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+<meta name="description" content="Using Pysketcher to Create Principal Sketches of Physics Problems">
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+<meta name="keywords" content="tree data structure,recursive function calls">
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+
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+<title>Using Pysketcher to Create Principal Sketches of Physics Problems</title>
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+
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+<!-- Bootstrap style: bootswatch_readable -->
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+<link href="http://netdna.bootstrapcdn.com/bootswatch/3.1.1/readable/bootstrap.min.css" rel="stylesheet">
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+</head>
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+
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+<!-- tocinfo
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+{'highest level': 1,
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+ 'sections': [('A first glimpse of Pysketcher', 1, None, '___sec0'),
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+ ('Basic construction of sketches', 2, None, '___sec1'),
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+ ('Basic drawing', 3, None, '___sec2'),
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+ ('Groups of objects', 3, None, '___sec3'),
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+ ('Changing line styles and colors', 3, None, '___sec4'),
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+ ('The figure composition as an object hierarchy',
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+ 3,
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+ None,
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+ '___sec5'),
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+ ('Animation: translating the vehicle', 3, None, '___sec6'),
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+ ('Animation: rolling the wheels',
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+ 3,
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+ 'sketcher:vehicle1:anim',
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+ 'sketcher:vehicle1:anim'),
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+ ('A simple pendulum',
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+ 1,
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+ 'sketcher:ex:pendulum',
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+ 'sketcher:ex:pendulum'),
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+ ('The basic physics sketch',
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+ 2,
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+ 'sketcher:ex:pendulum:basic',
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+ 'sketcher:ex:pendulum:basic'),
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+ ('The body diagram', 2, None, '___sec10'),
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+ ('Animated body diagram',
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+ 2,
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+ 'sketcher:ex:pendulum:anim',
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+ 'sketcher:ex:pendulum:anim'),
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+ ('Function for drawing the body diagram', 3, None, '___sec12'),
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+ ('Equations for the motion and forces', 3, None, '___sec13'),
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+ ('Numerical solution', 3, None, '___sec14'),
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+ ('Animation', 3, None, '___sec15'),
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+ ('Basic shapes', 1, None, '___sec16'),
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+ ('Axis', 2, None, '___sec17'),
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+ ('Distance with text', 2, None, '___sec18'),
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+ ('Rectangle', 2, None, '___sec19'),
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+ ('Triangle', 2, None, '___sec20'),
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+ ('Arc', 2, None, '___sec21'),
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+ ('Spring', 2, None, '___sec22'),
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+ ('Dashpot', 2, None, '___sec23'),
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+ ('Wavy', 2, None, '___sec24'),
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+ ('Stochastic curves', 2, None, '___sec25'),
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+ ('Inner workings of the Pysketcher tool', 1, None, '___sec26'),
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+ ('Example of classes for geometric objects',
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+ 2,
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+ None,
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+ '___sec27'),
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+ ('Simple geometric objects', 3, None, '___sec28'),
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+ ('Class curve', 3, None, '___sec29'),
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+ ('Compound geometric objects', 3, None, '___sec30'),
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+ ('Adding functionality via recursion', 2, None, '___sec31'),
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+ ('Basic principles of recursion', 3, None, '___sec32'),
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+ ('Explaining recursion', 3, None, '___sec33'),
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+ ('Scaling, translating, and rotating a figure',
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+ 2,
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+ 'sketcher:scaling',
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+ 'sketcher:scaling'),
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+ ('Scaling', 3, None, '___sec35'),
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+ ('Translation', 3, None, '___sec36'),
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+ ('Rotation', 3, None, '___sec37')]}
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+end of tocinfo -->
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+
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+<body>
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+ }
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+<script type="text/javascript"
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+</script>
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+
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+<!-- newcommands.tex -->
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+$$
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+\newcommand{\half}{\frac{1}{2}}
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+\newcommand{\tp}{\thinspace .}
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+\newcommand{\rpos}{\boldsymbol{r}}
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+\newcommand{\ii}{\boldsymbol{i}}
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+\newcommand{\ir}{\boldsymbol{i}_r}
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+\newcommand{\ith}{\boldsymbol{i}_{\theta}}
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+$$
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+
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+
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+
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+
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+
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+<!-- Bootstrap navigation bar -->
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+<div class="navbar navbar-default navbar-fixed-top">
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+ <div class="navbar-header">
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+ <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
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+ <span class="icon-bar"></span>
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+ <span class="icon-bar"></span>
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+ <span class="icon-bar"></span>
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+ </button>
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+ <a class="navbar-brand" href="pysketcher.html">Using Pysketcher to Create Principal Sketches of Physics Problems</a>
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+ </div>
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+
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+ <div class="navbar-collapse collapse navbar-responsive-collapse">
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+ <ul class="nav navbar-nav navbar-right">
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+ <li class="dropdown">
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+ <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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+ <ul class="dropdown-menu">
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec0" style="font-size: 80%;"><b>A first glimpse of Pysketcher</b></a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec1" style="font-size: 80%;"> Basic construction of sketches</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec2" style="font-size: 80%;"> Basic drawing</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec3" style="font-size: 80%;"> Groups of objects</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec4" style="font-size: 80%;"> Changing line styles and colors</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec5" style="font-size: 80%;"> The figure composition as an object hierarchy</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#___sec6" style="font-size: 80%;"> Animation: translating the vehicle</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher002.html#sketcher:vehicle1:anim" style="font-size: 80%;"> Animation: rolling the wheels</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#sketcher:ex:pendulum" style="font-size: 80%;"><b>A simple pendulum</b></a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#sketcher:ex:pendulum:basic" style="font-size: 80%;"> The basic physics sketch</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#___sec10" style="font-size: 80%;"> The body diagram</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#sketcher:ex:pendulum:anim" style="font-size: 80%;"> Animated body diagram</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#___sec12" style="font-size: 80%;"> Function for drawing the body diagram</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#___sec13" style="font-size: 80%;"> Equations for the motion and forces</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#___sec14" style="font-size: 80%;"> Numerical solution</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher003.html#___sec15" style="font-size: 80%;"> Animation</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;"><b>Basic shapes</b></a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;"> Axis</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec18" style="font-size: 80%;"> Distance with text</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;"> Rectangle</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;"> Triangle</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;"> Arc</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;"> Spring</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;"> Dashpot</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;"> Wavy</a></li>
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+ <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;"> Stochastic curves</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec26" style="font-size: 80%;"><b>Inner workings of the Pysketcher tool</b></a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec27" style="font-size: 80%;"> Example of classes for geometric objects</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec28" style="font-size: 80%;"> Simple geometric objects</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec29" style="font-size: 80%;"> Class curve</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec30" style="font-size: 80%;"> Compound geometric objects</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec31" style="font-size: 80%;"> Adding functionality via recursion</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec32" style="font-size: 80%;"> Basic principles of recursion</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec33" style="font-size: 80%;"> Explaining recursion</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#sketcher:scaling" style="font-size: 80%;"> Scaling, translating, and rotating a figure</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec35" style="font-size: 80%;"> Scaling</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec36" style="font-size: 80%;"> Translation</a></li>
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+ <!-- navigation toc: --> <li><a href="._pysketcher005.html#___sec37" style="font-size: 80%;"> Rotation</a></li>
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+
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+ </ul>
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+ </li>
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+ </ul>
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+ </div>
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+</div>
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+</div> <!-- end of navigation bar -->
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+
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+<div class="container">
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+
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+<p> </p><p> </p><p> </p> <!-- add vertical space -->
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+
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+<a name="part0004"></a>
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+<!-- !split -->
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+
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+<h1 id="___sec16">Basic shapes </h1>
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+
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+<p>
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+This section presents many of the basic shapes in Pysketcher:
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+<code>Axis</code>, <code>Distance_wText</code>, <code>Rectangle</code>, <code>Triangle</code>, <code>Arc</code>,
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+<code>Spring</code>, <code>Dashpot</code>, and <code>Wavy</code>.
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+Each shape is demonstrated with a figure and a
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+unit test that shows how the figure is constructed in Python code.
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+These demos rely heavily on the method <code>draw_dimensions</code> in
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+the shape classes, which annotates the basic drawing of the shape
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+with the various geometric parameters that govern the shape.
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+
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+<h2 id="___sec17">Axis </h2>
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+
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+<p>
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+The <code>Axis</code> object gives the possibility draw a single axis to
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+notify a coordinate system. Here is an example where we
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+draw \( x \) and \( y \) axis of three coordinate systems of different
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+rotation:
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
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+<center><p><img src="fig-tut/Axis.png" align="bottom" width=500></p></center>
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
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+The corresponding code looks like this:
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+
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+<p>
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+
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+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Axis</span>():
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+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
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+ xmin<span style="color: #666666">=0</span>, xmax<span style="color: #666666">=15</span>, ymin<span style="color: #666666">=-7</span>, ymax<span style="color: #666666">=8</span>, axis<span style="color: #666666">=</span><span style="color: #008000">True</span>,
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+ instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Axis.py'</span>)
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+ <span style="color: #408080; font-style: italic"># Draw normal x and y axis with origin at (7.5, 2)</span>
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+ <span style="color: #408080; font-style: italic"># in the coordinate system of the sketch: [0,15]x[-7,8]</span>
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+ x_axis <span style="color: #666666">=</span> Axis((<span style="color: #666666">7.5</span>,<span style="color: #666666">2</span>), <span style="color: #666666">5</span>, <span style="color: #BA2121">'x'</span>, rotation_angle<span style="color: #666666">=0</span>)
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+ y_axis <span style="color: #666666">=</span> Axis((<span style="color: #666666">7.5</span>,<span style="color: #666666">2</span>), <span style="color: #666666">5</span>, <span style="color: #BA2121">'y'</span>, rotation_angle<span style="color: #666666">=90</span>)
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+ system <span style="color: #666666">=</span> Composition({<span style="color: #BA2121">'x axis'</span>: x_axis, <span style="color: #BA2121">'y axis'</span>: y_axis})
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+ system<span style="color: #666666">.</span>draw()
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+ drawing_tool<span style="color: #666666">.</span>display()
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+
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+ <span style="color: #408080; font-style: italic"># Rotate this system 40 degrees counter clockwise</span>
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+ <span style="color: #408080; font-style: italic"># and draw it with dashed lines</span>
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+ system<span style="color: #666666">.</span>set_linestyle(<span style="color: #BA2121">'dashed'</span>)
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+ system<span style="color: #666666">.</span>rotate(<span style="color: #666666">40</span>, (<span style="color: #666666">7.5</span>,<span style="color: #666666">2</span>))
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+ system<span style="color: #666666">.</span>draw()
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+ drawing_tool<span style="color: #666666">.</span>display()
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+
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+ <span style="color: #408080; font-style: italic"># Rotate this system another 220 degrees and show</span>
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+ <span style="color: #408080; font-style: italic"># with dotted lines</span>
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+ system<span style="color: #666666">.</span>set_linestyle(<span style="color: #BA2121">'dotted'</span>)
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+ system<span style="color: #666666">.</span>rotate(<span style="color: #666666">220</span>, (<span style="color: #666666">7.5</span>,<span style="color: #666666">2</span>))
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+ system<span style="color: #666666">.</span>draw()
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+ drawing_tool<span style="color: #666666">.</span>display()
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+
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+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Axis'</span>)
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+</pre></div>
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+
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+<h2 id="___sec18">Distance with text </h2>
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+
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+<p>
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+The object <code>Distance_wText</code> is used to display an arrow, to indicate
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+a distance in a sketch, with an additional text in the middle of the arrow.
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+
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+<p>
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+The figure
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
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+<center><p><img src="fig-tut/Distance_wText.png" align="bottom" width=500></p></center>
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
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+was produced by this code:
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+
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+<p>
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+
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+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Distance_wText</span>():
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+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
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+ xmin<span style="color: #666666">=0</span>, xmax<span style="color: #666666">=10</span>, ymin<span style="color: #666666">=0</span>, ymax<span style="color: #666666">=6</span>,
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+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Distance_wText.py'</span>)
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+
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+ fontsize<span style="color: #666666">=14</span>
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+ t <span style="color: #666666">=</span> <span style="color: #BA2121">r'$ 2\pi R^2 $'</span> <span style="color: #408080; font-style: italic"># sample text</span>
|
|
|
+ examples <span style="color: #666666">=</span> Composition({
|
|
|
+ <span style="color: #BA2121">'a0'</span>: Distance_wText((<span style="color: #666666">4</span>,<span style="color: #666666">5</span>), (<span style="color: #666666">8</span>, <span style="color: #666666">5</span>), t, fontsize),
|
|
|
+ <span style="color: #BA2121">'a6'</span>: Distance_wText((<span style="color: #666666">4</span>,<span style="color: #666666">5</span>), (<span style="color: #666666">4</span>, <span style="color: #666666">4</span>), t, fontsize),
|
|
|
+ <span style="color: #BA2121">'a1'</span>: Distance_wText((<span style="color: #666666">0</span>,<span style="color: #666666">2</span>), (<span style="color: #666666">2</span>, <span style="color: #666666">4.5</span>), t, fontsize),
|
|
|
+ <span style="color: #BA2121">'a2'</span>: Distance_wText((<span style="color: #666666">0</span>,<span style="color: #666666">2</span>), (<span style="color: #666666">2</span>, <span style="color: #666666">0</span>), t, fontsize),
|
|
|
+ <span style="color: #BA2121">'a3'</span>: Distance_wText((<span style="color: #666666">2</span>,<span style="color: #666666">4.5</span>), (<span style="color: #666666">0</span>, <span style="color: #666666">5.5</span>), t, fontsize),
|
|
|
+ <span style="color: #BA2121">'a4'</span>: Distance_wText((<span style="color: #666666">8</span>,<span style="color: #666666">4</span>), (<span style="color: #666666">10</span>, <span style="color: #666666">3</span>), t, fontsize,
|
|
|
+ text_spacing<span style="color: #666666">=-1./60</span>),
|
|
|
+ <span style="color: #BA2121">'a5'</span>: Distance_wText((<span style="color: #666666">8</span>,<span style="color: #666666">2</span>), (<span style="color: #666666">10</span>, <span style="color: #666666">1</span>), t, fontsize,
|
|
|
+ text_spacing<span style="color: #666666">=-1./40</span>, alignment<span style="color: #666666">=</span><span style="color: #BA2121">'right'</span>),
|
|
|
+ <span style="color: #BA2121">'c1'</span>: Text_wArrow(<span style="color: #BA2121">'text_spacing=-1./60'</span>,
|
|
|
+ (<span style="color: #666666">4</span>, <span style="color: #666666">3.5</span>), (<span style="color: #666666">9</span>, <span style="color: #666666">3.2</span>),
|
|
|
+ fontsize<span style="color: #666666">=10</span>, alignment<span style="color: #666666">=</span><span style="color: #BA2121">'left'</span>),
|
|
|
+ <span style="color: #BA2121">'c2'</span>: Text_wArrow(<span style="color: #BA2121">'text_spacing=-1./40, alignment="right"'</span>,
|
|
|
+ (<span style="color: #666666">4</span>, <span style="color: #666666">0.5</span>), (<span style="color: #666666">9</span>, <span style="color: #666666">1.2</span>),
|
|
|
+ fontsize<span style="color: #666666">=10</span>, alignment<span style="color: #666666">=</span><span style="color: #BA2121">'left'</span>),
|
|
|
+ })
|
|
|
+ examples<span style="color: #666666">.</span>draw()
|
|
|
+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Distance_wText and text positioning'</span>)
|
|
|
+</pre></div>
|
|
|
+<p>
|
|
|
+Note the use of <code>Text_wArrow</code> to write an explaining text with an
|
|
|
+associated arrow, here used to explain how
|
|
|
+the <code>text_spacing</code> and <code>alignment</code> arguments can be used to adjust
|
|
|
+the appearance of the text that goes with the distance arrow.
|
|
|
+
|
|
|
+<h2 id="___sec19">Rectangle </h2>
|
|
|
+
|
|
|
+<p>
|
|
|
+<center><p><img src="fig-tut/Rectangle.png" align="bottom" width=500></p></center>
|
|
|
+
|
|
|
+<p>
|
|
|
+<br />
|
|
|
+<br />
|
|
|
+
|
|
|
+<p>
|
|
|
+The above figure can be produced by the following code.
|
|
|
+
|
|
|
+<p>
|
|
|
+
|
|
|
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
|
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Rectangle</span>():
|
|
|
+ L <span style="color: #666666">=</span> <span style="color: #666666">3.0</span>
|
|
|
+ W <span style="color: #666666">=</span> <span style="color: #666666">4.0</span>
|
|
|
+
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
|
|
|
+ xmin<span style="color: #666666">=0</span>, xmax<span style="color: #666666">=2*</span>W, ymin<span style="color: #666666">=-</span>L<span style="color: #666666">/2</span>, ymax<span style="color: #666666">=2*</span>L,
|
|
|
+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Rectangle.py'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'blue'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_grid(<span style="color: #008000">True</span>)
|
|
|
+
|
|
|
+ xpos <span style="color: #666666">=</span> W<span style="color: #666666">/2</span>
|
|
|
+ r <span style="color: #666666">=</span> Rectangle(lower_left_corner<span style="color: #666666">=</span>(xpos,<span style="color: #666666">0</span>), width<span style="color: #666666">=</span>W, height<span style="color: #666666">=</span>L)
|
|
|
+ r<span style="color: #666666">.</span>draw()
|
|
|
+ r<span style="color: #666666">.</span>draw_dimensions()
|
|
|
+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Rectangle'</span>)
|
|
|
+</pre></div>
|
|
|
+<p>
|
|
|
+Note that the <code>draw_dimension</code> method adds explanation of dimensions and various
|
|
|
+important argument in the construction of a shape. It adapts the annotations
|
|
|
+to the geometry of the current shape.
|
|
|
+
|
|
|
+<h2 id="___sec20">Triangle </h2>
|
|
|
+
|
|
|
+<p>
|
|
|
+<center><p><img src="fig-tut/Triangle.png" align="bottom" width=500></p></center>
|
|
|
+
|
|
|
+<p>
|
|
|
+<br />
|
|
|
+<br />
|
|
|
+
|
|
|
+<p>
|
|
|
+The code below produces the figure.
|
|
|
+
|
|
|
+<p>
|
|
|
+
|
|
|
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
|
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Triangle</span>():
|
|
|
+ L <span style="color: #666666">=</span> <span style="color: #666666">3.0</span>
|
|
|
+ W <span style="color: #666666">=</span> <span style="color: #666666">4.0</span>
|
|
|
+
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
|
|
|
+ xmin<span style="color: #666666">=0</span>, xmax<span style="color: #666666">=2*</span>W, ymin<span style="color: #666666">=-</span>L<span style="color: #666666">/2</span>, ymax<span style="color: #666666">=1.2*</span>L,
|
|
|
+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Triangle.py'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'blue'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_grid(<span style="color: #008000">True</span>)
|
|
|
+
|
|
|
+ xpos <span style="color: #666666">=</span> <span style="color: #666666">1</span>
|
|
|
+ t <span style="color: #666666">=</span> Triangle(p1<span style="color: #666666">=</span>(W<span style="color: #666666">/2</span>,<span style="color: #666666">0</span>), p2<span style="color: #666666">=</span>(<span style="color: #666666">3*</span>W<span style="color: #666666">/2</span>,W<span style="color: #666666">/2</span>), p3<span style="color: #666666">=</span>(<span style="color: #666666">4*</span>W<span style="color: #666666">/5.</span>,L))
|
|
|
+ t<span style="color: #666666">.</span>draw()
|
|
|
+ t<span style="color: #666666">.</span>draw_dimensions()
|
|
|
+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Triangle'</span>)
|
|
|
+</pre></div>
|
|
|
+<p>
|
|
|
+Here, the <code>draw_dimension</code> method writes the name of the corners at the
|
|
|
+position of the corners, which does not always look nice (the present figure
|
|
|
+is an example). For a high-quality sketch one would add some spacing
|
|
|
+to the location of the p1, p2, and even p3 texts.
|
|
|
+
|
|
|
+<h2 id="___sec21">Arc </h2>
|
|
|
+
|
|
|
+<p>
|
|
|
+<center><p><img src="fig-tut/Arc.png" align="bottom" width=400></p></center>
|
|
|
+
|
|
|
+<p>
|
|
|
+<br />
|
|
|
+<br />
|
|
|
+
|
|
|
+<p>
|
|
|
+An arc like the one above is produced by
|
|
|
+
|
|
|
+<p>
|
|
|
+
|
|
|
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
|
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Arc</span>():
|
|
|
+ L <span style="color: #666666">=</span> <span style="color: #666666">4.0</span>
|
|
|
+ W <span style="color: #666666">=</span> <span style="color: #666666">4.0</span>
|
|
|
+
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
|
|
|
+ xmin<span style="color: #666666">=-</span>W<span style="color: #666666">/2</span>, xmax<span style="color: #666666">=</span>W, ymin<span style="color: #666666">=-</span>L<span style="color: #666666">/2</span>, ymax<span style="color: #666666">=1.5*</span>L,
|
|
|
+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Arc.py'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'blue'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_grid(<span style="color: #008000">True</span>)
|
|
|
+
|
|
|
+ center <span style="color: #666666">=</span> point(<span style="color: #666666">0</span>,<span style="color: #666666">0</span>)
|
|
|
+ radius <span style="color: #666666">=</span> L<span style="color: #666666">/2</span>
|
|
|
+ start_angle <span style="color: #666666">=</span> <span style="color: #666666">60</span>
|
|
|
+ arc_angle <span style="color: #666666">=</span> <span style="color: #666666">45</span>
|
|
|
+ a <span style="color: #666666">=</span> Arc(center, radius, start_angle, arc_angle)
|
|
|
+ a<span style="color: #666666">.</span>draw()
|
|
|
+
|
|
|
+ R1 <span style="color: #666666">=</span> <span style="color: #666666">1.25*</span>radius
|
|
|
+ R2 <span style="color: #666666">=</span> <span style="color: #666666">1.5*</span>radius
|
|
|
+ R <span style="color: #666666">=</span> <span style="color: #666666">2*</span>radius
|
|
|
+ a<span style="color: #666666">.</span>dimensions <span style="color: #666666">=</span> {
|
|
|
+ <span style="color: #BA2121">'start_angle'</span>:
|
|
|
+ Arc_wText(
|
|
|
+ <span style="color: #BA2121">'start_angle'</span>, center, R1, start_angle<span style="color: #666666">=0</span>,
|
|
|
+ arc_angle<span style="color: #666666">=</span>start_angle, text_spacing<span style="color: #666666">=1/10.</span>),
|
|
|
+ <span style="color: #BA2121">'arc_angle'</span>:
|
|
|
+ Arc_wText(
|
|
|
+ <span style="color: #BA2121">'arc_angle'</span>, center, R2, start_angle<span style="color: #666666">=</span>start_angle,
|
|
|
+ arc_angle<span style="color: #666666">=</span>arc_angle, text_spacing<span style="color: #666666">=1/20.</span>),
|
|
|
+ <span style="color: #BA2121">'r=0'</span>:
|
|
|
+ Line(center, center <span style="color: #666666">+</span>
|
|
|
+ point(R<span style="color: #666666">*</span>cos(radians(start_angle)),
|
|
|
+ R<span style="color: #666666">*</span>sin(radians(start_angle)))),
|
|
|
+ <span style="color: #BA2121">'r=start_angle'</span>:
|
|
|
+ Line(center, center <span style="color: #666666">+</span>
|
|
|
+ point(R<span style="color: #666666">*</span>cos(radians(start_angle<span style="color: #666666">+</span>arc_angle)),
|
|
|
+ R<span style="color: #666666">*</span>sin(radians(start_angle<span style="color: #666666">+</span>arc_angle)))),
|
|
|
+ <span style="color: #BA2121">'r=start+arc_angle'</span>:
|
|
|
+ Line(center, center <span style="color: #666666">+</span>
|
|
|
+ point(R, <span style="color: #666666">0</span>))<span style="color: #666666">.</span>set_linestyle(<span style="color: #BA2121">'dashed'</span>),
|
|
|
+ <span style="color: #BA2121">'radius'</span>: Distance_wText(center, a(<span style="color: #666666">0</span>), <span style="color: #BA2121">'radius'</span>, text_spacing<span style="color: #666666">=1/40.</span>),
|
|
|
+ <span style="color: #BA2121">'center'</span>: Text(<span style="color: #BA2121">'center'</span>, center<span style="color: #666666">-</span>point(radius<span style="color: #666666">/10.</span>, radius<span style="color: #666666">/10.</span>)),
|
|
|
+ }
|
|
|
+ <span style="color: #008000; font-weight: bold">for</span> dimension <span style="color: #AA22FF; font-weight: bold">in</span> a<span style="color: #666666">.</span>dimensions:
|
|
|
+ <span style="color: #008000; font-weight: bold">if</span> dimension<span style="color: #666666">.</span>startswith(<span style="color: #BA2121">'r='</span>):
|
|
|
+ dim <span style="color: #666666">=</span> a<span style="color: #666666">.</span>dimensions[dimension]
|
|
|
+ dim<span style="color: #666666">.</span>set_linestyle(<span style="color: #BA2121">'dashed'</span>)
|
|
|
+ dim<span style="color: #666666">.</span>set_linewidth(<span style="color: #666666">1</span>)
|
|
|
+ dim<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'black'</span>)
|
|
|
+
|
|
|
+ a<span style="color: #666666">.</span>draw_dimensions()
|
|
|
+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Arc'</span>)
|
|
|
+</pre></div>
|
|
|
+
|
|
|
+<h2 id="___sec22">Spring </h2>
|
|
|
+
|
|
|
+<p>
|
|
|
+<center><p><img src="fig-tut/Spring.png" align="bottom" width=800></p></center>
|
|
|
+
|
|
|
+<p>
|
|
|
+<br />
|
|
|
+<br />
|
|
|
+
|
|
|
+<p>
|
|
|
+The code for making these two springs goes like this:
|
|
|
+
|
|
|
+<p>
|
|
|
+
|
|
|
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
|
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Spring</span>():
|
|
|
+ L <span style="color: #666666">=</span> <span style="color: #666666">5.0</span>
|
|
|
+ W <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
|
|
|
+
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
|
|
|
+ xmin<span style="color: #666666">=0</span>, xmax<span style="color: #666666">=7*</span>W, ymin<span style="color: #666666">=-</span>L<span style="color: #666666">/2</span>, ymax<span style="color: #666666">=1.5*</span>L,
|
|
|
+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Spring.py'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'blue'</span>)
|
|
|
+ drawing_tool<span style="color: #666666">.</span>set_grid(<span style="color: #008000">True</span>)
|
|
|
+
|
|
|
+ xpos <span style="color: #666666">=</span> W
|
|
|
+ s1 <span style="color: #666666">=</span> Spring((W,<span style="color: #666666">0</span>), L, teeth<span style="color: #666666">=</span><span style="color: #008000">True</span>)
|
|
|
+ s1_title <span style="color: #666666">=</span> Text(<span style="color: #BA2121">'Default Spring'</span>,
|
|
|
+ s1<span style="color: #666666">.</span>geometric_features()[<span style="color: #BA2121">'end'</span>] <span style="color: #666666">+</span> point(<span style="color: #666666">0</span>,L<span style="color: #666666">/10</span>))
|
|
|
+ s1<span style="color: #666666">.</span>draw()
|
|
|
+ s1_title<span style="color: #666666">.</span>draw()
|
|
|
+ <span style="color: #408080; font-style: italic">#s1.draw_dimensions()</span>
|
|
|
+ xpos <span style="color: #666666">+=</span> <span style="color: #666666">3*</span>W
|
|
|
+ s2 <span style="color: #666666">=</span> Spring(start<span style="color: #666666">=</span>(xpos,<span style="color: #666666">0</span>), length<span style="color: #666666">=</span>L, width<span style="color: #666666">=</span>W<span style="color: #666666">/2.</span>,
|
|
|
+ bar_length<span style="color: #666666">=</span>L<span style="color: #666666">/6.</span>, teeth<span style="color: #666666">=</span><span style="color: #008000">False</span>)
|
|
|
+ s2<span style="color: #666666">.</span>draw()
|
|
|
+ s2<span style="color: #666666">.</span>draw_dimensions()
|
|
|
+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Spring'</span>)
|
|
|
+</pre></div>
|
|
|
+
|
|
|
+<h2 id="___sec23">Dashpot </h2>
|
|
|
+
|
|
|
+<p>
|
|
|
+<center><p><img src="fig-tut/Dashpot.png" align="bottom" width=600></p></center>
|
|
|
+
|
|
|
+<p>
|
|
|
+<br />
|
|
|
+<br />
|
|
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+
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+<p>
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+This dashpot is produced by
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+
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+<p>
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+
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+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_Dashpot</span>():
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+ L <span style="color: #666666">=</span> <span style="color: #666666">5.0</span>
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+ W <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
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+ xpos <span style="color: #666666">=</span> <span style="color: #666666">0</span>
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+
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+ drawing_tool<span style="color: #666666">.</span>set_coordinate_system(
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+ xmin<span style="color: #666666">=</span>xpos, xmax<span style="color: #666666">=</span>xpos<span style="color: #666666">+5.5*</span>W, ymin<span style="color: #666666">=-</span>L<span style="color: #666666">/2</span>, ymax<span style="color: #666666">=1.5*</span>L,
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+ axis<span style="color: #666666">=</span><span style="color: #008000">True</span>, instruction_file<span style="color: #666666">=</span><span style="color: #BA2121">'tmp_Dashpot.py'</span>)
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+ drawing_tool<span style="color: #666666">.</span>set_linecolor(<span style="color: #BA2121">'blue'</span>)
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+ drawing_tool<span style="color: #666666">.</span>set_grid(<span style="color: #008000">True</span>)
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+
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+ <span style="color: #408080; font-style: italic"># Default (simple) dashpot</span>
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+ xpos <span style="color: #666666">=</span> <span style="color: #666666">1.5</span>
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+ d1 <span style="color: #666666">=</span> Dashpot(start<span style="color: #666666">=</span>(xpos,<span style="color: #666666">0</span>), total_length<span style="color: #666666">=</span>L)
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+ d1_title <span style="color: #666666">=</span> Text(<span style="color: #BA2121">'Dashpot (default)'</span>,
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+ d1<span style="color: #666666">.</span>geometric_features()[<span style="color: #BA2121">'end'</span>] <span style="color: #666666">+</span> point(<span style="color: #666666">0</span>,L<span style="color: #666666">/10</span>))
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+ d1<span style="color: #666666">.</span>draw()
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+ d1_title<span style="color: #666666">.</span>draw()
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+
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+ <span style="color: #408080; font-style: italic"># Dashpot for animation with fixed bar_length, dashpot_length and</span>
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+ <span style="color: #408080; font-style: italic"># prescribed piston_pos</span>
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+ xpos <span style="color: #666666">+=</span> <span style="color: #666666">2.5*</span>W
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+ d2 <span style="color: #666666">=</span> Dashpot(start<span style="color: #666666">=</span>(xpos,<span style="color: #666666">0</span>), total_length<span style="color: #666666">=1.2*</span>L, width<span style="color: #666666">=</span>W<span style="color: #666666">/2</span>,
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+ bar_length<span style="color: #666666">=</span>W, dashpot_length<span style="color: #666666">=</span>L<span style="color: #666666">/2</span>, piston_pos<span style="color: #666666">=2*</span>W)
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+ d2<span style="color: #666666">.</span>draw()
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+ d2<span style="color: #666666">.</span>draw_dimensions()
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+
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+ drawing_tool<span style="color: #666666">.</span>display(<span style="color: #BA2121">'Dashpot'</span>)
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+</pre></div>
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+
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+<h2 id="___sec24">Wavy </h2>
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+
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+<p>
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+Looks strange. Fix x axis.
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+
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+<h2 id="___sec25">Stochastic curves </h2>
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+
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+<p>
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+The <code>StochasticWavyCurve</code> object offers three precomputed
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+graphics that have a random variation:
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
|
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+<center><p><img src="fig-tut/StochasticWavyCurve.png" align="bottom" width=600></p></center>
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+
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+<p>
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+<br />
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+<br />
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+
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+<p>
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+The usage is simple. The construction
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+
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+<p>
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+
|
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+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
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+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%">curve <span style="color: #666666">=</span> StochasticWavyCurve(curve_no<span style="color: #666666">=1</span>, percentage<span style="color: #666666">=40</span>)
|
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+</pre></div>
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+<p>
|
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+picks the second curve (the three are numbered 0, 1, and 2),
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+and the first 40% of that curve. In case one desires another extent
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+of the axis, one can just scale the coordinates directly as these
|
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+are stored in the arrays <code>curve.x[curve_no]</code> and
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+<code>curve.y[curve_no]</code>.
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+
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+<p>
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+<p>
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+<!-- navigation buttons at the bottom of the page -->
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Hans Petter Langtangen
