160 lines
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HTML
160 lines
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<title>Regular polygons and ellipses in grid graphics</title>
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rel="stylesheet" type="text/css" />
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</head>
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<body>
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<h1 class="title toc-ignore">Regular polygons and ellipses in grid graphics</h1>
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<h4 class="author"><em>Baptiste Auguie</em></h4>
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<h4 class="date"><em>2017-09-09</em></h4>
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<div id="TOC">
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<ul>
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<li><a href="#basic-usage">Basic usage</a></li>
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<li><a href="#rotated-and-stretched-polygons">Rotated and stretched polygons</a></li>
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<li><a href="#ellipses">Ellipses</a></li>
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</ul>
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</div>
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<p>The <code>gridExtra</code> package provides a basic implementation of regular polygons, <code>ngonGrob()/grid.ngon</code>, and a convenience function to draw ellipses, <code>ellipseGrob()/grid.ellipse()</code>. We illustrate below the basic usage of these vectorised functions.</p>
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<div id="basic-usage" class="section level2">
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<h2>Basic usage</h2>
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<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(gridExtra)
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<span class="kw">library</span>(grid)
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<span class="kw">library</span>(grid)
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N <-<span class="st"> </span><span class="dv">5</span>
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xy <-<span class="st"> </span><span class="kw">polygon_regular</span>(N)<span class="op">*</span><span class="dv">2</span>
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<span class="co"># draw multiple polygons</span>
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g <-<span class="st"> </span><span class="kw">ngonGrob</span>(<span class="kw">unit</span>(xy[,<span class="dv">1</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="kw">unit</span>(xy[,<span class="dv">2</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="dt">n=</span><span class="kw">seq_len</span>(N)<span class="op">+</span><span class="dv">2</span>, <span class="dt">gp=</span><span class="kw">gpar</span>(<span class="dt">fill=</span><span class="dv">1</span><span class="op">:</span>N))
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<span class="kw">grid.newpage</span>()
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<span class="kw">grid.draw</span>(g)</code></pre></div>
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<p><img 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QJOAardzpIECBDoc4G5c+dW7ue/ySabGPz3ua4VEiBAgEAmIADYDwgQINAgAuecc07ltp7XXXdddHV1NUirNIMAAQIEiibgFKCiVVR/CBDIncAtt9wSH/nIRyJ7mq+JAAECBAjUW0AAqLew9RMgQGA5As8++2zlPP9JkyYtZw6/JkCAAAECfS/gFKC+N7VGAgQIrFCgvb09DjnkkHjTm94UBv8rpPImAQIECNRBQACoA6pVEiBAYHkCl1xySYwcOTJ+8IMfOM9/eUh+T4AAAQJ1FXAKUF15rZwAAQILBf74xz/GAQccEM888wwSAgQIECAwoAICwIDy2zgBAkUXePnllyu39bztttuK3lX9I0CAAIGcCDSlW82511xOiqWZBAjkT2C99daL7GLfok/Nzc3R0dFR9G7qHwECBAoh4BqAQpRRJwgQaFSBbbbZplGbpl0ECBAgUFIBAaCkhddtAgT6R+Caa66JG264IcaMGdM/G7QVAgQIECCwEgEBYCVA3iZAgMCqCuyxxx6RXQtw6qmnxqBBg1Z1dZYnQIAAAQKrJOAagFXiszABAgR6JzBr1qzYf//94xe/+EXvFmzwuV0D0OAF0jwCBAgsJeAIwFIYviVAgEC9BYYPHx4333xzPPTQQ7HRRhvVe3PWT4AAAQIEXicgALyOxC8IECBQf4HNNtssJk+eHFdeeWXlwWD136ItECBAgACBhQICgD2BAAECAyhw8MEHx/Tp0+NTn/pUtLS0DGBLbJoAAQIEyiLgGoCyVFo/CRBoeIEpU6bEXnvtFXl8aJhrABp+99JAAgQILBZwBGAxhW8IECAwsAJrrLFG/OEPf4i77747sgeImQgQIECAQD0EBIB6qFonAQIEVkEge3jY008/Hd/+9rdj2LBhq7AmixIgQIAAgdcLOAXo9SZ+Q4AAgYYRaG9vjyOPPDJ+8IMfRFdXV8O067UNcQrQa0X8TIAAgcYVEAAatzZaRoAAgcUCzz33XOy5554xadKkxb9rpG8EgEaqhrYQIEBgxQJOAVqxj3cJECDQEAJrr712/PnPf47f/OY3MW7cuIZok0YQIECAQD4FBIB81k2rCRAoqcCuu+4azz//fHzta1+Ltra2kiroNgECBAisioBTgFZFz7IECBAYQIG5c+dG9hyB66+/fsCvD3AK0ADuCDZNgACBXgoIAL0EMzsBAgQaTeDJJ5+MCRMmxMMPPzxgTRMABozehgkQINBrAacA9ZrMAgQIEGgsgQ033DAeeuihuO6662L06NGN1TitIUCAAIGGExAAGq4kGkSAAIHaBLKnCGdPE/785z8fra2tta3EUgQIECBQeAGnABW+xDpIgEAZBWbMmBH7779//OpXv+qX7jsFqF+YbYQAAQJ9IuAIQJ8wWgkBAgQaS2DkyJHxy1/+Mv7yl7/ERhtt1FiN0xoCBAgQGFABAWBA+W2cAAEC9RV4xzveEZMnT47/+q//ihEjRtR3Y9ZOgAABArkQEAByUSaNJECAwKoJfOxjH4vstKBjjjkmWlpaVm1lliZAgACBXAu4BiDX5dN4AgQI9F7g5Zdfjr333jtuv/323i+8nCVcA7AcGL8mQIBAAwo4AtCARdEkAgQI1FPgDW94Q9x2221x1113xbrrrlvPTVk3AQIECDSggADQgEXRJAIECPSHwLbbbhvPPPNMXHzxxTF06ND+2KRtECBAgEADCDgFqAGKoAkECBAYaIH29vY4/PDD48orr4yurq5eN8cpQL0mswABAgQGTEAAGDB6GyZAgEDjCTz77LMxYcKEuPfee3vVOAGgV1xmJkCAwIAKOAVoQPltnAABAo0lkF0TMGnSpMozBMaOHdtYjdMaAgQIEOgTAQGgTxithAABAsUS2H333eOFF16Is88+O9ra2orVOb0hQIBAyQWcAlTyHUD3CRAgsDKBuXPnxoc//OG4/vrrlzurU4CWS+MNAgQINJyAANBwJdEgAgQINKbA448/Hvvss0888sgjr2ugAPA6Er8gQIBAwwo4BahhS6NhBAgQaCyBTTbZJB5++OG45pprYtSoUY3VOK0hQIAAgaoFBICqqcxIgAABAplAdhRg6tSpcdJJJ0Vra2sFJTsCYCJAgACBfAg4BSgfddJKAgQINKTAjBkz4uMf/3hsscUWceqppzZkGzWKAAECBHoKCAA9PfxEgAABAgQIECBAoNACjtkWurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6R4AAAQIECBAgQKCngADQ08NPBAgQIECAAAECBAotIAAUurw6V2SBSZMmxaWXXhqdnZ1F7qa+ESBAgAABAn0s0NrH67M6AgT6QeD3v/99fOhDH4o5c+bEXXfdFd///vejuVme7wd6myBAYAUC7e3t8eCDD8Ydd9wRCxYsiOOOOy7a2tpWsIS3CBAYCIGmrjQNxIZtkwCB2gSWHvw3pVVk/wf+6Ec/KgTUxmkpAgRWQWDq1Klx9913Vz6IyD6MuPuee2L2q68uXuO2224b1157bay11lqLf+cbAgQGXkAAGPgaaAGBqgWWHvwfFs3x0WiJ8bEgsn9uhYCqGc1IgECNApMnT44777yzMuDPvj762GPpU4ienyO2brxxDNl++5hz663R8fTT8cY0+L/2mmtiu+22q3GrFiNAoK8FBIC+FrU+AnUSeO3g/z+jNZrS/+6MzvhXIaBO6lZLoLwCc+fOjXvvvXfxgD/7hP+ll17qAdI0ZEi0bbVVDEmD+8HplQ38W97whso8HS+/HC/uv3/M/d3vonXQoLj4m9+MT3ziEz2W9wMBAgMjIAAMjLutEuiVwPIG/90rEQK6JXwlQKBWgeeff37xqTzZp/v33ndfLJg/v8fqWt74xoUD/WzAnwb7g7fcMpraln+Of1dHR0w56aSYceGFlfUcccQR8a1vfSsGDx7cY71+IECgfwUEgP71tjUCvRZY2eC/e4VCQLeErwQIrEwgu3vYww8/vPhUnuzT/b///e89F0s3Fhi02WaVT/W7P+Ef9Ja39Jynyp9m/fjH8fKRR0ZXunHBNttsU7kuYJ111qlyabMRINDXAgJAX4taH4E+FKh28N+9SSGgW8JXAgSWFpg5c2bcky7Q7T5//4/pwt2ZM2YsPUs0jRgRg9/zniWn86QLeJvT7/pqmvfAA/HiXntF+//+b4wdNy6u+elPY8cdd+yr1VsPAQK9EBAAeoFlVgL9KdDbwX9324SAbglfCZRXYPr06XHTTTct/oT/wYceiq7XPDOk9c1vXnzefnb+ftvmm0dTnW8n3PHKK/HigQfG3N/8pnJdwEXp1KBjjz22vIXScwIDJCAADBC8zRJYkUCtg//udQoB3RK+EiinwA477FD5tH9x79vaYvC73lU5b79yOk86f781nc8/EFN2XcDUU0+N6eefX9n8oYceGhMnTowh6YJiEwEC/SMgAPSPs60QqFpgVQf/3RsSArolfCVQLoHfpE/X3//+90fzmDGxeroAN7szT3annuYGG2DPuvrqePnww6Nr9uzYKrXvuuuui/XWW69cxdJbAgMkIAAMELzNEliWQF8N/rvXLQR0S/hKoDwC733veyP7WzL6a1+LUZ//fEN3fH56avAL2XUB6QLkN6y5ZuW6gJ133rmh26xxBIogIAAUoYr6UAiBvh78d6MIAd0SvhIovkB2N5/t0yf+zaNGxXpPPRXNI0c2fKc70tOEXzrooJjzq19FS2tr/McFF8Txxx/f8O3WQAJ5FmjOc+O1nUBRBOo1+M980lAg/l8MitXS9z/84Q8jO982uwWgiQCB4gmcc845lU6NPO64XAz+s8a2jB4d426+OVZPRys62tvjhBNOiI997GMxJ90y1ESAQH0EHAGoj6u1EqhaoJ6D/6Ub4UjA0hq+J1A8gfvvvz+2zB7MtdpqlU//W9I1AHmbXr3mmnjpsMOia9asSl+y6wLWX3/9vHVDewk0vIAjAA1fIg0sskB/Df4zQ0cCirwn6RuBiMWf/h9zTORx8J/VcLV994210zMKWjfaKO5LTyJ+d7o4+NZbb1VeAgT6WMARgD4GtToC1Qr05+B/6TY5ErC0hu8JFEPgsccei03TU3ujrS3WTRfUtq61Vq471jFtWrx08MExJ50a1NzSEuefd1585jOfyXWfNJ5AIwk4AtBI1dCW0ggM1OA/A3YkoDS7mY6WSOBr6Y4/2YO+hqfbauZ98J+VrSVdxDzuxhtj9S98oXLN0mc/+9k4OAWC2emWoSYCBFZdwBGAVTe0BgK9EhjIwf/SDXUkYGkN3xPIr8D//M//xMZvfWt0NDXFupMnx6CCnTP/6vXXx0uHHBJdM2fGO9/5zrg+/bzBBhvkt2BaTqABBBwBaIAiaEJ5BBpl8J+JOxJQnv1OT4stcO6551bunjP8Ix8p3OA/q9xq6TkBa99zT7SmkPPAAw9UrgvIHnZmIkCgdgFHAGq3sySBXgk00uB/6YY7ErC0hu8J5EvgH//4R7z5LW+JBen2meum6wAGpUFyUafO6dPjxRRy5tx0U+W6gHPTaU8npScdmwgQ6L2AIwC9N7MEgV4LNOrgP+uIIwG9LqcFCDSMwL//+7/HgvnzY7X99iv04D8Db1599Rj385/HqDPOqFwXcPLJJ8eBBx4Yr776asPUQ0MI5EXAEYC8VEo7cyvQyIP/pVEdCVhaw/cEGl/gpZdeivXTufDZA7PWSafGtL3jHY3f6D5q4aspCLz80Y9G54wZMWHChMp1AX20aqshUAoBRwBKUWadHCiBvAz+Mx9HAgZqL7FdArUJXHjhhTEn3RVn2PjxpRr8Z1qr7bFHjE0hIJv+9re/Vb76DwEC1QsIANVbmZNArwTyNPjv7pgQ0C3hK4HGFpiW7pN/ybe+VWnk6qed1tiNrVPrWtZcs05rtloCxRcQAIpfYz0cAIE8Dv67mYSAbglfCTSuwCWXXBIz0+kvQ973vhiyzTaN21AtI0CgIQUEgIYsi0blWSDPg/9udyGgW8JXAo0nkF30euFFF1UaNio9KMtEgACB3goIAL0VMz+BFQgUYfDf3T0hoFvCVwKNJXDppZfGlFdeicHbbRdDd9mlsRqnNQQI5EJAAMhFmTQyDwJFGvx3ewsB3RK+EmgMgXnz5sW/X3BBpTGjTj+9MRqlFQQI5E5AAMhdyTS4EQWKOPjvdhYCuiV8JTDwApdffnk8/3//F21bbhnDPvjBgW+QFhAgkEsBASCXZdPoRhIo8uC/21kI6JbwlcDACbSnp/1+/etfrzRgVEnv/DNw+rZMoFgCAkCx6qk3/SxQhsF/N6kQ0C3hK4GBEbjyyivjqaeeikH/9E8xbO+9B6YRtkqAQCEEBIBClFEnBkKgTIP/bl8hoFvCVwL9K9DZ2RnnnntuZaPZp/9NTU392wBbI0CgUAICQKHKqTP9JVDGwX+3rRDQLeErgf4TuOaaa+Lxxx+P1re8JVY76KD+27AtESBQSAEBoJBl1al6CpR58N/tKgR0S/hKoP4CXV1dcc4551Q2tPopp0RTS0v9N2oLBAgUWkAAKHR5da6vBQz+l4gKAUssfEegngI33XRTPPjgg9Gyzjox4tBD67kp6yZAoCQCAkBJCq2bqy5g8P96QyHg9SZ+Q6CvBRZ/+n/SSdHU1tbXq7c+AgRKKCAAlLDoutx7AYP/5ZsJAcu38Q6BVRX47W9/G/fcc080r7lmjDjqqFVdneUJECBQERAA7AgEViJw9913x4c+9KGYM2dOHBbN8Z/RGk3pf6YlAq8NAR//+MeXvOk7AgRqFlj86f+nPx3Nw4bVvB4LEiBAYGkBAWBpDd8TWIbAr3/968rgf1B679PRYvC/DKPsV9slmfemgJRN119/feWr/xAgsGoC999/f2UFQ3bYYdVWZGkCBAgsJSAALIXhWwLLEjgpnXe76667xoL05m7pv49H57JmK/XvuqIrjo72uCnZDB06NK699tpSe+g8gb4SOProoyurmv4f/9FXq7QeAgQILPq4DgQBAssVyAa0N954YyUEPJ/mep8Q0MOqe/B/xaLB/8033xy77LJLj3n8QIBAbQKfTqf+DEl/g2bfcEPMf+SR2lZiKQIECLxGwBGA14D4kcCyBISAZalE+tx/4Sf/Bv/L9vFbAqsqMG7cuDjqyCPT/9m6YtqiZwGs6jotT4AAAQHAPkCgSgEhoCeUwX9PDz8RqJdAdhpi66BB8epPfhILnniiXpuxXgIESiQgAJSo2Lq66gJCwEJDg/9V35esgUC1Auutt14cesghER0dMe3cc6tdzHwECBBYroAAsFwabxBYtkDZQ4DB/7L3C78lUE+BU045JZpbWmLWD34Q7c88U89NWTcBAiUQEABKUGRd7HuBsoYAg/++35eskUA1AhtttFEceMABEQsWxLTzzqtmEfMQIEBguQICwHJpvEFgxQJlCwEG/yveH7xLoN4Cp512WkRTU8z63vei44UX6r056ydAoMACAkCBi6tr9RcoSwgw+K//vmQLBFYmsOmmm8ZeEyZEV3oquecCrEzL+wQIrEhAAFiRjvcIVCFQ9BBg8F/FTmAWAv0kUDkKkLY1Y+LE6Jg6tZ+2ajMECBRNQAAoWkX1Z0AEihoCDP4HZHeyUQLLFdhqq61i9913j66ZM2PGN76x3Pm8QYAAgRUJCAAr0vEegV4IFC0EGPz3ovhmJdCPAl/4whcqW5vxzW9GZwoCJgIECPRWQADorZj5CaxAoCghwOB/BUX2FoEBFthxxx1jp512is50ClB2KpCJAAECvRUQAHorZn4CKxHIewgw+F9Jgb1NoAEEuo8CZBcDd6aLgk0ECBDojYAA0Bst8xKoUiCvIcDgv8oCm43AAAvstttukV0P0JluBzrzu98d4NbYPAECeRMQAPJWMe3NjUDeQoDBf252LQ0lUBE4/fTTK1+nn39+dKUHhJVp6ursXBx8WtITkk0ECPROQADonZe5CfRKIC8hwOC/V2U1M4GGENhjjz1is802i45nnolZP/hBQ7SpPxrRMWVKvPDBD8aMCy+MltbW+MxnPtMfm7UNAoUSEAAKVU6daUSBRg8BBv+NuNdoE4GVCzSlpwJ3Pxdg2rnnRldHx8oXyvkc8x98MJ7beuuY8+tfx5pjx8atv/1tHHrooTnvleYT6H8BAaD/zW2xhAKNGgIM/ku4M+pyoQT233//2GijjaL9iSfi1auvLlTfXtuZWVddFc9tu220//3vsXUKAffde2/lbkivnc/PBAisXEAAWLmROQj0iUCjhQCD/z4pq5UQGFCB7Pz3U089tdKGaV/7WnR1dQ1oe+qx8ezIxpSTToqXDjooumbPjsMOOyxuv/32WHfddeuxOeskUAqBpvTHonh/LUpROp3Mq8CcdMu+8ePHx2/Toes3pk78JgbFJtG/WdzgP697j3YTeL3AgnQB8IYbbhjPpGsBxl5/faw2YcLrZ8rpbzpeeSVePOCAmJv+XrYOGhQXpfP+jz322Jz2RrMJNI5A/446GqffWkJgwAQG+kiAwf+Ald6GCdRFYFAaGJ988smVdU8755y6bGMgVjrvgQfiuXSr02zwP3bcuPjdrbca/A9EIWyzkAKOABSyrDqVB4GBOBJg8J+HPUMbCfReYO7cubH+BhvEi+m5AON++csYtvvuvV9JAy0x60c/ipePOiq60hHTbbbZJq699tpYZ511GqiFmkIg3wKOAOS7flqfY4H+PhJg8J/jnUXTCaxEYMiQIfG5z362MleejwJ0tbfHK+m2ni995COVwf+RRx4Zt912m8H/SurvbQK9FXAEoLdi5ifQxwL9cSTA4L+Pi2Z1BBpQYNasWfGm9dePqek++WulQfOQHXdswFYuv0kdL7208Hz/3/0uBrW1xcXf/GYcffTRy1/AOwQI1CzgCEDNdBYk0DcC9T4SYPDfN3WyFgKNLjB8+PA44fjjK83M21GAeemWnv/IzvdPg/83rrVW/OH3vzf4b/QdTvtyLeAIQK7Lp/FFEqjHkQCD/yLtIfpCYOUCU6dOrRwFmDVzZqz95z/H4DSobvRpZnqK8Svpk/6udB3DdtttF9dcc02slUKAiQCB+gk4AlA/W2sm0CuBvj4SYPDfK34zEyiEwOjRo+PYT36y0pdGPwpQOd8/HbF4+ZBDKoP/7HSf36UjAAb/hdgVdaLBBRwBaPACaV75BPriSIDBf/n2Gz0m0C3wQroT0AZvfnPMTXfQaVl77RicPlUfsv32lVfbO98ZTem2oQM9dbz4Yry4334xN12r0DZ4cHzrkksiu+DXRIBA/wgIAP3jbCsEeiWwKiHA4L9X1GYmUEiBiy++OM4666x4JT1Ia+mpaejQGLz11jE4CwTbblsJBy1jxiw9S92/n5dOTXph772j49lnY+10a8/r0i0+s1t9mggQ6D8BAaD/rG2JQK8EagkBBv+9IjYzgcIL/PWvf4277ror7rzzzsrXvz7+eERXV49+D3rb2xYfJciOFgzaZJNoamrqMU9f/TDziivilWOOia5582KHHXaonO8/Lj3ky0SAQP8KCAD9621rBHol0JsQYPDfK1ozEyilwJR0i9AsEHS//pQ+jZ8ze3YPi+Y11lgYCFIYyI4UZEcMmtORg1WZuhYsiFdOPDFmfvvbldV8Ml2ncNFFF0X2FGMTAQL9LyAA9L+5LRLolUA1IcDgv1ekZiZAYJFAe3rw1v3337/4CEEWDP7xj3/09EmD9Ozagcp1BFkoSK/WXjyVt/355yvn+8+7447K+f6XTpwYhx12WM9t+IkAgX4VEAD6ldvGCNQmsKIQYPBfm6mlCBBYtsBTTz21+AhBdurQXx58MDo7OnrM3JoeONZ9cXH2te0d74imlpYe82Q/zL3nnngxO9//uedinXXXjeuvuy62TkcUTAQIDKyAADCw/rZOoGqBZYWAt0ZTHB3tcUV0RnYb0Ztvvjl22WWXqtdpRgIECKxM4NVXX4277757cSjIvp82bVqPxZrSQ8gGpwt5hyw6QpBdYPzqT38arxx7bHTNnx8777xz/OQnP4mxY8f2WM4PBAgMjIAAMDDutkqgJoHXhoAdozl+avBfk6WFCBCoTaArXUT8yCOPVAJB98XFTzzxRM+VZRcRL7rY+Ph0r/8LLrggWltbe87jJwIEBkxAABgwehsmUJvA0iEgW4NP/mtztBQBAn0n8GK6r3/3hcVZKJh0773R3Nwcl/3nf8ZHP/rRvtuQNREg0CcCAkCfMFoJgf4VyELAhAkTKv/g3njjjU776V9+WyNAYCUC89JtPrPXyJEjVzKntwkQGAgBAWAg1G2TQB8JZP/ADk5P0TQRIECAAAECBKoVEACqlTIfAQIECBAgQIAAgQIINBegD7pAgAABAgQIECBAgECVAgJAlVBmI0CAAAECBAgQIFAEAQGgCFXUBwIECBAgQIAAAQJVCggAVUKZjQABAgQIECBAgEARBASAIlRRHwgQIECAAAECBAhUKSAAVAllNgIECBAgQIAAAQJFEBAAilBFfSBAgAABAgQIECBQpYAAUCWU2QgQIECAAAECBAgUQUAAKEIV9YEAAQIECBAgQIBAlQICQJVQZiNAgAABAgQIECBQBAEBoAhV1AcCBAgQIECAAAECVQoIAFVCmY0AAQIECBAgQIBAEQQEgCJUUR8IECBAgAABAgQIVCkgAFQJZTYCBAgQIECAAAECRRAQAIpQRX0gQIAAAQIECBAgUKWAAFAllNkIECBAgAABAgQIFEFAAChCFfWBAAECBAgQIECAQJUCAkCVUGYjQIAAAQIECBAgUAQBAaAIVdQHAgQIECBAgAABAlUKCABVQpmNAAECBAgQIECAQBEEBIAiVFEfCBAgQIAAAQIECFQpIABUCWU2AgQIECBAgAABAkUQEACKUEV9IECAAAECBAgQIFClgABQJZTZCBAgQIAAAQIECBRBQAAoQhX1gQABAgQIECBAgECVAgJAlVBmI0CAAAECBAgQIFAEAQGgCFXUBwIECBAgQIAAAQJVCggAVUKZjQABAgQIECBAgEARBASAIlRRHwgQIECAAAECBAhUKSAAVAllNgIECBAgQIAAAQJFEBAAilBFfSBAgAABAgQIECBQpYAAUCWU2QgQIECAAAECBAgUQUAAKEIV9YEAAQIECBAgQIBAlQICQJVQZiNAgAABAgQIECBQBAEBoAhV1AcCBAgQIECAAAECVQoIAFVCmY0AAQIECBAgQIBAEQQEgCJUUR8IECBAgAABAgQIVCkgAFQJZTYCBAgQIECAAAECRRAQAIpQRX0gQIAAAQIECBAgUKWAAFAllNkIECBAgAABAgQIFEFAAChCFfWBAAECBAgQIECAQJUCAkCVUGYjQIAAAQIECBAgUAQBAaAIVdQHAgQIECBAgAABAlUKCABVQpmNAAECBAgQIECAQBEEBIAiVFEfCBAgQIAAAQIECFQpIABUCWU2AgQIECBAgAABAkUQEACKUEV9IECAAAECBAgQIFClgABQJZTZCBAgQIAAAQIECBRBQAAoQhX1gQABAgQIECBAgECVAgJAlVBmI0CAAAECBAgQIFAEAQGgCFXUBwIECBAgQIAAAQJVCggAVUKZjQABAgQIECBAgEARBASAIlRRHwgQIECAAAECBAhUKSAAVAllNgIECBAgQIAAAQJFEBAAilBFfSBAgAABAgQIECBQpYAAUCWU2QgQIECAAAECBAgUQUAAKEIV9YEAAQIECBAgQIBAlQICQJVQZiNAgAABAgQIECBQBAEBoAhV1AcCBAgQIECAAAECVQoIAFVCmY0AAQIECBAgQIBAEQQEgCJUUR8IECBAgAABAgQIVCkgAFQJZTYCBAgQIECAAAECRRAQAIpQRX0gQIAAAQIECBAgUKWAAFAllNkIECBAgAABAgQIFEFAAChCFfWBAAECBAgQIECAQJUCAkCVUGYjQIAAAQIECBAgUAQBAaAIVdQHAgQIECBAgAABAlUKCABVQpmNAAECBAgQIECAQBEEBIAiVFEfCBAgQIAAAQIECFQpIABUCWU2AgQIECBAgAABAkUQEACKUEV9IECAAAECBAgQIFClgABQJZTZCBAgQIAAAQIECBRBQAAoQhX1gQABAgQIECBAgECVAgJAlVBmI0CAAAECBAgQIFAEAQGgCFXUBwIECBAgQIAAAQJVCggAVUKZjQABAgQIECBAgEARBASAIlRRHwgQIECAAAECBAhUKSAAVAllNgIECBAgQIAAAQJFEBAAilBFfSBAgAABAgQIECBQpYAAUCWU2QgQIECAAAECBAgUQUAAKEIV9YEAAQIECBAgQIBAlQICQJVQZiNAgAABAgQIECBQBAEBoAhV1AcCBAgQIECAAAECVQoIAFVCmY0AAQIECBAgQIBAEQQEgCJUUR8IECBAgAABAgQIVCkgAFQJZTYCBAgQIECAAAECRRAQAIpQRX0gQIAAAQIECBAgUKWAAFAllNkIECBAgAABAgQIFEFAAChCFfWBAAECBAgQIECAQJUCAkCVUGYjQIAAAQIECBAgUAQBAaAIVdQHAgQIECBAgAABAlUKCABVQpmNAIHaBZ544ok49thj46qrroqZM2fWviJLEiBAgAABAqss0NSVplVeixUQIEBgOQKzZ8+OrbbaKh577LHKHG1tbfGBD3wg9tlnnxg/fnyMHj16OUv6NQECBAgQIFAPAQGgHqrWSYDAYoEjjzwyvve970XLehEta0TMfzC9tehjh9bW1th1110rYWDChAmx5pprLl7ONwQIECBAgEB9BASA+rhaKwECSeCnP/1p7L///tHUFvGGK1pi0IZN0fFKV8z9fVfM+V1XzL8/JYGOhVTNzc2x8847V8LAXnvtFWuvvTZDAv0ucMcdd8QDDzzQ79td2Qaz/3986EMfig022GBls3qfAAECKxUQAFZKZAYCBGoReOqpp2KLLbaI6dOnx+onN8dqe7/+kqPO6SkM3LYwDMz7UwoD7Uu2tN1228W+++4bWRgw6Fni4rv6CTz66KPxjndsER0dS+2I9dtcr9f81re+NR5++OEYNGhQr5e1AAECBJYWEACW1vA9AQJ9ItDR0RE77bRT3HXXXTFkp6ZY47yWla6389UUBm5Pr1u7Yt49XdE1b8ki2TUE2TUDe++9d2SDIBOBegjstttuccstt6RV75xem9djE6uwzv+Xlv2fOP/88+Nzn/vcKqzHogQIEIgQAOwFBAj0ucDpp58e55xzTjSnU/rHXtkSzas39WobnXNSCLhr0ZGB9LVr9pLFN99880oYyALBZptttuQN3xFYBYGf//znseeee6Y1ZBelT06vMauwtnos+su00g/GyJGrx+TJf4uxY8fWYyPWSYBASQQEgJIUWjcJ9JfAH/7wh3jve9+brvPtijHfbonB7+rd4P+17eyan8LA3QvDwNw70lqXuotodjQgO00oCwNbbrnlaxf1M4GqBObPnx+bbrppZLerjbg4vT5V1XL9P9P4tMmbIruw/jvf+U7/b94WCRAojIAAUJhS6giBgReYMmVKZJ/QP/fcczH8iKYYedTKT/3pTau72lMY+HM6TShdQJxdO9A5bcnS2XUCWRDIXu95z3uiqWnVgseSNfuu6ALnnXdenHLKKambb0+vv6RXa4N2+W+pXZulfbsj7r13UrzrXe9q0HZqFgECjS4gADR6hbSPQI4Eslt53nDDDdH2jnQCxcSWaGqp3yC8qyPdReiBdGQgXTMw9w8pDLy8BCq7g1B2vUB2dGCHHXaIlpa+DSJLtuS7vAu88MILsfHGb00PqJuRuvKr9NqtwbuUnf9/QeUam+xom4kAAQK1CAgAtahZhgCB1wlccsklcdxxx0XT8Ig103n/rW+s3+D/tRvPnme44KFItxbtrNxitOP/lsyRPVsgu5NQdmQgOzXJHVSW2Pgu4ogjjojLL788UeyRXjfkgGR6amN2IfyLcfXVV1dus5uDRmsiAQINJiAANFhBNIdAHgUeeuih2HrrrWPevHkx+qvNMfRfXn/Lz/7s1/zHstOEOivPGuh4ZsmWR40aVbnQMwsD2R1fBg8evORN35VO4L777ktPqd46urqyU34eSa+NcmLw3dTOo2L99devPGF76NChOWm3ZhIg0CgCAkCjVEI7CORUYM6cOWkQtVVk91AfNqEpRn2+sU63WfBEdgFxOjKQrhto//sS5OHDh8f48eMrRwY++MEPxrBhw5a86btSCOy4446RPfgr4qT0Oi9Hfe5Mbd0qve6Ps846K84444wctV1TCRBoBAEBoBGqoA0Ecixw9NFHx2WXXRatG6RTf76fzvsf0n+n/vSWrf3pRdcMpECw4PElS2efoGYhIDsy8G//9m/pVosjl7zpu0IKXHXVVXHQQQelvo1Lr+zi2rzV/LbU5p1j6NBh8be/PR7rrrtu+tlEgACB6gQEgOqczEWAwDIErrnmmthvv/2iqS3iDZe3xKCNGnfw/9rmtz+38G5C2dGBBQ8vebetrS0uuuiiOOaYY5b80neFEsiOWm2yySbxzDPZ+WHfS6/Dc9q/A1K7fxIf/vCH40c/+lFO+6DZBAgMhIAAMBDqtkmgAAJPP/10bLHFFjFt2rRY/XPNsdq+A3ve/6qQdryYjgykOwnN+UUKA4+mxy2lowE333zzqqzSsg0scOaZZ1ZOnYnInh3x5/TK6777VGr7P6XXnMpTt7fddtv0vYkAAQIrF8jrX72V98wcBAjUTaCjoyMOPvjgyuB/8I5NuR78Z0gtY5ti+H7NMeLIhX8Ss7sKmYopkH3qf9555y/q3DfS1zz/M7h+an92/ULE8ccfny5mtt9WMPyHAIGVCuT5L99KO2cGAgTqI/DlL3+5cvFk85oRo08v0J+R/JzBVJ/ClmCtJ598csyZMzv19MD02qEAPc4eYLZuTJo0Kb7//e8XoD+6QIBAfwgU6F/u/uCyDQIEbr/99jj77LMj0mB59JnN0by6UbO9Ih8Cd955Z2QX/0Zkt83M011/VuSb3b3q65UZTj31tPRAs5krmtl7BAgQqAgIAHYEAgSqFpg6dWrlgsPOzs4YfmhTDH63PyFV45lxQAWyffaEE05Y1IbsU/P1BrQ9fbvxD6fVbRsvvPB8nHPOOX27amsjQKCQAv71LmRZdYpAfQSyp6Y+++yzMWjziBFH+PNRH2VrrYfAFVdcEffee29adTbwX3jefD22M3Dr/GbadFNceOFF8eSTTw5cM2yZAIFcCPgXPBdl0kgCAy8wceLEuP7666NptXTqz5fT/f5bnfoz8FXRgmoEstNiTjvtC4tmzU79yU6bKdqUPRjskJg/f1589rOfLVrn9IcAgT4WEAD6GNTqCBRR4JFHHonPfOYzla6NOrU5Wtcy+C9inYvap6985Svx4osvpO5tn17Zxb9Fnb6WOjYibrjhhvjtb39b1E7qFwECfSAgAPQBolUQKLLA3Llz48ADD4zs67A9mmLo+/zZKHK9i9a3J554Ij3Yrft2n9nXIk9vTJ1beKTjxBNPjOx2vSYCBAgsS8C/5MtS8TsCBBYLfPrTn46HH344WtMtx0d+xp+MxTC+yYVAduRqwYL5qa2Hpte7c9HmVWvkiWnxDSv/n7300ktXbVWWJkCgsAL+NS9saXWMwKoLZOf8Z4OIpkHpvP+zW6J5iFN/Vl3VGvpL4JZbbokbb7wxbW5Een21vzY7wNsZnLb/75U2nHHGlyK7c5eJAAECrxUQAF4r4mcCBCoC2d1+srv+ZNOI45pj0MYG/xUM/8mFQHt7e2SnwSycvpi+jMtFu/umkRPSanaNKVNeiS996Ut9s0prIUCgUAICQKHKqTME+kYgO3f44IMPrnx6OHj7phi+vz8VfSNrLf0lkN216tFHH02b2yi9uu//319bb4TtXJQa0RLf/na3QyO0SRsIEGgUAf+qN0oltINAAwlkDxO67bbbovkNEaO+6M9EA5VGU6oQmDJlSvrk+8xFc16QvrZVsVTRZtksdegT6ULgpY+EFK2P+kOAQK0C/mWvVc5yBAoqcMcdd8RZZ52VPVMoRp/ZHC2jnPpT0FIXtltnnHFGOno1JfXv/em1R2H7ufKOpf8fx+jIroX4+c9/vvLZzUGAQGkEBIDSlFpHCaxcILtgMDv1p7OzM4Z/rCkGb+VPxMrVzNFIAtkdqyZOzO5+05pe2WkwZZ7GpM5nISAqDwebPz+7G5KJAAECEf51txcQILBY4Kijjoqnn346Bm2aLvw9yp+HxTC+yY1AduFvZ2d2//tj0uvtuWl3/Rq60CF7HsI3vlH05yDUT9GaCRRNwL/wRauo/hCoUeCyyy6La6+9NppWSycNfKUlmlqd+lMjpcUGSOBnP/vZoifgrpFacOYAtaLRNrvkSMhXvnJ2vPBC9kRkEwECZRcQAMq+B+g/gSSQ3S3lhBMW3ill1CnN0bq2wb8dI18C8+bNi8997nOLGv3l9DULAaaFAtm1EONj5swZcdppp0EhQICAU4DsAwTKLjB37tw48MADI/s69N+aYuhuPhco+z6Rx/5fdNFF8eSTT6amL7z7TR77UN82/0dafVtcccX347777qvvpqydAIGGF/AvfcOXSAMJ1Fcg+9T0oYceipY3Raz+WX8S6qtt7fUQeP755+Pss89ZtOoL09eWemwm5+tc+DyErq7OxUf7ct4hzSdAYBUE/Gu/CngWJZB3gZtvvjm+9a1vVW6YskY67795aMlP/enKe0XL2f4vfOELMWvWzNT5PdPrfeVEqKrXp6e5xkV2q9+rr766qiXMRIBAMQUEgGLWVa8IVCWQ3R88mwZtkjLAW6taxEwEGk4gG9AunP6t4drWWA0amZqzY6VJd955Z2M1TWsIEOhXAQGgX7ltjEBjCZx00kkxZsyYWPBIxKs/9vF39vAzU/4Esv144XR2+jI3fx3otxZn5/5fF4MGtcVxxx3Xb1u1IQIEGk9AAGi8mmgRgX4TWHvttdNFgVdUtjdjYmfM/6sQ0G/4NtRnAocffni8853vTOt7Kr3O67P1Fm9F2Z2+OuPEE0+IjTfeuHjd0yMCBKoWEACqpjIjgWIKjB8/Po4//viI9oipX+yIztlCQDErXdxeNTc3L/WQq6+njv6juJ2tuWdXpSXviDXXHBunn55dC2AiQKDMAgJAmauv7wQWCZx33nmxxRZbRMczEdPP7+RCIHcCO+20U+y///6p3bPT6+Tctb++DZ6TVn9KZRPnnvu1GDkyuxbARIBAmQUEgDJXX98JLBIYPHhwXHXVVTF06NCY84uumP0rIcDOkT+BLMgOHjwkNfy/0+uP+etA3VqcHRV5Orbccss49NBD67YVKyZAID8CAkB+aqWlBOoq8La3vS0uvvjiyjamn9cZ7f9wKlBdwa28zwXWX3/9OPnk7ILgbN/Nzne3D0ekw3pxfnpF5TSp7HQpEwECBPwlsA8QILBY4Igjjoj99tsvul5deD1AV7sB1GIc3+RC4POf/3ysvfY6qa1/Tq//ykWb69vI7HSo2ZWnfe+www713ZS1EyCQGwEBIDel0lAC/SNw2WWXRfZJ6oJHI2Ze6lSg/lG3lb4SGDZsWJx/fvedgE5Lq53VV6vO4Xqye/1fFUOGDI2vfz07DchEgACBhQICgD2BAIEeAqNGjYof//jHkZ0qMOvKrpj3JyGgB5AfGl7goIMOim233Ta18//SK3s2QBmn7tOg0uW/p5wcb3rTm8qIoM8ECCxHQABYDoxfEyizwHbbbRdf/vKXKwRTz+qMjqlOBSrz/pC3vjc1NS26LWj2ZLeL0uvveetCH7T3irSOe2O99dZL10W4K1IfgFoFgUIJCACFKqfOEOg7gVNPPTV22WWX6HwlYtpXHAXoO1lr6g+BrbfeOt3x5pC0qXnp9dn+2GQDbWNmakt2+lN6LFq6M1J2WpSJAAECSwsIAEtr+J4AgcUC2SlAV155Zayxxhox766umPXfQsBiHN/kQuCrX/1qrLba8NTWn6XXb3PR5r5p5FfSal6I7bffvnLxb9+s01oIECiSgABQpGrqC4E+FlhnnXXi8ssvr6x1xrc6Y8HjTgXqY2Krq6PAWmutFV/8YvdTb09MW+qo49YaZdVPpIZ8I726T4NqlHZpBwECjSQgADRSNbSFQAMK7LnnnvGpT30qoj1iyhc7onOOENCAZdKk5QiceOKJ8Za3vCW9+3B6XbqcuYr06+x0p/lx+OGHxbvf/e4idUxfCBDoQwEBoA8xrYpAUQXOP//82HzzzaPj6YjpFzgVqKh1LmK/sqdcX3DBBYu69qX0dWoRu7moT7ekrz+P4cNHRHb6k4kAAQLLExAAlifj9wQILBYYMmRIXHVVdj/xITHnpq6Y82shYDGObxpeYMKECbHrrrumdqYr2iMLAUWc0iG6+HSlY2ec8cUYN25cETupTwQI9JGAANBHkFZDoOgCb3/72+Ob3/xmpZvTvt4Z7c85FajoNS9S/y666KL0bIuW1KWJ6ZWecle4KevXI7HRRhvFCSecULje6RABAn0rIAD0rae1ESi0wFFHHRX77LNPdL2aTqRI1wN0tQsBhS54gTq32WabxSc+cXTq0ZJPyovTvSmpK2dWupOd7tTW1lacrukJAQJ1ERAA6sJqpQSKK/Cd73yn8nChBY9EzLzMqUDFrXTxepY93G7UqNGpY79OrxsL1MEzUl+mxPvf//7YY489CtQvXSFAoF4CAkC9ZK2XQEEFRo8eHT9s/1D2AAAPsklEQVT+8Y/T6RTNMeuHXTFvkhBQ0FIXrltjxoxJT7g+a1G/Ft4tJ/+dTEk83d2opaU1Lrzwwvx3Rw8IEOgXAQGgX5hthECxBHbYYYf40pfSxZTpDKCpZ3ZGx7RinArUObNYddKb1wscc8wxkV3PEjE5vbL75ed9Wvh8g2OO+URsuummee+M9hMg0E8CTV1p6qdt2QwBAgUS6OjoiH/5l3+J2267LQZv3xRjLsgusMzftOB/u2Lu77NXetDZXxe2PzuN4oYbbshfZ7S4KoFf//rXsfvuu6d5R6bX39Irr3fMyfbRCTF69BrxxBOTK0/tTr8wESBAYKUCjgCslMgMBAgsS6ClpSV+9KMfpcHH6Jh3Z1fMujo/pwIteKIrZlzWES8e1B4vHdgRMy9dOPgfPnx4HHjggXHuuecuq8t+VxCB3XbbLcaPH596MyO9vpDTXs1P7c5OY4r4yle+bPBfkfAfAgSqFXAEoFop8xEgsEyB66+/Pvbee+9oGhTxhstbYtDGTcucb6B/Of+v6VP+Wztjzu+6ouOZJa3JAkz2iX92d6NsYJg9OMpUfIHJkyenU2Y2iwULsrsC/Tm9tsxZp7+e2vv5ymk/f/nLX9I1APk8ApczdM0lUBgBAaAwpdQRAgMn8MlPfjImTpwYreunEPBfLdE8ZOBDQHZ244KHIg34O2NuNuh/fonP2LFjY88996wM+rMHRLW2ti5503elETj55JMje8p1xA7pdXuO+p3tzG9Nr5lxyy23xPve974ctV1TCRBoBAEBoBGqoA0Eci4wZ86c+Od//ud4+OGHY9j4phj1hYH5NLKroyvmP5CeVHzrwvP6O7MHvy6a1llnndhrr70qg/6ddtqpchej7vd8LafAjBkzYuON3xovvvhCAvjv9DowJxCHp3ZeUQmxP/vZz3LSZs0kQKCRBASARqqGthDIsUA2+N96661j7ty5Mfqc5hi6a/9cYpQ9jGzepDTgT5/yZxfzdk5fgvjmN7+5cnpSdnrPe97znmhqGvgjE0ta57tGEPje974XRx55ZGrKeun1eHoNbYRmraANk9J7/xyDBg2Kxx57NDbccMMVzOstAgQILFtAAFi2i98SIFCDwKWXXhrZbRabhkes+cOWaF2rPgPurnlp0H9P+qQ/G/Tf3hVds5Y0dpNNNlk86H/3u9+95A3fEViGQGdnZyW43nfffendM9PrS8uYq5F+tX1qzF1xyimnuFi9kcqiLQRyJiAA5Kxgmkug0QWyC4KzC4MHbZ6uB5jYEk2tfRMCOuekQf8fFw76592RBv1zlkhsvvnmlVN7sk/6N9tssyVv+I5AFQJ33HFH7LjjjmnOYemV3Qs2OxrQiNOPU6MOjnHj3hiTJ/8tRowY0YiN1CYCBHIgIADkoEiaSCBPAlOmTIktttginn322Rh+WFOMPLr26wE6Z6VP+NNgPzu9Z97dadA/b4lE9ul+NuDfd99903ncGy95w3cEahDIbv969dVXpyWz6wCy6wEabZqdGrRJej0bl19+eRx22GGN1kDtIUAgRwICQI6KpakE8iKQPRzsve99b3R2dcaYS5pj8Lurvx6gc3oa8N+26JP+P6XnFGZ3aVw0bbfddos/6V9//XTLIROBPhJ4+umnY5NN3pauYckOLd2RXtmpNo00ZacmfTm22mqr+NOf/uR6lkYqjbYQyKGAAJDDomkygTwInHnmmXHWWWdF85oRY69MtwZdffmnAnW8kgb9f1g46J9/Xxr0dyzsYXNzc+y8886VQX92atFaa62Vh65rY04FuvfZiNbUg7YG60UWTLrizjvvjCwImwgQILAqAgLAquhZlgCB5Qp0dHTELrvsEtn51YN3bIox5/c8FajjhUUX8ab79M9/MK0mjfuzKbsnf3Zv/uz0ngkTJsSaa6YEYSLQDwKzZ8+u3M72kUce6Yet9X4Tn/jEJyrP2+j9kpYgQIBATwEBoKeHnwgQ6EOB7LSK7HqAadOmxeqfS6cCvaepcqvOOemJvAseXbKh7Om7u+++e2XQnz2Vd9SoUUve9B2BfhTIHiCXPdei0absaNiQIUMarVnaQ4BATgUEgJwWTrMJ5EXg2muvrVyoG9kZQIs+5c/aPmzYsPjXf/3XyqA/+zp8eLp3qIkAAQIECBCou4AAUHdiGyBAIHs2QPaMgJEjR8b48eMrg/4PfOADMXRooz90Se0IECBAgEDxBASA4tVUjwg0nEB2WkX2oKXsfv1tbY12cWXDcWkQAQIECBCoq4AAUFdeKydAgAABAgQIECDQWALV35y7sdqtNQQIECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUICAA1oFmEAAECBAgQIECAQF4FBIC8Vk67CRAgQIAAAQIECNQgIADUgGYRAgQIECBAgAABAnkVEADyWjntJkCAAAECBAgQIFCDgABQA5pFCBAgQIAAAQIECORVQADIa+W0mwABAgQIECBAgEANAgJADWgWIUCAAAECBAgQIJBXAQEgr5XTbgIECBAgQIAAAQI1CAgANaBZhAABAgQIECBAgEBeBQSAvFZOuwkQIECAAAECBAjUICAA1IBmEQIECBAgQIAAAQJ5FRAA8lo57SZAgAABAgQIECBQg4AAUAOaRQgQIECAAAECBAjkVUAAyGvltJsAAQIECBAgQIBADQICQA1oFiFAgAABAgQIECCQVwEBIK+V024CBAgQIECAAAECNQgIADWgWYQAAQIECBAgQIBAXgUEgLxWTrsJECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUICAA1oFmEAAECBAgQIECAQF4FBIC8Vk67CRAgQIAAAQIECNQgIADUgGYRAgQIECBAgAABAnkVEADyWjntJkCAAAECBAgQIFCDgABQA5pFCBAgQIAAAQIECORVQADIa+W0mwABAgQIECBAgEANAgJADWgWIUCAAAECBAgQIJBXAQEgr5XTbgIECBAgQIAAAQI1CAgANaBZhAABAgQIECBAgEBeBQSAvFZOuwkQIECAAAECBAjUICAA1IBmEQIECBAgQIAAAQJ5FRAA8lo57SZAgAABAgQIECBQg4AAUAOaRQgQIECAAAECBAjkVUAAyGvltJsAAQIECBAgQIBADQICQA1oFiFAgAABAgQIECCQVwEBIK+V024CBAgQIECAAAECNQgIADWgWYQAAQIECBAgQIBAXgUEgLxWTrsJECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUICAA1oFmEAAECBAgQIECAQF4FBIC8Vk67CRAgQIAAAQIECNQgIADUgGYRAgQIECBAgAABAnkVEADyWjntJkCAAAECBAgQIFCDgABQA5pFCBAgQIAAAQIECORVQADIa+W0mwABAgQIECBAgEANAgJADWgWIUCAAAECBAgQIJBXAQEgr5XTbgIECBAgQIAAAQI1CAgANaBZhAABAgQIECBAgEBeBQSAvFZOuwkQIECAAAECBAjUICAA1IBmEQIECBAgQIAAAQJ5FRAA8lo57SZAgAABAgQIECBQg4AAUAOaRQgQIECAAAECBAjkVUAAyGvltJsAAQIECBAgQIBADQICQA1oFiFAgAABAgQIECCQVwEBIK+V024CBAgQIECAAAECNQgIADWgWYQAAQIECBAgQIBAXgUEgLxWTrsJECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUICAA1oFmEAAECBAgQIECAQF4FBIC8Vk67CRAgQIAAAQIECNQgIADUgGYRAgQIECBAgAABAnkVEADyWjntJkCAAAECBAgQIFCDgABQA5pFCBAgQIAAAQIECORVQADIa+W0mwABAgQIECBAgEANAgJADWgWIUCAAAECBAgQIJBXAQEgr5XTbgIECBAgQIAAAQI1CAgANaBZhAABAgQIECBAgEBeBQSAvFZOuwkQIECAAAECBAjUICAA1IBmEQIECBAgQIAAAQJ5FRAA8lo57SZAgAABAgQIECBQg4AAUAOaRQgQIECAAAECBAjkVUAAyGvltJsAAQIECBAgQIBADQICQA1oFiFAgAABAgQIECCQVwEBIK+V024CBAgQIECAAAECNQgIADWgWYQAAQIECBAgQIBAXgUEgLxWTrsJECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUICAA1oFmEAAECBAgQIECAQF4FBIC8Vk67CRAgQIAAAQIECNQgIADUgGYRAgQIECBAgAABAnkVEADyWjntJkCAAAECBAgQIFCDgABQA5pFCBAgQIAAAQIECORVQADIa+W0mwABAgQIECBAgEANAgJADWgWIUCAAAECBAgQIJBXAQEgr5XTbgIECBAgQIAAAQI1CAgANaBZhAABAgQIECBAgEBeBQSAvFZOuwkQIECAAAECBAjUICAA1IBmEQIECBAgQIAAAQJ5FRAA8lo57SZAgAABAgQIECBQg4AAUAOaRQgQIECAAAECBAjkVUAAyGvltJsAAQIECBAgQIBADQICQA1oFiFAgAABAgQIECCQVwEBIK+V024CBAgQIECAAAECNQgIADWgWYQAAQIECBAgQIBAXgUEgLxWTrsJECBAgAABAgQI1CAgANSAZhECBAgQIECAAAECeRUQAPJaOe0mQIAAAQIECBAgUIOAAFADmkUIECBAgAABAgQI5FVAAMhr5bSbAAECBAgQIECAQA0CAkANaBYhQIAAAQIECBAgkFcBASCvldNuAgQIECBAgAABAjUI/H8bh7akqJPl6QAAAABJRU5ErkJggg==" width="384" /></p>
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</div>
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<div id="rotated-and-stretched-polygons" class="section level2">
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<h2>Rotated and stretched polygons</h2>
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<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">g2 <-<span class="st"> </span><span class="kw">ngonGrob</span>(<span class="kw">unit</span>(xy[,<span class="dv">1</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="kw">unit</span>(xy[,<span class="dv">2</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="dt">n=</span><span class="kw">seq_len</span>(N)<span class="op">+</span><span class="dv">2</span>, <span class="dt">ar=</span><span class="kw">seq_len</span>(N),
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<span class="dt">phase=</span><span class="dv">0</span>, <span class="dt">angle=</span>pi<span class="op">/</span>(<span class="kw">seq_len</span>(N)<span class="op">+</span><span class="dv">2</span>),
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<span class="dt">size=</span><span class="dv">1</span><span class="op">:</span>N<span class="op">+</span><span class="dv">5</span>, <span class="dt">gp=</span><span class="kw">gpar</span>(<span class="dt">fill=</span><span class="dv">1</span><span class="op">:</span>N))
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<span class="kw">grid.newpage</span>()
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<span class="kw">grid.draw</span>(g2)</code></pre></div>
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<p><img 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" width="384" /></p>
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</div>
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<div id="ellipses" class="section level2">
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<h2>Ellipses</h2>
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<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">g3 <-<span class="st"> </span><span class="kw">ellipseGrob</span>(<span class="kw">unit</span>(xy[,<span class="dv">1</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="kw">unit</span>(xy[,<span class="dv">2</span>],<span class="st">"cm"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">unit</span>(<span class="fl">0.5</span>,<span class="st">"npc"</span>),
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<span class="dt">angle=</span><span class="op">-</span><span class="dv">2</span><span class="op">*</span><span class="kw">seq</span>(<span class="dv">0</span>,N<span class="op">-</span><span class="dv">1</span>)<span class="op">*</span>pi<span class="op">/</span>N<span class="op">+</span>pi<span class="op">/</span><span class="dv">2</span>,
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<span class="dt">size=</span><span class="dv">5</span>, <span class="dt">ar=</span><span class="dv">3</span>, <span class="dt">gp=</span><span class="kw">gpar</span>(<span class="dt">fill=</span><span class="dv">1</span><span class="op">:</span>N))
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<span class="kw">grid.newpage</span>()
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<span class="kw">grid.draw</span>(g3)</code></pre></div>
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<p><img 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