286 \node[left=18] at (c) {$f$}; |
286 \node[left=18] at (c) {$f$}; |
287 \clip (0,0) circle (0.5cm); |
287 \clip (0,0) circle (0.5cm); |
288 \foreach \y in {1,0.86,...,-1} { |
288 \foreach \y in {1,0.86,...,-1} { |
289 \draw[green!50!brown] (-1,\y)--(1,\y); |
289 \draw[green!50!brown] (-1,\y)--(1,\y); |
290 } |
290 } |
291 \end{tikzpicture} |
291 \end{tikzpicture} \\ |
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292 \begin{tikzpicture}[baseline] |
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293 \begin{scope} |
|
294 \clip (-1.3,-2) rectangle (0,2); |
|
295 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
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296 \end{scope} |
|
297 \begin{scope} |
|
298 \clip (1,-2) rectangle (0,2); |
|
299 \node[draw] (d) at (0,-0.4) [ellipse, minimum height=1.2cm, minimum width=1.5cm] {}; |
|
300 \end{scope} |
|
301 \draw (c.north) -- (d.north); |
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302 \draw[dashed] (d.north) -- (d.south); |
|
303 \node[right=8,below=4] at (c) {$g$}; |
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304 \node[left=10] at (c) {$f$}; |
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305 \end{tikzpicture} & = |
|
306 \begin{tikzpicture}[baseline] |
|
307 \begin{scope} |
|
308 \clip (-1.3,-2) rectangle (0,2); |
|
309 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
|
310 \end{scope} |
|
311 \draw[dashed] (c.north) to[out=-120,in=120] (c.south); |
|
312 \draw[dashed] (c.south) to[out=60,in=-90] (0.35,0) node (m) {}; |
|
313 \draw (m.center) to[out=90,in=-60] (c.north); |
|
314 \begin{scope} |
|
315 \clip (c.north) to[out=-120,in=120] (c.south) to[out=60,in=-90] (m) to[out=90,in=-60] (c.north); |
|
316 \foreach \y in {1,0.86,...,-1} { |
|
317 \draw[green!50!brown] (-1,\y)--(1,\y); |
|
318 } |
|
319 \end{scope} |
|
320 \draw (m.center) .. controls +(1,0) and +(1,0) .. (c.south); |
|
321 \node[right=15,below=8] at (c) {$g$}; |
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322 \node[left=12] at (c) {$f$}; |
|
323 \end{tikzpicture} |
292 \end{align*} |
324 \end{align*} |
293 \todo{fourth case} |
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294 \caption{Examples of inserting or deleting product regions.} |
325 \caption{Examples of inserting or deleting product regions.} |
295 \label{fig:product-regions} |
326 \label{fig:product-regions} |
296 \end{figure} |
327 \end{figure} |
297 |
328 |
298 |
329 |