161 as shown in Figure \ref{fzo2}. |
161 as shown in Figure \ref{fzo2}. |
162 \begin{figure}[t] |
162 \begin{figure}[t] |
163 \begin{tikzpicture} |
163 \begin{tikzpicture} |
164 \newcommand{\rr}{6} |
164 \newcommand{\rr}{6} |
165 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}} |
165 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}} |
|
166 \newcommand{\namedvertex}[1]{node[circle,fill=black,inner sep=1pt] (#1) {}} |
166 |
167 |
167 \node(A) at (0,0) { |
168 \node(A) at (0,0) { |
168 \begin{tikzpicture} |
169 \begin{tikzpicture} |
169 \node[red,left] at (0,0) {$y$}; |
170 \node[red,left] at (0,0) {$y$}; |
170 \draw (0,0) \vertex arc (-120:-105:\rr) node[red,below] {$a$} arc(-105:-90:\rr) \vertex node[red,below](x2) {$x$}; |
171 \draw (0,0) \vertex arc (-120:-105:\rr) node[red,below] {$a$} arc(-105:-90:\rr) \vertex node[red,below](x2) {$x$}; |
182 \node(B) at (-4,-4) { |
183 \node(B) at (-4,-4) { |
183 \begin{tikzpicture} |
184 \begin{tikzpicture} |
184 \node[red,left] at (0,0) {$y$}; |
185 \node[red,left] at (0,0) {$y$}; |
185 \draw (0,0) \vertex |
186 \draw (0,0) \vertex |
186 arc (120:105:\rr) node[red,above] {$a$} |
187 arc (120:105:\rr) node[red,above] {$a$} |
187 arc (105:90:\rr) node[red,above] {$x$} \vertex |
188 arc (105:90:\rr) node[red,above] {$x$} \namedvertex{x1}; |
188 arc (90:75:\rr) node[red,above] {$x \times I$} |
189 % arc (90:75:\rr) node[red,above] {$x \times I$}; |
189 arc (75:60:\rr) \vertex node[red,right] {$x$} |
190 % arc (75:60:\rr) \vertex node[red,right] {$x$} |
190 arc (-60:-90:\rr) node[red,below] {$a$} |
191 % arc (-60:-90:\rr) node[red,below] {$a$} |
191 arc (-90:-120:\rr); |
192 % arc (-90:-120:\rr); |
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193 \draw (0,0) |
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194 arc (-120:-90:\rr) node[red,below] {$a$} |
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195 arc (-90:-61:\rr) \namedvertex{x2} node[red,right] {$x$}; |
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196 \draw (x1) -- node[red, above=3pt] {$x \times I$} (x2); |
192 \begin{scope} |
197 \begin{scope} |
193 \path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
198 \path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
194 \foreach \x in {0,0.48,...,9} { |
199 \foreach \x in {0,0.48,...,9} { |
195 \draw[green!50!brown] (\x/4,1) -- (\x,-1); |
200 \draw[green!50!brown] (\x/4,1) -- (\x,-1); |
196 } |
201 } |
201 \node(C) at (4,-4) { |
206 \node(C) at (4,-4) { |
202 \begin{tikzpicture}[y=-1cm] |
207 \begin{tikzpicture}[y=-1cm] |
203 \node[red,left] at (0,0) {$y$}; |
208 \node[red,left] at (0,0) {$y$}; |
204 \draw (0,0) \vertex |
209 \draw (0,0) \vertex |
205 arc (120:105:\rr) node[red,below] {$a$} |
210 arc (120:105:\rr) node[red,below] {$a$} |
206 arc (105:90:\rr) node[red,below] {$x$} \vertex |
211 arc (105:90:\rr) node[red,below] {$x$} \namedvertex{x1}; |
207 arc (90:75:\rr) node[red,below] {$x \times I$} |
212 % arc (90:75:\rr) node[red,below] {$x \times I$} |
208 arc (75:60:\rr) \vertex node[red,right] {$x$} |
213 % arc (75:60:\rr) \vertex node[red,right] {$x$} |
209 arc (-60:-90:\rr) node[red,above] {$a$} |
214 % arc (-60:-90:\rr) node[red,above] {$a$} |
210 arc (-90:-120:\rr); |
215 % arc (-90:-120:\rr); |
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216 \draw (0,0) |
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217 arc (-120:-90:\rr) node[red,above] {$a$} |
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218 arc (-90:-61:\rr) \namedvertex{x2} node[red,right] {$x$}; |
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219 \draw (x1) -- node[red, below=3pt] {$x \times I$} (x2); |
211 \begin{scope} |
220 \begin{scope} |
212 \path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
221 \path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
213 \foreach \x in {0,0.48,...,9} { |
222 \foreach \x in {0,0.48,...,9} { |
214 \draw[green!50!brown] (\x/4,1) -- (\x,-1); |
223 \draw[green!50!brown] (\x/4,1) -- (\x,-1); |
215 } |
224 } |