*{\bullet}="RU"+(1,3)*{x^{\ast}};
 (16,-3)*{\bullet}="RD"+(2.5,2)*{x^{\ast}};
 (-16,2)*{\bullet}="LU"+(-1,2)*{x};
 (-20,-3)*{\bullet}="LD"+(-1,2)*{x};
 "RU";"RD" **\crv{(4,2) & (4,-1)}; ?(.1)*\dir{<}; ?(.85)*\dir{<};
 "LD";"LU" **\crv{(-4,-2) & (-4,1)};
 ?(.08)*\dir{<}; ?(.85)*\dir{<};
 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 "x1"; "x2" **\crv{(7,-10) & (-7,-10)};
 (16,-20)*{\bullet}="RDD"+(2.5,-1)*{x^{\ast}};
 (-20,-20)*{\bullet}="LDD"+(-1,-3)*{x};
 (20,-12.5)*{\bullet}="RUD"+(3.5,1)*{x^{\ast}};
 (-16,-15)*{\bullet}="LUD";
 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 "RD"; "RDD" **\dir{-};
 "LD"; "LDD" **\dir{-};
 "A"; "LUD" **\dir{.};
 "RDD"; "LDD" **\crv{(0,-17)}; ?(.57)*\dir{>};
 "RU"; "RUD" **\dir{-};
 "LU"; "A" **\dir{-};
 "B"; "RUD" **\crv{(18,-14.15)};
 "B"; "LUD" **\crv{~*=<4pt>{.}(0,-18)}; ?(.4)*\dir{<};
\endxy
\qquad
\xy 0;/r.18pc/:
 (-10,-12)*{\bullet}="A"+(-3,1)*{x};
 (-20,-6)*{\bullet}="B"+(-3,1)*{x^{\ast}};
 (10,10)*{\bullet}="a"+(1,3)*{x^{\ast}};
 (20,6)*{\bullet}="b"+(3,1)*{x};
 (-10,-24)*{\bullet}="A1"+(-3,1)*{x};
 (-20,-20)*{\bullet}="B1"+(-3,1)*{x^{\ast}};
 (10,2)*{}="a1"; (10,-4)*{}="a11";
 (20,-6)*{\bullet}="b1"+(3,-1)*{x};
 "A";"B" **\crv{(0,0) & (-10,0)}; ?(.85)*\dir{<}; ?(.05)*\dir{<};
 "a";"b" **\crv{(0,0) & (10,0)};?(.85)*\dir{<}; ?(.05)*\dir{<};
 (-6,-3)*{}="X"; (6,3)*{}="x";
 (-10,-14.5)*{}="P";
 "X";"x" **\crv{(1,-16)};
 "A";"A1" **\dir{-};
 "B";"B1" **\dir{-};
 "b";"b1" **\dir{-};
 "a";"a1" **\dir{-};
 "a11";"a1" **\dir{.};
 "P";"a11" **\dir{.};
 "B1";"P" **\dir{-}; ?(.55)*\dir{>};
 "A1";"b1" **\dir{-}; ?(.45)*\dir{<};
\endxy
\]
\end{document}