text/appendixes/comparing_defs.tex
changeset 966 d9e4d7e1cbf6
parent 965 987af9e53631
child 967 6e4f0ed47e0e
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965:987af9e53631 966:d9e4d7e1cbf6
  1031 \label{fig:horizontal-composition}
  1031 \label{fig:horizontal-composition}
  1032 \end{figure}
  1032 \end{figure}
  1033 \begin{figure}[t]
  1033 \begin{figure}[t]
  1034 \begin{align*}
  1034 \begin{align*}
  1035 \mathfig{0.4}{triangle/triangle4f} \\
  1035 \mathfig{0.4}{triangle/triangle4f} \\
  1036 \mathfig{0.4}{triangle/triangle4f_i}
  1036 \begin{tikzpicture}
       
  1037 \node[circle,fill=black,inner sep=1pt] (A) at (1.73,0) {};
       
  1038 \node[circle,fill=black,inner sep=1pt] (B) at (-1.73,0) {};
       
  1039 \draw[dashed] (A) -- (B);
       
  1040 \node[circle,fill=black,inner sep=1pt] (C) at (0,0) {};
       
  1041 \node[circle,fill=black,inner sep=1pt] (D) at (0.8,0) {};
       
  1042 \begin{scope}[yshift=-1cm]
       
  1043 \path[clip] (0,0) circle (2);
       
  1044 \begin{scope}[yshift=2cm]
       
  1045 \draw (0,0) circle (2);
       
  1046 \node[circle,fill=black,inner sep=1pt] (L2) at (-90:2) {};
       
  1047 \node[circle,fill=black,inner sep=1pt] (L1) at (-120:2) {};
       
  1048 \end{scope}
       
  1049 \end{scope}
       
  1050 \begin{scope}[yshift=1cm]
       
  1051 \path[clip] (0,0) circle (2);
       
  1052 \begin{scope}[yshift=-2cm]
       
  1053 \draw (0,0) circle (2);
       
  1054 \node[circle,fill=black,inner sep=1pt] (U) at (90:2) {};
       
  1055 \end{scope}
       
  1056 \end{scope}
       
  1057 \begin{scope}
       
  1058 \path[clip] (0,1) circle (2);
       
  1059 \path[clip] (0,-1) circle (2);
       
  1060 \foreach \n in {1,...,6} {
       
  1061 	\path (B) to[out=0,in=-180] node[coordinate,pos=\n/6] (BC\n) {} (C);
       
  1062 	\draw[green!50!brown] (BC\n) -- +(0,1);
       
  1063 	\draw[green!50!brown] (BC\n) -- +(-1.5,-1);
       
  1064 }
       
  1065 \foreach \n in {0,...,5} {
       
  1066 	\path (C) to[out=0,in=-180] node[coordinate,pos=\n/5] (CD\n) {} (D);
       
  1067 	\path (L1) to[out=-30,in=-180] node[coordinate,pos=\n/5] (L1L2\n) {} (L2);
       
  1068 	\draw[blue] (CD\n) -- (L1L2\n);
       
  1069 }
       
  1070 \foreach \n in {0,...,5} {
       
  1071 	\path (L1) to[out=40,in=-140] node[coordinate,pos=\n/5] (L1C\n) {} (C);
       
  1072 	\path (L2) to[out=50,in=-130] node[coordinate,pos=\n/5] (L2D\n) {} (D);
       
  1073 	\draw[blue] (L1C\n) -- (L2D\n);
       
  1074 }
       
  1075 \foreach \n in {1,3,...,9} {
       
  1076 	\path(C) to[out=30,in=150] node[coordinate,pos=\n/10] (CA\n) {} (A);
       
  1077 	\path(D) to[out=0,in=180] node[coordinate,pos=\n/10] (DA\n) {} (A);
       
  1078 	\path(L2) to[out=0,in=-120] node[coordinate,pos=\n/10] (L2A\n) {} (A);
       
  1079 	\draw[brown] (CA\n) -- +(0,1);
       
  1080 	\draw[brown] (CA\n) to[out=0] (DA\n) -- (L2A\n);
       
  1081 }
       
  1082 \draw[dashed] (U) -- (C) -- (L1) (L2) -- (D);
       
  1083 \end{scope}
       
  1084 \end{tikzpicture}
  1037 \end{align*}
  1085 \end{align*}
  1038 \caption{Vertical composition in the triangle axiom.}
  1086 \caption{Vertical composition in the triangle axiom.}
  1039 \label{fig:vertical-composition}
  1087 \label{fig:vertical-composition}
  1040 \end{figure}
  1088 \end{figure}
  1041 \begin{figure}[t]
  1089 \begin{figure}[t]