1339 lines
77 KiB
HTML
Executable File
1339 lines
77 KiB
HTML
Executable File
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<!DOCTYPE html>
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<html lang="en" class="">
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<title>apollon/apollon.py at master · lsandig/apollon · GitHub</title>
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<meta name="description" content="Create apollonian gaskets">
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<body class="logged_out env-production linux vis-public page-blob">
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class="js-site-search-focus js-site-search-field is-clearable chromeless-input"
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data-hotkey="s"
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name="q"
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placeholder="Search"
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aria-label="Search this repository"
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data-global-scope-placeholder="Search GitHub"
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data-repo-scope-placeholder="Search"
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tabindex="1"
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autocapitalize="off">
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<div class="container">
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<div class="clearfix">
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<li>
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<a href="/login?return_to=%2Flsandig%2Fapollon"
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class="btn btn-sm btn-with-count tooltipped tooltipped-n"
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Watch
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class="btn btn-sm btn-with-count tooltipped tooltipped-n"
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<h1 itemscope itemtype="http://data-vocabulary.org/Breadcrumb" class="entry-title public ">
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<span class="author"><a href="/lsandig" class="url fn" itemprop="url" rel="author"><span itemprop="title">lsandig</span></a></span><!--
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--><span class="path-divider">/</span><!--
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--><strong><a href="/lsandig/apollon" data-pjax="#js-repo-pjax-container">apollon</a></strong>
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<span class="page-context-loader">
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<img alt="" height="16" src="https://assets-cdn.github.com/images/spinners/octocat-spinner-32.gif" width="16" />
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<nav class="sunken-menu repo-nav js-repo-nav js-sidenav-container-pjax js-octicon-loaders"
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<li class="tooltipped tooltipped-w" aria-label="Code">
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data-protocol-type="http">
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<h3><span class="text-emphasized">HTTPS</span> clone URL</h3>
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<input type="text" class="input-mini input-monospace js-url-field js-zeroclipboard-target"
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value="https://github.com/lsandig/apollon.git" readonly="readonly" aria-label="HTTPS clone URL">
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<span class="input-group-button">
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<button aria-label="Copy to clipboard" class="js-zeroclipboard btn btn-sm zeroclipboard-button tooltipped tooltipped-s" data-copied-hint="Copied!" type="button"><span class="octicon octicon-clippy"></span></button>
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<div class="js-clone-url clone-url "
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data-protocol-type="subversion">
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<input type="text" class="input-mini input-monospace js-url-field js-zeroclipboard-target"
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value="https://github.com/lsandig/apollon" readonly="readonly" aria-label="Subversion checkout URL">
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<button aria-label="Copy to clipboard" class="js-zeroclipboard btn btn-sm zeroclipboard-button tooltipped tooltipped-s" data-copied-hint="Copied!" type="button"><span class="octicon octicon-clippy"></span></button>
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<div class="clone-options">You can clone with
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<!-- </textarea> --><!-- '"` --><form accept-charset="UTF-8" action="/users/set_protocol?protocol_selector=http&protocol_type=clone" class="inline-form js-clone-selector-form " data-form-nonce="d135def5190eb999fd06cf4a9dfe501489c4ed8b" data-remote="true" method="post"><div style="margin:0;padding:0;display:inline"><input name="utf8" type="hidden" value="✓" /><input name="authenticity_token" type="hidden" value="6Fk7ms+1SxO5huJPXVtd3hR0EOOulCyS+pXhE0z7PToQIkjJ7Skwe5vVH6Jd4xcsJZ/00ilXagicQxiwlfZCEg==" /></div><button class="btn-link js-clone-selector" data-protocol="http" type="submit">HTTPS</button></form> or <!-- </textarea> --><!-- '"` --><form accept-charset="UTF-8" action="/users/set_protocol?protocol_selector=subversion&protocol_type=clone" class="inline-form js-clone-selector-form " data-form-nonce="d135def5190eb999fd06cf4a9dfe501489c4ed8b" data-remote="true" method="post"><div style="margin:0;padding:0;display:inline"><input name="utf8" type="hidden" value="✓" /><input name="authenticity_token" type="hidden" value="XRS2F6VB0Ns3FHU4T2Y1eMtZ0rfowWxJBqc9NOJcgmx2ooROCBmoEbEw9T8CyDn5FFTv/S+ilTr8N64T/RLb2Q==" /></div><button class="btn-link js-clone-selector" data-protocol="subversion" type="submit">Subversion</button></form>.
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<a href="https://help.github.com/articles/which-remote-url-should-i-use" class="help tooltipped tooltipped-n" aria-label="Get help on which URL is right for you.">
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<a href="/lsandig/apollon/archive/master.zip"
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class="btn btn-sm sidebar-button"
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aria-label="Download the contents of lsandig/apollon as a zip file"
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title="Download the contents of lsandig/apollon as a zip file"
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rel="nofollow">
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<span class="octicon octicon-cloud-download"></span>
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Download ZIP
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<div id="js-repo-pjax-container" class="repository-content context-loader-container" data-pjax-container>
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<a href="/lsandig/apollon/blob/d61916a99bff38a1fc598411a16658a503bf38ef/apollon.py" class="hidden js-permalink-shortcut" data-hotkey="y">Permalink</a>
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<div class="select-menu js-menu-container js-select-menu left">
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<span class="btn btn-sm select-menu-button js-menu-target css-truncate" data-hotkey="w"
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title="master"
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role="button" aria-label="Switch branches or tags" tabindex="0" aria-haspopup="true">
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<i>Branch:</i>
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<span class="js-select-button css-truncate-target">master</span>
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</span>
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<div class="select-menu-modal-holder js-menu-content js-navigation-container" data-pjax aria-hidden="true">
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<div class="select-menu-modal">
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<span class="select-menu-title">Switch branches/tags</span>
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<span class="author"><a href="/lsandig" rel="author">lsandig</a></span>
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<time datetime="2014-08-28T20:05:07Z" is="relative-time">Aug 28, 2014</time>
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<a href="/lsandig/apollon/commit/4dbf52d213cf0d5afc2a8eeb4d87b8a61c9693f6" class="message" data-pjax="true" title="Add crash prevention for impossible curvatures, fix boilerplate GPL text">Add crash prevention for impossible curvatures, fix boilerplate GPL text</a>
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196 lines (164 sloc)
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<div class="blob-wrapper data type-python">
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<td id="L1" class="blob-num js-line-number" data-line-number="1"></td>
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<td id="LC1" class="blob-code blob-code-inner js-file-line"><span class="pl-c">#!/usr/bin/python3</span></td>
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<td id="L2" class="blob-num js-line-number" data-line-number="2"></td>
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<td id="L3" class="blob-num js-line-number" data-line-number="3"></td>
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<td id="LC3" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># Generate Apollonian Gaskets -- the math part.</span></td>
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<td id="L4" class="blob-num js-line-number" data-line-number="4"></td>
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<td id="L5" class="blob-num js-line-number" data-line-number="5"></td>
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<td id="LC5" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># Copyright (c) 2014 Ludger Sandig</span></td>
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<td id="L6" class="blob-num js-line-number" data-line-number="6"></td>
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<td id="LC6" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># This file is part of apollon.</span></td>
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<td id="L7" class="blob-num js-line-number" data-line-number="7"></td>
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<td id="L8" class="blob-num js-line-number" data-line-number="8"></td>
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<td id="LC8" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># Apollon is free software: you can redistribute it and/or modify</span></td>
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<td id="L9" class="blob-num js-line-number" data-line-number="9"></td>
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<td id="LC9" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># it under the terms of the GNU General Public License as published by</span></td>
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<td id="L10" class="blob-num js-line-number" data-line-number="10"></td>
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<td id="LC10" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># the Free Software Foundation, either version 3 of the License, or</span></td>
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<td id="L11" class="blob-num js-line-number" data-line-number="11"></td>
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<td id="LC11" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># (at your option) any later version.</span></td>
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<td id="L12" class="blob-num js-line-number" data-line-number="12"></td>
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<td id="L13" class="blob-num js-line-number" data-line-number="13"></td>
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<td id="LC13" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># Apollon is distributed in the hope that it will be useful,</span></td>
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<td id="L14" class="blob-num js-line-number" data-line-number="14"></td>
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<td id="LC14" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># but WITHOUT ANY WARRANTY; without even the implied warranty of</span></td>
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<td id="L15" class="blob-num js-line-number" data-line-number="15"></td>
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<td id="LC15" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></td>
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<td id="L16" class="blob-num js-line-number" data-line-number="16"></td>
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<td id="LC16" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># GNU General Public License for more details.</span></td>
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<td id="LC18" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># You should have received a copy of the GNU General Public License</span></td>
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<td id="L19" class="blob-num js-line-number" data-line-number="19"></td>
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<td id="LC19" class="blob-code blob-code-inner js-file-line"><span class="pl-c"># along with Apollon. If not, see <http://www.gnu.org/licenses/>.</span></td>
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<td id="LC21" class="blob-code blob-code-inner js-file-line"><span class="pl-k">from</span> cmath <span class="pl-k">import</span> <span class="pl-k">*</span></td>
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<td id="L22" class="blob-num js-line-number" data-line-number="22"></td>
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<td id="LC22" class="blob-code blob-code-inner js-file-line"><span class="pl-k">import</span> random</td>
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<td id="L24" class="blob-num js-line-number" data-line-number="24"></td>
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<td id="LC24" class="blob-code blob-code-inner js-file-line"><span class="pl-k">class</span> <span class="pl-en">Circle</span>(<span class="pl-e"><span class="pl-c1">object</span></span>):</td>
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<td id="LC25" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L26" class="blob-num js-line-number" data-line-number="26"></td>
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<td id="LC26" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> A circle represented by center point as complex number and radius.</span></td>
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<td id="L27" class="blob-num js-line-number" data-line-number="27"></td>
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<td id="LC28" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en"><span class="pl-c1">__init__</span></span> ( <span class="pl-smi">self</span>, <span class="pl-smi">mx</span>, <span class="pl-smi">my</span>, <span class="pl-smi">r</span> ):</td>
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<td id="LC29" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L33" class="blob-num js-line-number" data-line-number="33"></td>
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<td id="LC36" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="LC37" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.r <span class="pl-k">=</span> r</td>
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<td id="LC38" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.m <span class="pl-k">=</span> (mx <span class="pl-k">+</span>my<span class="pl-k">*</span><span class="pl-c1">1j</span>)</td>
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<td id="LC40" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en"><span class="pl-c1">__repr__</span></span> ( <span class="pl-smi">self</span> ):</td>
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<td id="LC42" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Pretty printing</span></td>
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<td id="L43" class="blob-num js-line-number" data-line-number="43"></td>
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<td id="LC44" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> <span class="pl-s"><span class="pl-pds">"</span>Circle( self, <span class="pl-c1">%s</span>, <span class="pl-c1">%s</span>, <span class="pl-c1">%s</span> )<span class="pl-pds">"</span></span> <span class="pl-k">%</span> (<span class="pl-v">self</span>.m.real, <span class="pl-v">self</span>.m.imag, <span class="pl-v">self</span>.r)</td>
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<td id="LC46" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en"><span class="pl-c1">__str__</span></span> ( <span class="pl-smi">self</span> ):</td>
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<td id="L50" class="blob-num js-line-number" data-line-number="50"></td>
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<td id="LC50" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> <span class="pl-s"><span class="pl-pds">"</span>Circle x:<span class="pl-c1">%.3f</span> y:<span class="pl-c1">%.3f</span> r:<span class="pl-c1">%.3f</span> [cur:<span class="pl-c1">%.3f</span>]<span class="pl-pds">"</span></span> <span class="pl-k">%</span> (<span class="pl-v">self</span>.m.real, <span class="pl-v">self</span>.m.imag, <span class="pl-v">self</span>.r.real, <span class="pl-v">self</span>.curvature().real)</td>
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<td id="L51" class="blob-num js-line-number" data-line-number="51"></td>
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<td id="LC51" class="blob-code blob-code-inner js-file-line">
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<td id="L52" class="blob-num js-line-number" data-line-number="52"></td>
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<td id="LC52" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en">curvature</span> (<span class="pl-smi">self</span>):</td>
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<td id="L53" class="blob-num js-line-number" data-line-number="53"></td>
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<td id="LC53" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L54" class="blob-num js-line-number" data-line-number="54"></td>
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<td id="LC54" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Get circle's curvature.</span></td>
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<td id="L55" class="blob-num js-line-number" data-line-number="55"></td>
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<td id="LC55" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @rtype: float</span></td>
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<td id="L56" class="blob-num js-line-number" data-line-number="56"></td>
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<td id="LC56" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @return: Curvature of the circle.</span></td>
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<td id="L57" class="blob-num js-line-number" data-line-number="57"></td>
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<td id="LC57" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L58" class="blob-num js-line-number" data-line-number="58"></td>
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<td id="LC58" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> <span class="pl-c1">1</span><span class="pl-k">/</span><span class="pl-v">self</span>.r</td>
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<td id="L59" class="blob-num js-line-number" data-line-number="59"></td>
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<td id="LC59" class="blob-code blob-code-inner js-file-line">
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</td>
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<td id="L60" class="blob-num js-line-number" data-line-number="60"></td>
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<td id="LC60" class="blob-code blob-code-inner js-file-line"><span class="pl-k">def</span> <span class="pl-en">outerTangentCircle</span>( <span class="pl-smi">circle1</span>, <span class="pl-smi">circle2</span>, <span class="pl-smi">circle3</span> ):</td>
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<td id="L61" class="blob-num js-line-number" data-line-number="61"></td>
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<td id="LC61" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L62" class="blob-num js-line-number" data-line-number="62"></td>
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<td id="LC62" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Takes three externally tangent circles and calculates the fourth one enclosing them.</span></td>
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<td id="L63" class="blob-num js-line-number" data-line-number="63"></td>
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<td id="LC63" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param circle1: first circle</span></td>
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<td id="L64" class="blob-num js-line-number" data-line-number="64"></td>
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<td id="LC64" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param circle2: second circle</span></td>
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<td id="L65" class="blob-num js-line-number" data-line-number="65"></td>
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<td id="LC65" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param circle3: third circle</span></td>
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<td id="L66" class="blob-num js-line-number" data-line-number="66"></td>
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<td id="LC66" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type circle1: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L67" class="blob-num js-line-number" data-line-number="67"></td>
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<td id="LC67" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type circle2: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L68" class="blob-num js-line-number" data-line-number="68"></td>
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<td id="LC68" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type circle3: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L69" class="blob-num js-line-number" data-line-number="69"></td>
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<td id="LC69" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @return: The enclosing circle</span></td>
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<td id="L70" class="blob-num js-line-number" data-line-number="70"></td>
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<td id="LC70" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @rtype: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L71" class="blob-num js-line-number" data-line-number="71"></td>
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<td id="LC71" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L72" class="blob-num js-line-number" data-line-number="72"></td>
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<td id="LC72" class="blob-code blob-code-inner js-file-line"> cur1 <span class="pl-k">=</span> circle1.curvature()</td>
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<td id="L73" class="blob-num js-line-number" data-line-number="73"></td>
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<td id="LC73" class="blob-code blob-code-inner js-file-line"> cur2 <span class="pl-k">=</span> circle2.curvature()</td>
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<tr>
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<td id="L74" class="blob-num js-line-number" data-line-number="74"></td>
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<td id="LC74" class="blob-code blob-code-inner js-file-line"> cur3 <span class="pl-k">=</span> circle3.curvature()</td>
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</tr>
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<tr>
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<td id="L75" class="blob-num js-line-number" data-line-number="75"></td>
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<td id="LC75" class="blob-code blob-code-inner js-file-line"> m1 <span class="pl-k">=</span> circle1.m</td>
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<tr>
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<td id="L76" class="blob-num js-line-number" data-line-number="76"></td>
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<td id="LC76" class="blob-code blob-code-inner js-file-line"> m2 <span class="pl-k">=</span> circle2.m</td>
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<tr>
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<td id="L77" class="blob-num js-line-number" data-line-number="77"></td>
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<td id="LC77" class="blob-code blob-code-inner js-file-line"> m3 <span class="pl-k">=</span> circle3.m</td>
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<tr>
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<td id="L78" class="blob-num js-line-number" data-line-number="78"></td>
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<td id="LC78" class="blob-code blob-code-inner js-file-line"> cur4 <span class="pl-k">=</span> <span class="pl-k">-</span><span class="pl-c1">2</span> <span class="pl-k">*</span> sqrt( cur1<span class="pl-k">*</span>cur2 <span class="pl-k">+</span> cur2<span class="pl-k">*</span>cur3 <span class="pl-k">+</span> cur1 <span class="pl-k">*</span> cur3 ) <span class="pl-k">+</span> cur1 <span class="pl-k">+</span> cur2 <span class="pl-k">+</span> cur3</td>
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</tr>
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<tr>
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<td id="L79" class="blob-num js-line-number" data-line-number="79"></td>
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<td id="LC79" class="blob-code blob-code-inner js-file-line"> m4 <span class="pl-k">=</span> ( <span class="pl-k">-</span><span class="pl-c1">2</span> <span class="pl-k">*</span> sqrt( cur1<span class="pl-k">*</span>m1<span class="pl-k">*</span>cur2<span class="pl-k">*</span>m2 <span class="pl-k">+</span> cur2<span class="pl-k">*</span>m2<span class="pl-k">*</span>cur3<span class="pl-k">*</span>m3 <span class="pl-k">+</span> cur1<span class="pl-k">*</span>m1<span class="pl-k">*</span>cur3<span class="pl-k">*</span>m3 ) <span class="pl-k">+</span> cur1<span class="pl-k">*</span>m1 <span class="pl-k">+</span> cur2<span class="pl-k">*</span>m2 <span class="pl-k">+</span> cur3<span class="pl-k">*</span>m3 ) <span class="pl-k">/</span> cur4</td>
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<tr>
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<td id="L80" class="blob-num js-line-number" data-line-number="80"></td>
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<td id="LC80" class="blob-code blob-code-inner js-file-line"> circle4 <span class="pl-k">=</span> Circle( m4.real, m4.imag, <span class="pl-c1">1</span><span class="pl-k">/</span>cur4 )</td>
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<td id="L81" class="blob-num js-line-number" data-line-number="81"></td>
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<td id="LC81" class="blob-code blob-code-inner js-file-line"> </td>
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<td id="L82" class="blob-num js-line-number" data-line-number="82"></td>
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<td id="LC82" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> circle4</td>
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<td id="L83" class="blob-num js-line-number" data-line-number="83"></td>
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<td id="LC83" class="blob-code blob-code-inner js-file-line"> </td>
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<td id="L84" class="blob-num js-line-number" data-line-number="84"></td>
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<td id="LC84" class="blob-code blob-code-inner js-file-line">
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</td>
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<td id="L85" class="blob-num js-line-number" data-line-number="85"></td>
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<td id="LC85" class="blob-code blob-code-inner js-file-line"><span class="pl-k">def</span> <span class="pl-en">tangentCirclesFromRadii</span>( <span class="pl-smi">r2</span>, <span class="pl-smi">r3</span>, <span class="pl-smi">r4</span> ):</td>
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<tr>
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<td id="L86" class="blob-num js-line-number" data-line-number="86"></td>
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<td id="LC86" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<tr>
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<td id="L87" class="blob-num js-line-number" data-line-number="87"></td>
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<td id="LC87" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Takes three radii and calculates the corresponding externally</span></td>
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</tr>
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<tr>
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<td id="L88" class="blob-num js-line-number" data-line-number="88"></td>
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<td id="LC88" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> tangent circles as well as a fourth one enclosing them. The enclosing</span></td>
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</tr>
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<tr>
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<td id="L89" class="blob-num js-line-number" data-line-number="89"></td>
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<td id="LC89" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> circle is the first one.</span></td>
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</tr>
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<tr>
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<td id="L90" class="blob-num js-line-number" data-line-number="90"></td>
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<td id="LC90" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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</tr>
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<tr>
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<td id="L91" class="blob-num js-line-number" data-line-number="91"></td>
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<td id="LC91" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param r2, r3, r4: Radii of the circles to calculate</span></td>
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</tr>
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<tr>
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<td id="L92" class="blob-num js-line-number" data-line-number="92"></td>
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<td id="LC92" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type r2: int or float</span></td>
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</tr>
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<tr>
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<td id="L93" class="blob-num js-line-number" data-line-number="93"></td>
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<td id="LC93" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type r3: int or float</span></td>
|
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</tr>
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<tr>
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<td id="L94" class="blob-num js-line-number" data-line-number="94"></td>
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<td id="LC94" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type r4: int or float</span></td>
|
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</tr>
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<tr>
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<td id="L95" class="blob-num js-line-number" data-line-number="95"></td>
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<td id="LC95" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @return: The four circles, where the first one is the enclosing one.</span></td>
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</tr>
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<tr>
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<td id="L96" class="blob-num js-line-number" data-line-number="96"></td>
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<td id="LC96" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @rtype: (L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>)</span></td>
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</tr>
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<tr>
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<td id="L97" class="blob-num js-line-number" data-line-number="97"></td>
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<td id="LC97" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<tr>
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<td id="L98" class="blob-num js-line-number" data-line-number="98"></td>
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<td id="LC98" class="blob-code blob-code-inner js-file-line"> circle2 <span class="pl-k">=</span> Circle( <span class="pl-c1">0</span>, <span class="pl-c1">0</span>, r2 )</td>
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</tr>
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<tr>
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<td id="L99" class="blob-num js-line-number" data-line-number="99"></td>
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<td id="LC99" class="blob-code blob-code-inner js-file-line"> circle3 <span class="pl-k">=</span> Circle( r2 <span class="pl-k">+</span> r3, <span class="pl-c1">0</span>, r3 )</td>
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</tr>
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<tr>
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<td id="L100" class="blob-num js-line-number" data-line-number="100"></td>
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<td id="LC100" class="blob-code blob-code-inner js-file-line"> m4x <span class="pl-k">=</span> (r2<span class="pl-k">*</span>r2 <span class="pl-k">+</span> r2<span class="pl-k">*</span>r4 <span class="pl-k">+</span> r2<span class="pl-k">*</span>r3 <span class="pl-k">-</span> r3<span class="pl-k">*</span>r4) <span class="pl-k">/</span> (r2 <span class="pl-k">+</span> r3)</td>
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</tr>
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<tr>
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<td id="L101" class="blob-num js-line-number" data-line-number="101"></td>
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<td id="LC101" class="blob-code blob-code-inner js-file-line"> m4y <span class="pl-k">=</span> sqrt( (r2 <span class="pl-k">+</span> r4) <span class="pl-k">*</span> (r2 <span class="pl-k">+</span> r4) <span class="pl-k">-</span> m4x<span class="pl-k">*</span>m4x )</td>
|
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</tr>
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<tr>
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<td id="L102" class="blob-num js-line-number" data-line-number="102"></td>
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<td id="LC102" class="blob-code blob-code-inner js-file-line"> circle4 <span class="pl-k">=</span> Circle( m4x, m4y, r4 )</td>
|
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</tr>
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<tr>
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<td id="L103" class="blob-num js-line-number" data-line-number="103"></td>
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<td id="LC103" class="blob-code blob-code-inner js-file-line"> circle1 <span class="pl-k">=</span> outerTangentCircle( circle2, circle3, circle4 )</td>
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</tr>
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<tr>
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<td id="L104" class="blob-num js-line-number" data-line-number="104"></td>
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<td id="LC104" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> ( circle1, circle2, circle3, circle4 )</td>
|
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</tr>
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<tr>
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<td id="L105" class="blob-num js-line-number" data-line-number="105"></td>
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<td id="LC105" class="blob-code blob-code-inner js-file-line">
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</td>
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</tr>
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<tr>
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<td id="L106" class="blob-num js-line-number" data-line-number="106"></td>
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<td id="LC106" class="blob-code blob-code-inner js-file-line"><span class="pl-k">def</span> <span class="pl-en">secondSolution</span>( <span class="pl-smi">fixed</span>, <span class="pl-smi">c1</span>, <span class="pl-smi">c2</span>, <span class="pl-smi">c3</span> ):</td>
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<tr>
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<td id="L107" class="blob-num js-line-number" data-line-number="107"></td>
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<td id="LC107" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<tr>
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<td id="L108" class="blob-num js-line-number" data-line-number="108"></td>
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<td id="LC108" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> If given four tangent circles, calculate the other one that is tangent</span></td>
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</tr>
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<tr>
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<td id="L109" class="blob-num js-line-number" data-line-number="109"></td>
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<td id="LC109" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> to the last three.</span></td>
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</tr>
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<tr>
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<td id="L110" class="blob-num js-line-number" data-line-number="110"></td>
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<td id="LC110" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> </span></td>
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</tr>
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<tr>
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<td id="L111" class="blob-num js-line-number" data-line-number="111"></td>
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<td id="LC111" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param fixed: The fixed circle touches the other three, but not</span></td>
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</tr>
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<tr>
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<td id="L112" class="blob-num js-line-number" data-line-number="112"></td>
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<td id="LC112" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> the one to be calculated.</span></td>
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</tr>
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<tr>
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<td id="L113" class="blob-num js-line-number" data-line-number="113"></td>
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<td id="LC113" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> </span></td>
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<td id="L114" class="blob-num js-line-number" data-line-number="114"></td>
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<td id="LC114" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param c1, c2, c3: Three circles to which the other tangent circle</span></td>
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<td id="L115" class="blob-num js-line-number" data-line-number="115"></td>
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<td id="LC115" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> is to be calculated.</span></td>
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<td id="L116" class="blob-num js-line-number" data-line-number="116"></td>
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<td id="LC116" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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<td id="L117" class="blob-num js-line-number" data-line-number="117"></td>
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<td id="LC117" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type fixed: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L118" class="blob-num js-line-number" data-line-number="118"></td>
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<td id="LC118" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c1: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L119" class="blob-num js-line-number" data-line-number="119"></td>
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<td id="LC119" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c2: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L120" class="blob-num js-line-number" data-line-number="120"></td>
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<td id="LC120" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c3: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L121" class="blob-num js-line-number" data-line-number="121"></td>
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<td id="LC121" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @return: The circle.</span></td>
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<td id="L122" class="blob-num js-line-number" data-line-number="122"></td>
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<td id="LC122" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @rtype: L<span class="pl-c1">{Circle}</span></span></td>
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<td id="L123" class="blob-num js-line-number" data-line-number="123"></td>
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<td id="LC123" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L124" class="blob-num js-line-number" data-line-number="124"></td>
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<td id="LC124" class="blob-code blob-code-inner js-file-line"> </td>
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<td id="L125" class="blob-num js-line-number" data-line-number="125"></td>
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<td id="LC125" class="blob-code blob-code-inner js-file-line"> curf <span class="pl-k">=</span> fixed.curvature()</td>
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<td id="L126" class="blob-num js-line-number" data-line-number="126"></td>
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<td id="LC126" class="blob-code blob-code-inner js-file-line"> cur1 <span class="pl-k">=</span> c1.curvature()</td>
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<td id="L127" class="blob-num js-line-number" data-line-number="127"></td>
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<td id="LC127" class="blob-code blob-code-inner js-file-line"> cur2 <span class="pl-k">=</span> c2.curvature()</td>
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<td id="L128" class="blob-num js-line-number" data-line-number="128"></td>
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<td id="LC128" class="blob-code blob-code-inner js-file-line"> cur3 <span class="pl-k">=</span> c3.curvature()</td>
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<td id="L129" class="blob-num js-line-number" data-line-number="129"></td>
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<td id="LC129" class="blob-code blob-code-inner js-file-line">
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<td id="L130" class="blob-num js-line-number" data-line-number="130"></td>
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<td id="LC130" class="blob-code blob-code-inner js-file-line"> curn <span class="pl-k">=</span> <span class="pl-c1">2</span> <span class="pl-k">*</span> (cur1 <span class="pl-k">+</span> cur2 <span class="pl-k">+</span> cur3) <span class="pl-k">-</span> curf</td>
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<td id="L131" class="blob-num js-line-number" data-line-number="131"></td>
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<td id="LC131" class="blob-code blob-code-inner js-file-line"> mn <span class="pl-k">=</span> (<span class="pl-c1">2</span> <span class="pl-k">*</span> (cur1<span class="pl-k">*</span>c1.m <span class="pl-k">+</span> cur2<span class="pl-k">*</span>c2.m <span class="pl-k">+</span> cur3<span class="pl-k">*</span>c3.m) <span class="pl-k">-</span> curf<span class="pl-k">*</span>fixed.m ) <span class="pl-k">/</span> curn</td>
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<td id="L132" class="blob-num js-line-number" data-line-number="132"></td>
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<td id="LC132" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span> Circle( mn.real, mn.imag, <span class="pl-c1">1</span><span class="pl-k">/</span>curn )</td>
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<td id="L133" class="blob-num js-line-number" data-line-number="133"></td>
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<td id="LC133" class="blob-code blob-code-inner js-file-line">
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<td id="L134" class="blob-num js-line-number" data-line-number="134"></td>
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<td id="LC134" class="blob-code blob-code-inner js-file-line"><span class="pl-k">class</span> <span class="pl-en">ApollonianGasket</span>(<span class="pl-e"><span class="pl-c1">object</span></span>):</td>
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<td id="L135" class="blob-num js-line-number" data-line-number="135"></td>
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<td id="LC135" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L136" class="blob-num js-line-number" data-line-number="136"></td>
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<td id="LC136" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Container for an Apollonian Gasket.</span></td>
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<td id="L137" class="blob-num js-line-number" data-line-number="137"></td>
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<td id="LC137" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L138" class="blob-num js-line-number" data-line-number="138"></td>
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<td id="LC138" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en"><span class="pl-c1">__init__</span></span>(<span class="pl-smi">self</span>, <span class="pl-smi">c1</span>, <span class="pl-smi">c2</span>, <span class="pl-smi">c3</span>):</td>
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<td id="L139" class="blob-num js-line-number" data-line-number="139"></td>
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<td id="LC139" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L140" class="blob-num js-line-number" data-line-number="140"></td>
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<td id="LC140" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Creates a basic apollonian Gasket with four circles. </span></td>
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<td id="L141" class="blob-num js-line-number" data-line-number="141"></td>
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<td id="LC141" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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<td id="L142" class="blob-num js-line-number" data-line-number="142"></td>
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<td id="LC142" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param c1, c2, c3: The curvatures of the three inner circles of the</span></td>
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<td id="L143" class="blob-num js-line-number" data-line-number="143"></td>
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<td id="LC143" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> starting set (i.e. depth 0 of the recursion). The fourth,</span></td>
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<td id="L144" class="blob-num js-line-number" data-line-number="144"></td>
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<td id="LC144" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> enclosing circle will be calculated from them.</span></td>
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<td id="L145" class="blob-num js-line-number" data-line-number="145"></td>
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<td id="LC145" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c1: int or float</span></td>
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<td id="L146" class="blob-num js-line-number" data-line-number="146"></td>
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<td id="LC146" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c2: int or float</span></td>
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<td id="L147" class="blob-num js-line-number" data-line-number="147"></td>
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<td id="LC147" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type c3: int or float</span></td>
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<td id="L148" class="blob-num js-line-number" data-line-number="148"></td>
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<td id="LC148" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L149" class="blob-num js-line-number" data-line-number="149"></td>
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<td id="LC149" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.start <span class="pl-k">=</span> tangentCirclesFromRadii( <span class="pl-c1">1</span><span class="pl-k">/</span>c1, <span class="pl-c1">1</span><span class="pl-k">/</span>c2, <span class="pl-c1">1</span><span class="pl-k">/</span>c3 )</td>
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<td id="L150" class="blob-num js-line-number" data-line-number="150"></td>
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<td id="LC150" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.genCircles <span class="pl-k">=</span> <span class="pl-c1">list</span>(<span class="pl-v">self</span>.start)</td>
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<td id="L151" class="blob-num js-line-number" data-line-number="151"></td>
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<td id="LC151" class="blob-code blob-code-inner js-file-line">
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<td id="L152" class="blob-num js-line-number" data-line-number="152"></td>
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<td id="LC152" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en">recurse</span>(<span class="pl-smi">self</span>, <span class="pl-smi">circles</span>, <span class="pl-smi">depth</span>, <span class="pl-smi">maxDepth</span>):</td>
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<td id="L153" class="blob-num js-line-number" data-line-number="153"></td>
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<td id="LC153" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span>Recursively calculate the smaller circles of the AG up to the</span></td>
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<td id="L154" class="blob-num js-line-number" data-line-number="154"></td>
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<td id="LC154" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> given depth. Note that for depth n we get 2*3^{n+1} circles.</span></td>
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<td id="L155" class="blob-num js-line-number" data-line-number="155"></td>
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<td id="LC155" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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<td id="L156" class="blob-num js-line-number" data-line-number="156"></td>
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<td id="LC156" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param maxDepth: Maximal depth of the recursion.</span></td>
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<td id="L157" class="blob-num js-line-number" data-line-number="157"></td>
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<td id="LC157" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type maxDepth: int</span></td>
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<td id="L158" class="blob-num js-line-number" data-line-number="158"></td>
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<td id="LC158" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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<td id="L159" class="blob-num js-line-number" data-line-number="159"></td>
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<td id="LC159" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param circles: 4-Tuple of circles for which the second</span></td>
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<td id="L160" class="blob-num js-line-number" data-line-number="160"></td>
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<td id="LC160" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> solutions are calculated</span></td>
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<td id="L161" class="blob-num js-line-number" data-line-number="161"></td>
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<td id="LC161" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type circles: (L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>, L<span class="pl-c1">{Circle}</span>)</span></td>
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<td id="L162" class="blob-num js-line-number" data-line-number="162"></td>
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<td id="LC162" class="blob-code blob-code-inner js-file-line"><span class="pl-s"></span></td>
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<td id="L163" class="blob-num js-line-number" data-line-number="163"></td>
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<td id="LC163" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param depth: Current depth</span></td>
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<td id="L164" class="blob-num js-line-number" data-line-number="164"></td>
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<td id="LC164" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type depth: int</span></td>
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<td id="L165" class="blob-num js-line-number" data-line-number="165"></td>
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<td id="LC165" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L166" class="blob-num js-line-number" data-line-number="166"></td>
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<td id="LC166" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">if</span>( depth <span class="pl-k">==</span> maxDepth ):</td>
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<td id="L167" class="blob-num js-line-number" data-line-number="167"></td>
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<td id="LC167" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">return</span></td>
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<td id="L168" class="blob-num js-line-number" data-line-number="168"></td>
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<td id="LC168" class="blob-code blob-code-inner js-file-line"> (c1, c2, c3, c4) <span class="pl-k">=</span> circles</td>
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<td id="L169" class="blob-num js-line-number" data-line-number="169"></td>
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<td id="LC169" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">if</span>( depth <span class="pl-k">==</span> <span class="pl-c1">0</span> ):</td>
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<td id="L170" class="blob-num js-line-number" data-line-number="170"></td>
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<td id="LC170" class="blob-code blob-code-inner js-file-line"> <span class="pl-c"># First recursive step, this is the only time we need to</span></td>
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<td id="L171" class="blob-num js-line-number" data-line-number="171"></td>
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<td id="LC171" class="blob-code blob-code-inner js-file-line"> <span class="pl-c"># calculate 4 new circles.</span></td>
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<td id="L172" class="blob-num js-line-number" data-line-number="172"></td>
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<td id="LC172" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">del</span> <span class="pl-v">self</span>.genCircles[<span class="pl-c1">4</span>:]</td>
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<td id="L173" class="blob-num js-line-number" data-line-number="173"></td>
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<td id="LC173" class="blob-code blob-code-inner js-file-line"> cspecial <span class="pl-k">=</span> secondSolution( c1, c2, c3, c4 )</td>
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<td id="L174" class="blob-num js-line-number" data-line-number="174"></td>
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<td id="LC174" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.genCircles.append( cspecial )</td>
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<td id="L175" class="blob-num js-line-number" data-line-number="175"></td>
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<td id="LC175" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.recurse( (cspecial, c2, c3, c4), <span class="pl-c1">1</span>, maxDepth )</td>
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<td id="L176" class="blob-num js-line-number" data-line-number="176"></td>
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<td id="LC176" class="blob-code blob-code-inner js-file-line">
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<td id="L177" class="blob-num js-line-number" data-line-number="177"></td>
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<td id="LC177" class="blob-code blob-code-inner js-file-line"> cn2 <span class="pl-k">=</span> secondSolution( c2, c1, c3, c4 )</td>
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<td id="L178" class="blob-num js-line-number" data-line-number="178"></td>
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<td id="LC178" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.genCircles.append( cn2 )</td>
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<td id="L179" class="blob-num js-line-number" data-line-number="179"></td>
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<td id="LC179" class="blob-code blob-code-inner js-file-line"> cn3 <span class="pl-k">=</span> secondSolution( c3, c1, c2, c4 )</td>
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<td id="L180" class="blob-num js-line-number" data-line-number="180"></td>
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<td id="LC180" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.genCircles.append( cn3 )</td>
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<td id="L181" class="blob-num js-line-number" data-line-number="181"></td>
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<td id="LC181" class="blob-code blob-code-inner js-file-line"> cn4 <span class="pl-k">=</span> secondSolution( c4, c1, c2, c3 )</td>
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</tr>
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<tr>
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<td id="L182" class="blob-num js-line-number" data-line-number="182"></td>
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<td id="LC182" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.genCircles.append( cn4 ) </td>
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<td id="L183" class="blob-num js-line-number" data-line-number="183"></td>
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<td id="LC183" class="blob-code blob-code-inner js-file-line">
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</td>
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<td id="L184" class="blob-num js-line-number" data-line-number="184"></td>
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<td id="LC184" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.recurse( (cn2, c1, c3, c4), depth<span class="pl-k">+</span><span class="pl-c1">1</span>, maxDepth )</td>
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<td id="L185" class="blob-num js-line-number" data-line-number="185"></td>
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<td id="LC185" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.recurse( (cn3, c1, c2, c4), depth<span class="pl-k">+</span><span class="pl-c1">1</span>, maxDepth )</td>
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<td id="L186" class="blob-num js-line-number" data-line-number="186"></td>
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<td id="LC186" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.recurse( (cn4, c1, c2, c3), depth<span class="pl-k">+</span><span class="pl-c1">1</span>, maxDepth )</td>
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<td id="L187" class="blob-num js-line-number" data-line-number="187"></td>
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<td id="L188" class="blob-num js-line-number" data-line-number="188"></td>
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<td id="LC188" class="blob-code blob-code-inner js-file-line"> <span class="pl-k">def</span> <span class="pl-en">generate</span>(<span class="pl-smi">self</span>, <span class="pl-smi">depth</span>):</td>
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<td id="L189" class="blob-num js-line-number" data-line-number="189"></td>
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<td id="LC189" class="blob-code blob-code-inner js-file-line"> <span class="pl-s"><span class="pl-pds">"""</span></span></td>
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<td id="L190" class="blob-num js-line-number" data-line-number="190"></td>
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<td id="LC190" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> Wrapper for the recurse function. Generate the AG,</span></td>
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<td id="L191" class="blob-num js-line-number" data-line-number="191"></td>
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<td id="LC191" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @param depth: Recursion depth of the Gasket</span></td>
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<td id="L192" class="blob-num js-line-number" data-line-number="192"></td>
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<td id="LC192" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> @type depth: int</span></td>
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<td id="L193" class="blob-num js-line-number" data-line-number="193"></td>
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<td id="LC193" class="blob-code blob-code-inner js-file-line"><span class="pl-s"> <span class="pl-pds">"""</span></span></td>
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<td id="L194" class="blob-num js-line-number" data-line-number="194"></td>
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<td id="LC194" class="blob-code blob-code-inner js-file-line"> <span class="pl-v">self</span>.recurse(<span class="pl-v">self</span>.start, <span class="pl-c1">0</span>, depth)</td>
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<td id="L195" class="blob-num js-line-number" data-line-number="195"></td>
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