# HG changeset patch # User Scott Morrison # Date 1323812054 28800 # Node ID 27c075c688169ad5d7b6392d85c764bd0904c5d3 # Parent bbf14d934cb1ddfa9a7d8a991584065df6853f50 final tweaks to figures in C2 diff -r bbf14d934cb1 -r 27c075c68816 text/appendixes/comparing_defs.tex --- a/text/appendixes/comparing_defs.tex Tue Dec 13 09:13:41 2011 -0800 +++ b/text/appendixes/comparing_defs.tex Tue Dec 13 13:34:14 2011 -0800 @@ -247,7 +247,7 @@ } \end{scope} \draw[->,blue] (1.5,-1) node[below] {$a \times I$} -- (0.75,0); -\end{tikzpicture} \\ +\end{tikzpicture} & \begin{tikzpicture}[baseline] \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; \draw[dashed] (c.north) -- (c.south); @@ -284,11 +284,12 @@ \draw[dashed] (c.north) -- (d.north) (d.south) -- (c.south); \node[right=18] at (c) {$g$}; \node[left=18] at (c) {$f$}; +\draw[->,blue] (.75,-1.25) node[below] {$a \times I$} -- (0,-0.25); \clip (0,0) circle (0.5cm); \foreach \y in {1,0.86,...,-1} { \draw[green!50!brown] (-1,\y)--(1,\y); } -\end{tikzpicture} \\ +\end{tikzpicture} & \begin{tikzpicture}[baseline] \begin{scope} \clip (-1.3,-2) rectangle (0,2); @@ -320,6 +321,7 @@ \draw (m.center) .. controls +(1,0) and +(1,0) .. (c.south); \node[right=15,below=8] at (c) {$g$}; \node[left=12] at (c) {$f$}; +\draw[->,blue] (.65,-1.25) node[below] {$a \times I$} -- (0,-0.25); \end{tikzpicture} \end{align*} \caption{Examples of inserting or deleting product regions.} @@ -788,7 +790,7 @@ .. controls +(1,.4) and +(-1,1) .. (g2) .. controls +(-1,.4) and +(1,.4) .. (g1) .. controls +(-1,-.4) and +(1,-1) .. (f1); -\foreach \x in {0,0.1, ..., 6} { +\foreach \x in {0,0.2, ..., 6} { \draw[green!50!brown] (\x,-2) -- + (0,4); } \end{tikzpicture} @@ -814,7 +816,7 @@ .. controls +(1,.4) and +(-1,1) .. (g2) .. controls +(-1,.4) and +(1,.4) .. (g1) .. controls +(-1,-.4) and +(1,-1) .. (f1); -\foreach \x in {0,0.1, ..., 6} { +\foreach \x in {0,0.2, ..., 6} { \draw[green!50!brown] (\x,-2) -- + (0,4); } \end{scope} @@ -822,7 +824,7 @@ \path[clip] (f1) .. controls +(1,1.5) and +(-1,2).. (g2) .. controls +(-1,1) and +(1,.4) .. (f2) .. controls +(-1,.8) and + (1,.8) .. (f1); -\foreach \x in {0,0.1, ..., 6} { +\foreach \x in {0,0.2, ..., 6} { \draw[green!50!brown] (\x,-2) -- + (0,4); } \end{scope} @@ -847,7 +849,7 @@ \path[clip] (f1) .. controls +(1,1.5) and +(-1,1.5).. (g2) .. controls +(-1,.8) and +(1,.8) .. (f2) .. controls +(-1,.8) and + (1,.8) .. (f1); -\foreach \x in {0,0.1, ..., 6} { +\foreach \x in {0,0.2, ..., 6} { \draw[green!50!brown] (\x,-2) -- + (0,4); } \end{scope} @@ -935,6 +937,35 @@ %\mathfig{0.4}{triangle/triangle4c} %\end{align*} \begin{align*} +u & = +\begin{tikzpicture}[baseline] +\coordinate (P) at (0,0); +\coordinate (Q) at (3,0); +\coordinate (R) at (1.5,-0.5); +\draw (P) \vertex to[out=40,in=140] node[above] {$a$} (Q) \vertex -- node[below] {\scriptsize $y \times I$} (R) \vertex to[out=-180,in=-40] node[below] {$a$} (P); +\clip (P) to[out=40,in=140] (Q) -- (R) to[out=-180,in=-40] (P); +\foreach \x in {1,...,9} { + \path (P) to[out=40,in=140] node[pos=\x/10] (PQ\x) {} (Q); + \path (P) to[out=-40,in=-180] node[pos=\x/10] (PR\x) {} (R); + \draw[green!50!brown] (PQ\x.center) -- (PR\x.center); +} +\end{tikzpicture} & +v & = +\begin{tikzpicture}[baseline] +\coordinate (P) at (0,0); +\coordinate (Q) at (3,0); +\coordinate (R) at (1.5,-0.5); +\draw (P) \vertex to[out=40,in=140] node[above] {$b$} (Q) \vertex to[out=-140,in=0] node[below] {$b$} (R) -- node[below] {\scriptsize $y \times I$} (P); +\clip (P) to[out=40,in=140] (Q) to[out=-140,in=0] (R) -- (P); +\foreach \x in {1,...,9} { + \path (P) to[out=40,in=140] node[pos=\x/10] (PQ\x) {} (Q); + \path (R) to[out=0,in=-140] node[pos=\x/10] (RQ\x) {} (Q); + \draw[brown] (PQ\x.center) -- (RQ\x.center); +} +\end{tikzpicture} +\end{align*} +\vspace{-2cm} +\begin{align*} \alpha & = \begin{tikzpicture}[baseline] \node[circle,fill=black,inner sep=1pt] at (1.73,0) {}; @@ -973,7 +1004,7 @@ \draw[blue!50!brown] (\t,-1) -- +(1.19,2); } \foreach \t in {0.1,0.3,...,2.5} { - \draw[red!50!brown] (\t,-1) -- +(1.19,2); + \draw[brown] (\t,-1) -- +(1.19,2); } \foreach \x in {0,1,...,10} { \path (L1) to[out=60,in=-120] node[pos=\x/10] (p1\x) {}(U1); @@ -984,34 +1015,9 @@ \draw[->, thick, blue!75!yellow] (-2,0.5) node[black, left] {$a\times I$} -- (-1,0.5); \draw[->, thick, blue!75!yellow] (-0.1,-1.5) node[black, below] {$y\times I \times I$} -- (-0.25,-0.5); \draw[->, thick, blue!75!yellow] (2,-0.5) node[black, right] {$b\times I$} -- (1,-0.5); -\end{tikzpicture} \\ -u & = -\begin{tikzpicture}[baseline] -\coordinate (P) at (0,0); -\coordinate (Q) at (3,0); -\coordinate (R) at (1.5,-0.5); -\draw (P) \vertex to[out=40,in=140] node[above] {$a$} (Q) \vertex -- node[below] {\scriptsize $y \times I$} (R) \vertex to[out=-180,in=-40] node[below] {$a$} (P); -\clip (P) to[out=40,in=140] (Q) -- (R) to[out=-180,in=-40] (P); -\foreach \x in {1,...,9} { - \path (P) to[out=40,in=140] node[pos=\x/10] (PQ\x) {} (Q); - \path (P) to[out=-40,in=-180] node[pos=\x/10] (PR\x) {} (R); - \draw[green!50!brown] (PQ\x.center) -- (PR\x.center); -} -\end{tikzpicture} \\ -v & = -\begin{tikzpicture}[baseline] -\coordinate (P) at (0,0); -\coordinate (Q) at (3,0); -\coordinate (R) at (1.5,-0.5); -\draw (P) \vertex to[out=40,in=140] node[above] {$b$} (Q) \vertex to[out=-140,in=0] node[below] {$b$} (R) -- node[below] {\scriptsize $y \times I$} (P); -\clip (P) to[out=40,in=140] (Q) to[out=-140,in=0] (R) -- (P); -\foreach \x in {1,...,9} { - \path (P) to[out=40,in=140] node[pos=\x/10] (PQ\x) {} (Q); - \path (R) to[out=0,in=-140] node[pos=\x/10] (RQ\x) {} (Q); - \draw[brown] (PQ\x.center) -- (RQ\x.center); -} -\end{tikzpicture} \\ +\end{tikzpicture} \end{align*} +\vspace{-1cm} \caption{Ingredients for the triangle axiom.} \label{fig:ingredients-triangle-axiom} \end{figure} @@ -1056,7 +1062,7 @@ \path (T) to[out=0,in=140] node[coordinate,pos=\n/8] (TR\n) {} (R); \draw[brown] (MR\n) -- (TR\n); } -\end{tikzpicture} \\ +\end{tikzpicture} & (a \times I) *_h v & = \begin{tikzpicture}[baseline] \coordinate (L) at (0,0); @@ -1090,6 +1096,7 @@ \label{fig:horizontal-composition} \end{figure} \begin{figure}[t] +\vspace{-1.5cm} \begin{align*} %\mathfig{0.4}{triangle/triangle4f} \\ \begin{tikzpicture} @@ -1124,12 +1131,12 @@ \foreach \n in {0,...,5} { \path (C) to[out=0,in=-180] node[coordinate,pos=\n/5] (CD\n) {} (D); \path (L1) to[out=-30,in=-180] node[coordinate,pos=\n/5] (L1L2\n) {} (L2); - \draw[blue] (CD\n) -- (L1L2\n); + \draw[blue!50!brown] (CD\n) -- (L1L2\n); } \foreach \n in {0,...,5} { \path (L1) to[out=40,in=-140] node[coordinate,pos=\n/5] (L1C\n) {} (C); \path (L2) to[out=50,in=-130] node[coordinate,pos=\n/5] (L2D\n) {} (D); - \draw[blue] (L1C\n) -- (L2D\n); + \draw[blue!50!brown] (L1C\n) -- (L2D\n); } \foreach \n in {1,3,...,9} { \path(C) to[out=30,in=150] node[coordinate,pos=\n/10] (CA\n) {} (A); @@ -1142,6 +1149,7 @@ \end{scope} \end{tikzpicture} \end{align*} +\vspace{-2.5cm} \caption{Vertical composition in the triangle axiom.} \label{fig:vertical-composition} \end{figure} @@ -1189,8 +1197,8 @@ \path (B') to[out=-30,in=180] node[coordinate,pos=\n/6] (B'X\n) {} (X); \path (M') to[out=-90,in=90] node[coordinate,pos=\n/6] (M'X\n) {} (X); \path (B') to[out=30,in=-150] node[coordinate,pos=\n/6] (B'M'\n) {} (M'); - \draw[blue] (B'X\n) -- (M'X\n); - \draw[blue] (B'M'\n) -- (B'X\n); + \draw[blue!50!brown] (B'X\n) -- (M'X\n); + \draw[blue!50!brown] (B'M'\n) -- (B'X\n); } \end{tikzpicture} \xrightarrow{\text{collar}} @@ -1234,8 +1242,8 @@ \path (B') to[out=-30,in=180] node[coordinate,pos=\n/6] (B'X\n) {} (X); \path (M') to[out=-90,in=90] node[coordinate,pos=\n/6] (M'X\n) {} (X); \path (B') to[out=30,in=-150] node[coordinate,pos=\n/6] (B'M'\n) {} (M'); - \draw[blue] (B'X\n) -- (M'X\n); - \draw[blue] (B'M'\n) -- (B'X\n); + \draw[blue!50!brown] (B'X\n) -- (M'X\n); + \draw[blue!50!brown] (B'M'\n) -- (B'X\n); } \end{tikzpicture} \end{align*}