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  77.   <div class="section" id="pysketcher-create-principal-sketches-of-physics-problems">
    78. 

  78. <h1>Pysketcher: Create Principal Sketches of Physics Problems<a class="headerlink" href="#pysketcher-create-principal-sketches-of-physics-problems" title="Permalink to this headline">¶</a></h1>
    79. 

  79. <table class="docutils field-list" frame="void" rules="none">
    80. 

  80. <col class="field-name" />
    81. 

  81. <col class="field-body" />
    82. 

  82. <tbody valign="top">
    83. 

  83. <tr class="field-odd field"><th class="field-name">Authors:</th><td class="field-body">Hans Petter Langtangen</td>
    84. 

  84. </tr>
    85. 

  85. <tr class="field-even field"><th class="field-name">Date:</th><td class="field-body">Dec 23, 2015</td>
    86. 

  86. </tr>
    87. 

  87. </tbody>
    88. 

  88. </table>
    89. 

  89. <p>This document is derived from Chapter 9 in the book
    90. 

  90. <a class="reference external" href="http://www.amazon.com/Scientific-Programming-Computational-Science-Engineering/dp/3642549586/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1407225588&amp;sr=1-2&amp;keywords=langtangen">A Primer on Scientific Programming with Python</a>, by H. P. Langtangen,
    91. 

  91. 4th edition, Springer, 2014.</p>
    92. 

  92. <p><em>Abstract.</em> Pysketcher is a Python package which allows principal sketches of
    93. 

  93. physics and mechanics problems to be realized through short programs
    94. 

  94. instead of interactive (and potentially tedious and inaccurate)
    95. 

  95. drawing.  Elements of the sketch, such as lines, circles, angles,
    96. 

  96. forces, coordinate systems, etc., are realized as objects and
    97. 

  97. collected in hierarchical structures. Parts of the hierarchical
    98. 

  98. structures can easily change line styles and colors, or be copied,
    99. 

  99. scaled, translated, and rotated. These features make it
    100. 

  100. straightforward to move parts of the sketch to create animation,
    101. 

  101. usually in accordance with the physics of the underlying problem.
    102. 

  102. Exact dimensioning of the elements in the sketch is trivial to obtain
    103. 

  103. since distances are specified in computer code.</p>
    104. 

  104. <p>Pysketcher is easy to learn from a number of examples. Beyond
    105. 

  105. essential Python programming and a knowledge about mechanics problems,
    106. 

  106. no further background is required.</p>
    107. 

  107. <div class="section" id="a-first-glimpse-of-pysketcher">
    108. 

  108. <h2>A first glimpse of Pysketcher<a class="headerlink" href="#a-first-glimpse-of-pysketcher" title="Permalink to this headline">¶</a></h2>
    109. 

  109. <p>Formulation of physical problems makes heavy use of <em>principal sketches</em>
    110. 

  110. such as the one in Figure <a class="reference internal" href="#sketcher-fig-inclinedplane"><span class="std std-ref">Sketch of a physics problem</span></a>.
    111. 

  111. This particular sketch illustrates the classical mechanics problem
    112. 

  112. of a rolling wheel on an inclined plane.
    113. 

  113. The figure
    114. 

  114. is made up many individual elements: a rectangle
    115. 

  115. filled with a pattern (the inclined plane), a hollow circle with color
    116. 

  116. (the wheel), arrows with labels (the <span class="math">\(N\)</span> and <span class="math">\(Mg\)</span> forces, and the <span class="math">\(x\)</span>
    117. 

  117. axis), an angle with symbol <span class="math">\(\theta\)</span>, and a dashed line indicating the
    118. 

  118. starting location of the wheel.</p>
    119. 

  119. <p>Drawing software and plotting programs can produce such figures quite
    120. 

  120. easily in principle, but the amount of details the user needs to
    121. 

  121. control with the mouse can be substantial. Software more tailored to
    122. 

  122. producing sketches of this type would work with more convenient
    123. 

  123. abstractions, such as circle, wall, angle, force arrow, axis, and so
    124. 

  124. forth. And as soon we start <em>programming</em> to construct the figure we
    125. 

  125. get a range of other powerful tools at disposal. For example, we can
    126. 

  126. easily translate and rotate parts of the figure and make an animation
    127. 

  127. that illustrates the physics of the problem.
    128. 

  128. Programming as a superior alternative to interactive drawing is
    129. 

  129. the mantra of this section.</p>
    130. 

  130. <div class="figure" id="id2">
    131. 

  131. <span id="sketcher-fig-inclinedplane"></span><a class="reference internal image-reference" href="_images/wheel_on_inclined_plane.png"><img alt="_images/wheel_on_inclined_plane.png" src="_images/wheel_on_inclined_plane.png" style="width: 400px;" /></a>
    132. 

  132. <p class="caption"><span class="caption-text"><em>Sketch of a physics problem</em></span></p>
    133. 

  133. </div>
    134. 

  134. <div class="section" id="basic-construction-of-sketches">
    135. 

  135. <h3>Basic construction of sketches<a class="headerlink" href="#basic-construction-of-sketches" title="Permalink to this headline">¶</a></h3>
    136. 

  136. <p>Before attacking real-life sketches as in Figure <a class="reference internal" href="#sketcher-fig-inclinedplane"><span class="std std-ref">Sketch of a physics problem</span></a>
    137. 

  137. we focus on the significantly simpler drawing shown
    138. 

  138. in Figure <a class="reference internal" href="#sketcher-fig-vehicle0"><span class="std std-ref">Sketch of a simple figure</span></a>.  This toy sketch consists of
    139. 

  139. several elements: two circles, two rectangles, and a &#8220;ground&#8221; element.</p>
    140. 

  140. <div class="figure" id="id3">
    141. 

  141. <span id="sketcher-fig-vehicle0"></span><a class="reference internal image-reference" href="_images/vehicle0_dim.png"><img alt="_images/vehicle0_dim.png" src="_images/vehicle0_dim.png" style="width: 600px;" /></a>
    142. 

  142. <p class="caption"><span class="caption-text"><em>Sketch of a simple figure</em></span></p>
    143. 

  143. </div>
    144. 

  144. <p>When the sketch is defined in terms of computer code, it is natural to
    145. 

  145. parameterize geometric features, such as the radius of the wheel (<span class="math">\(R\)</span>),
    146. 

  146. the center point of the left wheel (<span class="math">\(w_1\)</span>), as well as the height (<span class="math">\(H\)</span>) and
    147. 

  147. length (<span class="math">\(L\)</span>) of the main part. The simple vehicle in
    148. 

  148. Figure <a class="reference internal" href="#sketcher-fig-vehicle0"><span class="std std-ref">Sketch of a simple figure</span></a> is quickly drawn in almost any interactive
    149. 

  149. tool. However, if we want to change the radius of the wheels, you need a
    150. 

  150. sophisticated drawing tool to avoid redrawing the whole figure, while
    151. 

  151. in computer code this is a matter of changing the <span class="math">\(R\)</span> parameter and
    152. 

  152. rerunning the program.
    153. 

  153. For example, Figure <a class="reference internal" href="#sketcher-fig-vehicle0b"><span class="std std-ref">Redrawing a figure with other geometric parameters</span></a> shows
    154. 

  154. a variation of the drawing in
    155. 

  155. Figure <a class="reference internal" href="#sketcher-fig-vehicle0"><span class="std std-ref">Sketch of a simple figure</span></a> obtained by just setting
    156. 

  156. <span class="math">\(R=0.5\)</span>, <span class="math">\(L=5\)</span>, <span class="math">\(H=2\)</span>, and <span class="math">\(R=2\)</span>. Being able
    157. 

  157. to quickly change geometric sizes is key to many problem settings in
    158. 

  158. physics and engineering, but then a program must define the geometry.</p>
    159. 

  159. <div class="figure" id="id4">
    160. 

  160. <span id="sketcher-fig-vehicle0b"></span><a class="reference internal image-reference" href="_images/vehicle_v2.png"><img alt="_images/vehicle_v2.png" src="_images/vehicle_v2.png" style="width: 500px;" /></a>
    161. 

  161. <p class="caption"><span class="caption-text"><em>Redrawing a figure with other geometric parameters</em></span></p>
    162. 

  162. </div>
    163. 

  163. <div class="section" id="basic-drawing">
    164. 

  164. <h4>Basic drawing<a class="headerlink" href="#basic-drawing" title="Permalink to this headline">¶</a></h4>
    165. 

  165. <p>A typical program creating these five elements is shown next.
    166. 

  166. After importing the <code class="docutils literal"><span class="pre">pysketcher</span></code> package, the first task is always to
    167. 

  167. define a coordinate system:</p>
    168. 

  168. <div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">pysketcher</span> <span class="kn">import</span> <span class="o">*</span>
    169. 

  169. 

  170. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    171. 

  171.     <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
    172. 

  172. </pre></div>
    173. 

  173. </div>
    174. 

  174. <p>Instead of working with lengths expressed by specific numbers it is
    175. 

  175. highly recommended to use variables to parameterize lengths as
    176. 

  176. this makes it easier to change dimensions later.
    177. 

  177. Here we introduce some key lengths for the radius of the wheels,
    178. 

  178. distance between the wheels, etc.:</p>
    179. 

  179. <div class="highlight-python"><div class="highlight"><pre><span class="n">R</span> <span class="o">=</span> <span class="mi">1</span>    <span class="c"># radius of wheel</span>
    180. 

  180. <span class="n">L</span> <span class="o">=</span> <span class="mi">4</span>    <span class="c"># distance between wheels</span>
    181. 

  181. <span class="n">H</span> <span class="o">=</span> <span class="mi">2</span>    <span class="c"># height of vehicle body</span>
    182. 

  182. <span class="n">w_1</span> <span class="o">=</span> <span class="mi">5</span>  <span class="c"># position of front wheel</span>
    183. 

  183. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span><span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="n">w_1</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">L</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">R</span><span class="p">,</span>
    184. 

  184.                                    <span class="n">ymin</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">H</span><span class="p">)</span>
    185. 

  185. </pre></div>
    186. 

  186. </div>
    187. 

  187. <p>With the drawing area in place we can make the first <code class="docutils literal"><span class="pre">Circle</span></code> object
    188. 

  188. in an intuitive fashion:</p>
    189. 

  189. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheel1</span> <span class="o">=</span> <span class="n">Circle</span><span class="p">(</span><span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">),</span> <span class="n">radius</span><span class="o">=</span><span class="n">R</span><span class="p">)</span>
    190. 

  190. </pre></div>
    191. 

  191. </div>
    192. 

  192. <p>to change dimensions later.</p>
    193. 

  193. <p>To translate the geometric information about the <code class="docutils literal"><span class="pre">wheel1</span></code> object to
    194. 

  194. instructions for the plotting engine (in this case Matplotlib), one calls the
    195. 

  195. <code class="docutils literal"><span class="pre">wheel1.draw()</span></code>. To display all drawn objects, one issues
    196. 

  196. <code class="docutils literal"><span class="pre">drawing_tool.display()</span></code>. The typical steps are hence:</p>
    197. 

  197. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheel1</span> <span class="o">=</span> <span class="n">Circle</span><span class="p">(</span><span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">),</span> <span class="n">radius</span><span class="o">=</span><span class="n">R</span><span class="p">)</span>
    198. 

  198. <span class="n">wheel1</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    199. 

  199. 

  200. <span class="c"># Define other objects and call their draw() methods</span>
    201. 

  201. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    202. 

  202. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="s">&#39;tmp.png&#39;</span><span class="p">)</span>  <span class="c"># store picture</span>
    203. 

  203. </pre></div>
    204. 

  204. </div>
    205. 

  205. <p>The next wheel can be made by taking a copy of <code class="docutils literal"><span class="pre">wheel1</span></code> and
    206. 

  206. translating the object to the right according to a
    207. 

  207. displacement vector <span class="math">\((L,0)\)</span>:</p>
    208. 

  208. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheel2</span> <span class="o">=</span> <span class="n">wheel1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
    209. 

  209. <span class="n">wheel2</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">L</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span>
    210. 

  210. </pre></div>
    211. 

  211. </div>
    212. 

  212. <p>The two rectangles are also made in an intuitive way:</p>
    213. 

  213. <div class="highlight-python"><div class="highlight"><pre><span class="n">under</span> <span class="o">=</span> <span class="n">Rectangle</span><span class="p">(</span><span class="n">lower_left_corner</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">),</span>
    214. 

  214.                   <span class="n">width</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span> <span class="o">+</span> <span class="n">L</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="n">H</span><span class="p">)</span>
    215. 

  215. <span class="n">over</span>  <span class="o">=</span> <span class="n">Rectangle</span><span class="p">(</span><span class="n">lower_left_corner</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span> <span class="o">+</span> <span class="n">H</span><span class="p">),</span>
    216. 

  216.                   <span class="n">width</span><span class="o">=</span><span class="mf">2.5</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="mf">1.25</span><span class="o">*</span><span class="n">H</span><span class="p">)</span>
    217. 

  217. </pre></div>
    218. 

  218. </div>
    219. 

  219. </div>
    220. 

  220. <div class="section" id="groups-of-objects">
    221. 

  221. <h4>Groups of objects<a class="headerlink" href="#groups-of-objects" title="Permalink to this headline">¶</a></h4>
    222. 

  222. <p>Instead of calling the <code class="docutils literal"><span class="pre">draw</span></code> method of every object, we can
    223. 

  223. group objects and call <code class="docutils literal"><span class="pre">draw</span></code>, or perform other operations, for
    224. 

  224. the whole group. For example, we may collect the two wheels
    225. 

  225. in a <code class="docutils literal"><span class="pre">wheels</span></code> group and the <code class="docutils literal"><span class="pre">over</span></code> and <code class="docutils literal"><span class="pre">under</span></code> rectangles
    226. 

  226. in a <code class="docutils literal"><span class="pre">body</span></code> group. The whole vehicle is a composition
    227. 

  227. of its <code class="docutils literal"><span class="pre">wheels</span></code> and <code class="docutils literal"><span class="pre">body</span></code> groups. The code goes like</p>
    228. 

  228. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheels</span>  <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;wheel1&#39;</span><span class="p">:</span> <span class="n">wheel1</span><span class="p">,</span> <span class="s">&#39;wheel2&#39;</span><span class="p">:</span> <span class="n">wheel2</span><span class="p">})</span>
    229. 

  229. <span class="n">body</span>    <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;under&#39;</span><span class="p">:</span> <span class="n">under</span><span class="p">,</span> <span class="s">&#39;over&#39;</span><span class="p">:</span> <span class="n">over</span><span class="p">})</span>
    230. 

  230. 

  231. <span class="n">vehicle</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;wheels&#39;</span><span class="p">:</span> <span class="n">wheels</span><span class="p">,</span> <span class="s">&#39;body&#39;</span><span class="p">:</span> <span class="n">body</span><span class="p">})</span>
    232. 

  232. </pre></div>
    233. 

  233. </div>
    234. 

  234. <p>The ground is illustrated by an object of type <code class="docutils literal"><span class="pre">Wall</span></code>,
    235. 

  235. mostly used to indicate walls in sketches of mechanical systems.
    236. 

  236. A <code class="docutils literal"><span class="pre">Wall</span></code> takes the <code class="docutils literal"><span class="pre">x</span></code> and <code class="docutils literal"><span class="pre">y</span></code> coordinates of some curve,
    237. 

  237. and a <code class="docutils literal"><span class="pre">thickness</span></code> parameter, and creates a thick curve filled
    238. 

  238. with a simple pattern. In this case the curve is just a flat
    239. 

  239. line so the construction is made of two points on the
    240. 

  240. ground line (<span class="math">\((w_1-L,0)\)</span> and <span class="math">\((w_1+3L,0)\)</span>):</p>
    241. 

  241. <div class="highlight-python"><div class="highlight"><pre><span class="n">ground</span> <span class="o">=</span> <span class="n">Wall</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="n">w_1</span> <span class="o">-</span> <span class="n">L</span><span class="p">,</span> <span class="n">w_1</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">L</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">thickness</span><span class="o">=-</span><span class="mf">0.3</span><span class="o">*</span><span class="n">R</span><span class="p">)</span>
    242. 

  242. </pre></div>
    243. 

  243. </div>
    244. 

  244. <p>The negative thickness makes the pattern-filled rectangle appear below
    245. 

  245. the defined line, otherwise it appears above.</p>
    246. 

  246. <p>We may now collect all the objects in a &#8220;top&#8221; object that contains
    247. 

  247. the whole figure:</p>
    248. 

  248. <div class="highlight-python"><div class="highlight"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;vehicle&#39;</span><span class="p">:</span> <span class="n">vehicle</span><span class="p">,</span> <span class="s">&#39;ground&#39;</span><span class="p">:</span> <span class="n">ground</span><span class="p">})</span>
    249. 

  249. <span class="n">fig</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>  <span class="c"># send all figures to plotting backend</span>
    250. 

  250. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    251. 

  251. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="s">&#39;tmp.png&#39;</span><span class="p">)</span>
    252. 

  252. </pre></div>
    253. 

  253. </div>
    254. 

  254. <p>The <code class="docutils literal"><span class="pre">fig.draw()</span></code> call will visit
    255. 

  255. all subgroups, their subgroups,
    256. 

  256. and so forth in the hierarchical tree structure of
    257. 

  257. figure elements,
    258. 

  258. and call <code class="docutils literal"><span class="pre">draw</span></code> for every object.</p>
    259. 

  259. </div>
    260. 

  260. <div class="section" id="changing-line-styles-and-colors">
    261. 

  261. <h4>Changing line styles and colors<a class="headerlink" href="#changing-line-styles-and-colors" title="Permalink to this headline">¶</a></h4>
    262. 

  262. <p>Controlling the line style, line color, and line width is
    263. 

  263. fundamental when designing figures. The <code class="docutils literal"><span class="pre">pysketcher</span></code>
    264. 

  264. package allows the user to control such properties in
    265. 

  265. single objects, but also set global properties that are
    266. 

  266. used if the object has no particular specification of
    267. 

  267. the properties. Setting the global properties are done like</p>
    268. 

  268. <div class="highlight-python"><div class="highlight"><pre><span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;dashed&#39;</span><span class="p">)</span>
    269. 

  269. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;black&#39;</span><span class="p">)</span>
    270. 

  270. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
    271. 

  271. </pre></div>
    272. 

  272. </div>
    273. 

  273. <p>At the object level the properties are specified in a similar
    274. 

  274. way:</p>
    275. 

  275. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheels</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;solid&#39;</span><span class="p">)</span>
    276. 

  276. <span class="n">wheels</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;red&#39;</span><span class="p">)</span>
    277. 

  277. </pre></div>
    278. 

  278. </div>
    279. 

  279. <p>and so on.</p>
    280. 

  280. <p>Geometric figures can be specified as <em>filled</em>, either with a color or with a
    281. 

  281. special visual pattern:</p>
    282. 

  282. <div class="highlight-python"><div class="highlight"><pre><span class="c"># Set filling of all curves</span>
    283. 

  283. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="s">&#39;blue&#39;</span><span class="p">,</span> <span class="n">pattern</span><span class="o">=</span><span class="s">&#39;/&#39;</span><span class="p">)</span>
    284. 

  284. 

  285. <span class="c"># Turn off filling of all curves</span>
    286. 

  286. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="bp">False</span><span class="p">)</span>
    287. 

  287. 

  288. <span class="c"># Fill the wheel with red color</span>
    289. 

  289. <span class="n">wheel1</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="s">&#39;red&#39;</span><span class="p">)</span>
    290. 

  290. </pre></div>
    291. 

  291. </div>
    292. 

  292. </div>
    293. 

  293. <div class="section" id="the-figure-composition-as-an-object-hierarchy">
    294. 

  294. <h4>The figure composition as an object hierarchy<a class="headerlink" href="#the-figure-composition-as-an-object-hierarchy" title="Permalink to this headline">¶</a></h4>
    295. 

  295. <p>The composition of objects making up the figure
    296. 

  296. is hierarchical, similar to a family, where
    297. 

  297. each object has a parent and a number of children. Do a
    298. 

  298. <code class="docutils literal"><span class="pre">print</span> <span class="pre">fig</span></code> to display the relations:</p>
    299. 

  299. <div class="highlight-text"><div class="highlight"><pre>ground
    300. 

  300.     wall
    301. 

  301. vehicle
    302. 

  302.     body
    303. 

  303.         over
    304. 

  304.             rectangle
    305. 

  305.         under
    306. 

  306.             rectangle
    307. 

  307.     wheels
    308. 

  308.         wheel1
    309. 

  309.             arc
    310. 

  310.         wheel2
    311. 

  311.             arc
    312. 

  312. </pre></div>
    313. 

  313. </div>
    314. 

  314. <p>The indentation reflects how deep down in the hierarchy (family)
    315. 

  315. we are.
    316. 

  316. This output is to be interpreted as follows:</p>
    317. 

  317. <blockquote>
    318. 

  318. <div><ul class="simple">
    319. 

  319. <li><code class="docutils literal"><span class="pre">fig</span></code> contains two objects, <code class="docutils literal"><span class="pre">ground</span></code> and <code class="docutils literal"><span class="pre">vehicle</span></code></li>
    320. 

  320. <li><code class="docutils literal"><span class="pre">ground</span></code> contains an object <code class="docutils literal"><span class="pre">wall</span></code></li>
    321. 

  321. <li><code class="docutils literal"><span class="pre">vehicle</span></code> contains two objects, <code class="docutils literal"><span class="pre">body</span></code> and <code class="docutils literal"><span class="pre">wheels</span></code></li>
    322. 

  322. <li><code class="docutils literal"><span class="pre">body</span></code> contains two objects, <code class="docutils literal"><span class="pre">over</span></code> and <code class="docutils literal"><span class="pre">under</span></code></li>
    323. 

  323. <li><code class="docutils literal"><span class="pre">wheels</span></code> contains two objects, <code class="docutils literal"><span class="pre">wheel1</span></code> and <code class="docutils literal"><span class="pre">wheel2</span></code></li>
    324. 

  324. </ul>
    325. 

  325. </div></blockquote>
    326. 

  326. <p>In this listing there are also objects not defined by the
    327. 

  327. programmer: <code class="docutils literal"><span class="pre">rectangle</span></code> and <code class="docutils literal"><span class="pre">arc</span></code>. These are of type <code class="docutils literal"><span class="pre">Curve</span></code>
    328. 

  328. and automatically generated by the classes <code class="docutils literal"><span class="pre">Rectangle</span></code> and <code class="docutils literal"><span class="pre">Circle</span></code>.</p>
    329. 

  329. <p>More detailed information can be printed by</p>
    330. 

  330. <div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">fig</span><span class="o">.</span><span class="n">show_hierarchy</span><span class="p">(</span><span class="s">&#39;std&#39;</span><span class="p">)</span>
    331. 

  331. </pre></div>
    332. 

  332. </div>
    333. 

  333. <p>yielding the output</p>
    334. 

  334. <div class="highlight-text"><div class="highlight"><pre>ground (Wall):
    335. 

  335.     wall (Curve): 4 coords fillcolor=&#39;white&#39; fillpattern=&#39;/&#39;
    336. 

  336. vehicle (Composition):
    337. 

  337.     body (Composition):
    338. 

  338.         over (Rectangle):
    339. 

  339.             rectangle (Curve): 5 coords
    340. 

  340.         under (Rectangle):
    341. 

  341.             rectangle (Curve): 5 coords
    342. 

  342.     wheels (Composition):
    343. 

  343.         wheel1 (Circle):
    344. 

  344.             arc (Curve): 181 coords
    345. 

  345.         wheel2 (Circle):
    346. 

  346.             arc (Curve): 181 coords
    347. 

  347. </pre></div>
    348. 

  348. </div>
    349. 

  349. <p>Here we can see the class type for each figure object, how many
    350. 

  350. coordinates that are involved in basic figures (<code class="docutils literal"><span class="pre">Curve</span></code> objects), and
    351. 

  351. special settings of the basic figure (fillcolor, line types, etc.).
    352. 

  352. For example, <code class="docutils literal"><span class="pre">wheel2</span></code> is a <code class="docutils literal"><span class="pre">Circle</span></code> object consisting of an <code class="docutils literal"><span class="pre">arc</span></code>,
    353. 

  353. which is a <code class="docutils literal"><span class="pre">Curve</span></code> object consisting of 181 coordinates (the
    354. 

  354. points needed to draw a smooth circle). The <code class="docutils literal"><span class="pre">Curve</span></code> objects are the
    355. 

  355. only objects that really holds specific coordinates to be drawn.
    356. 

  356. The other object types are just compositions used to group
    357. 

  357. parts of the complete figure.</p>
    358. 

  358. <p>One can also get a graphical overview of the hierarchy of figure objects
    359. 

  359. that build up a particular figure <code class="docutils literal"><span class="pre">fig</span></code>.
    360. 

  360. Just call <code class="docutils literal"><span class="pre">fig.graphviz_dot('fig')</span></code> to produce a file <code class="docutils literal"><span class="pre">fig.dot</span></code> in
    361. 

  361. the <em>dot format</em>. This file contains relations between parent and
    362. 

  362. child objects in the figure and can be turned into an image,
    363. 

  363. as in Figure <a class="reference internal" href="#sketcher-fig-vehicle0-hier1"><span class="std std-ref">Hierarchical relation between figure objects</span></a>, by
    364. 

  364. running the <code class="docutils literal"><span class="pre">dot</span></code> program:</p>
    365. 

  365. <div class="highlight-text"><div class="highlight"><pre>Terminal&gt; dot -Tpng -o fig.png fig.dot
    366. 

  366. </pre></div>
    367. 

  367. </div>
    368. 

  368. <div class="figure" id="id5">
    369. 

  369. <span id="sketcher-fig-vehicle0-hier1"></span><a class="reference internal image-reference" href="_images/vehicle0_hier1.png"><img alt="_images/vehicle0_hier1.png" src="_images/vehicle0_hier1.png" style="width: 500px;" /></a>
    370. 

  370. <p class="caption"><span class="caption-text"><em>Hierarchical relation between figure objects</em></span></p>
    371. 

  371. </div>
    372. 

  372. <p>The call <code class="docutils literal"><span class="pre">fig.graphviz_dot('fig',</span> <span class="pre">classname=True)</span></code> makes a <code class="docutils literal"><span class="pre">fig.dot</span></code> file
    373. 

  373. where the class type of each object is also visible, see
    374. 

  374. Figure <span class="xref std std-ref">sketcher:fig:vehicle0:hier2</span>. The ability to write out the
    375. 

  375. object hierarchy or view it graphically can be of great help when
    376. 

  376. working with complex figures that involve layers of subfigures.</p>
    377. 

  377. <div class="figure" id="id6">
    378. 

  378. <span id="sketcher-fig-vehicle0-hier2"></span><a class="reference internal image-reference" href="_images/Vehicle0_hier2.png"><img alt="_images/Vehicle0_hier2.png" src="_images/Vehicle0_hier2.png" style="width: 500px;" /></a>
    379. 

  379. <p class="caption"><span class="caption-text"><em>Hierarchical relation between figure objects, including their class names</em></span></p>
    380. 

  380. </div>
    381. 

  381. <p>Any of the objects can in the program be reached through their names, e.g.,</p>
    382. 

  382. <div class="highlight-python"><div class="highlight"><pre><span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">]</span>
    383. 

  383. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">]</span>
    384. 

  384. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">]</span>
    385. 

  385. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">][</span><span class="s">&#39;arc&#39;</span><span class="p">]</span>
    386. 

  386. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">][</span><span class="s">&#39;arc&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">x</span>  <span class="c"># x coords</span>
    387. 

  387. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">][</span><span class="s">&#39;arc&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">y</span>  <span class="c"># y coords</span>
    388. 

  388. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">][</span><span class="s">&#39;arc&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">linestyle</span>
    389. 

  389. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">][</span><span class="s">&#39;arc&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">linetype</span>
    390. 

  390. </pre></div>
    391. 

  391. </div>
    392. 

  392. <p>Grabbing a part of the figure this way is handy for
    393. 

  393. changing properties of that part, for example, colors, line styles
    394. 

  394. (see Figure <a class="reference internal" href="#sketcher-fig-vehicle0-v2"><span class="std std-ref">Left: Basic line-based drawing. Right: Thicker lines and filled parts</span></a>):</p>
    395. 

  395. <div class="highlight-python"><div class="highlight"><pre><span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    396. 

  396. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
    397. 

  397. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;black&#39;</span><span class="p">)</span>
    398. 

  398. 

  399. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;under&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="s">&#39;red&#39;</span><span class="p">)</span>
    400. 

  400. 

  401. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;over&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="n">pattern</span><span class="o">=</span><span class="s">&#39;/&#39;</span><span class="p">)</span>
    402. 

  402. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;over&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">14</span><span class="p">)</span>
    403. 

  403. <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;over&#39;</span><span class="p">][</span><span class="s">&#39;rectangle&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">linewidth</span> <span class="o">=</span> <span class="mi">4</span>
    404. 

  404. </pre></div>
    405. 

  405. </div>
    406. 

  406. <p>The last line accesses the <code class="docutils literal"><span class="pre">Curve</span></code> object directly, while the line above,
    407. 

  407. accesses the <code class="docutils literal"><span class="pre">Rectangle</span></code> object, which will then set the linewidth of
    408. 

  408. its <code class="docutils literal"><span class="pre">Curve</span></code> object, and other objects if it had any.
    409. 

  409. The result of the actions above is shown in Figure <a class="reference internal" href="#sketcher-fig-vehicle0-v2"><span class="std std-ref">Left: Basic line-based drawing. Right: Thicker lines and filled parts</span></a>.</p>
    410. 

  410. <div class="figure" id="id7">
    411. 

  411. <span id="sketcher-fig-vehicle0-v2"></span><a class="reference internal image-reference" href="_images/vehicle0.png"><img alt="_images/vehicle0.png" src="_images/vehicle0.png" style="width: 700px;" /></a>
    412. 

  412. <p class="caption"><span class="caption-text"><em>Left: Basic line-based drawing. Right: Thicker lines and filled parts</em></span></p>
    413. 

  413. </div>
    414. 

  414. <p>We can also change position of parts of the figure and thereby make
    415. 

  415. animations, as shown next.</p>
    416. 

  416. </div>
    417. 

  417. <div class="section" id="animation-translating-the-vehicle">
    418. 

  418. <h4>Animation: translating the vehicle<a class="headerlink" href="#animation-translating-the-vehicle" title="Permalink to this headline">¶</a></h4>
    419. 

  419. <p>Can we make our little vehicle roll? A first attempt will be to
    420. 

  420. fake rolling by just displacing all parts of the vehicle.
    421. 

  421. The relevant parts constitute the <code class="docutils literal"><span class="pre">fig['vehicle']</span></code> object.
    422. 

  422. This part of the figure can be translated, rotated, and scaled.
    423. 

  423. A translation along the ground means a translation in <span class="math">\(x\)</span> direction,
    424. 

  424. say a length <span class="math">\(L\)</span> to the right:</p>
    425. 

  425. <div class="highlight-python"><div class="highlight"><pre><span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">L</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span>
    426. 

  426. </pre></div>
    427. 

  427. </div>
    428. 

  428. <p>You need to erase, draw, and display to see the movement:</p>
    429. 

  429. <div class="highlight-python"><div class="highlight"><pre><span class="n">drawing_tool</span><span class="o">.</span><span class="n">erase</span><span class="p">()</span>
    430. 

  430. <span class="n">fig</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    431. 

  431. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    432. 

  432. </pre></div>
    433. 

  433. </div>
    434. 

  434. <p>Without erasing, the old drawing of the vehicle will remain in
    435. 

  435. the figure so you get two vehicles. Without <code class="docutils literal"><span class="pre">fig.draw()</span></code> the
    436. 

  436. new coordinates of the vehicle will not be communicated to
    437. 

  437. the drawing tool, and without calling display the updated
    438. 

  438. drawing will not be visible.</p>
    439. 

  439. <p>A figure that moves in time is conveniently realized by the
    440. 

  440. function <code class="docutils literal"><span class="pre">animate</span></code>:</p>
    441. 

  441. <div class="highlight-python"><div class="highlight"><pre><span class="n">animate</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">tp</span><span class="p">,</span> <span class="n">action</span><span class="p">)</span>
    442. 

  442. </pre></div>
    443. 

  443. </div>
    444. 

  444. <p>Here, <code class="docutils literal"><span class="pre">fig</span></code> is the entire figure, <code class="docutils literal"><span class="pre">tp</span></code> is an array of
    445. 

  445. time points, and <code class="docutils literal"><span class="pre">action</span></code> is a user-specified function that changes
    446. 

  446. <code class="docutils literal"><span class="pre">fig</span></code> at a specific time point. Typically, <code class="docutils literal"><span class="pre">action</span></code> will move
    447. 

  447. parts of <code class="docutils literal"><span class="pre">fig</span></code>.</p>
    448. 

  448. <p>In the present case we can define the movement through a velocity
    449. 

  449. function <code class="docutils literal"><span class="pre">v(t)</span></code> and displace the figure <code class="docutils literal"><span class="pre">v(t)*dt</span></code> for small time
    450. 

  450. intervals <code class="docutils literal"><span class="pre">dt</span></code>. A possible velocity function is</p>
    451. 

  451. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">v</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
    452. 

  452.     <span class="k">return</span> <span class="o">-</span><span class="mi">8</span><span class="o">*</span><span class="n">R</span><span class="o">*</span><span class="n">t</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">t</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">))</span>
    453. 

  453. </pre></div>
    454. 

  454. </div>
    455. 

  455. <p>Our action function for horizontal displacements <code class="docutils literal"><span class="pre">v(t)*dt</span></code> becomes</p>
    456. 

  456. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">move</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">fig</span><span class="p">):</span>
    457. 

  457.     <span class="n">x_displacement</span> <span class="o">=</span> <span class="n">dt</span><span class="o">*</span><span class="n">v</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    458. 

  458.     <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">x_displacement</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
    459. 

  459. </pre></div>
    460. 

  460. </div>
    461. 

  461. <p>Since our velocity is negative for <span class="math">\(t\in [0,2R]\)</span> the displacement is
    462. 

  462. to the left.</p>
    463. 

  463. <p>The <code class="docutils literal"><span class="pre">animate</span></code> function will for each time point <code class="docutils literal"><span class="pre">t</span></code> in <code class="docutils literal"><span class="pre">tp</span></code> erase
    464. 

  464. the drawing, call <code class="docutils literal"><span class="pre">action(t,</span> <span class="pre">fig)</span></code>, and show the new figure by
    465. 

  465. <code class="docutils literal"><span class="pre">fig.draw()</span></code> and <code class="docutils literal"><span class="pre">drawing_tool.display()</span></code>.
    466. 

  466. Here we choose a resolution of the animation corresponding to
    467. 

  467. 25 time points in the time interval <span class="math">\([0,2R]\)</span>:</p>
    468. 

  468. <div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">numpy</span>
    469. 

  469. <span class="n">tp</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
    470. 

  470. <span class="n">dt</span> <span class="o">=</span> <span class="n">tp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">tp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c"># time step</span>
    471. 

  471. 

  472. <span class="n">animate</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">tp</span><span class="p">,</span> <span class="n">move</span><span class="p">,</span> <span class="n">pause_per_frame</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    473. 

  473. </pre></div>
    474. 

  474. </div>
    475. 

  475. <p>The <code class="docutils literal"><span class="pre">pause_per_frame</span></code> adds a pause, here 0.2 seconds, between
    476. 

  476. each frame in the animation.</p>
    477. 

  477. <p>We can also ask <code class="docutils literal"><span class="pre">animate</span></code> to store each frame in a file:</p>
    478. 

  478. <div class="highlight-python"><div class="highlight"><pre><span class="n">files</span> <span class="o">=</span> <span class="n">animate</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">tp</span><span class="p">,</span> <span class="n">move_vehicle</span><span class="p">,</span> <span class="n">moviefiles</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
    479. 

  479.                 <span class="n">pause_per_frame</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
    480. 

  480. </pre></div>
    481. 

  481. </div>
    482. 

  482. <p>The <code class="docutils literal"><span class="pre">files</span></code> variable, here <code class="docutils literal"><span class="pre">'tmp_frame_%04d.png'</span></code>,
    483. 

  483. is the printf-specification used to generate the individual
    484. 

  484. plot files. We can use this specification to make a video
    485. 

  485. file via <code class="docutils literal"><span class="pre">ffmpeg</span></code> (or <code class="docutils literal"><span class="pre">avconv</span></code> on Debian-based Linux systems such
    486. 

  486. as Ubuntu). Videos in the Flash and WebM formats can be created
    487. 

  487. by</p>
    488. 

  488. <div class="highlight-text"><div class="highlight"><pre>Terminal&gt; ffmpeg -r 12 -i tmp_frame_%04d.png -vcodec flv mov.flv
    489. 

  489. Terminal&gt; ffmpeg -r 12 -i tmp_frame_%04d.png -vcodec libvpx mov.webm
    490. 

  490. </pre></div>
    491. 

  491. </div>
    492. 

  492. <p>An animated GIF movie can also be made using the <code class="docutils literal"><span class="pre">convert</span></code> program
    493. 

  493. from the ImageMagick software suite:</p>
    494. 

  494. <div class="highlight-text"><div class="highlight"><pre>Terminal&gt; convert -delay 20 tmp_frame*.png mov.gif
    495. 

  495. Terminal&gt; animate mov.gif  # play movie
    496. 

  496. </pre></div>
    497. 

  497. </div>
    498. 

  498. <p>The delay between frames, in units of 1/100 s,
    499. 

  499. governs the speed of the movie.
    500. 

  500. To play the animated GIF file in a web page, simply insert
    501. 

  501. <code class="docutils literal"><span class="pre">&lt;img</span> <span class="pre">src=&quot;mov.gif&quot;&gt;</span></code> in the HTML code.</p>
    502. 

  502. <p>The individual PNG frames can be directly played in a web
    503. 

  503. browser by running</p>
    504. 

  504. <div class="highlight-text"><div class="highlight"><pre>Terminal&gt; scitools movie output_file=mov.html fps=5 tmp_frame*
    505. 

  505. </pre></div>
    506. 

  506. </div>
    507. 

  507. <p>or calling</p>
    508. 

  508. <div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">scitools.std</span> <span class="kn">import</span> <span class="n">movie</span>
    509. 

  509. <span class="n">movie</span><span class="p">(</span><span class="n">files</span><span class="p">,</span> <span class="n">encoder</span><span class="o">=</span><span class="s">&#39;html&#39;</span><span class="p">,</span> <span class="n">output_file</span><span class="o">=</span><span class="s">&#39;mov.html&#39;</span><span class="p">)</span>
    510. 

  510. </pre></div>
    511. 

  511. </div>
    512. 

  512. <p>in Python. Load the resulting file <code class="docutils literal"><span class="pre">mov.html</span></code> into a web browser
    513. 

  513. to play the movie.</p>
    514. 

  514. <p>Try to run <a class="reference external" href="http://tinyurl.com/ot733jn/vehicle0.py">vehicle0.py</a> and
    515. 

  515. then load <code class="docutils literal"><span class="pre">mov.html</span></code> into a browser, or play one of the <code class="docutils literal"><span class="pre">mov.*</span></code>
    516. 

  516. video files.  Alternatively, you can view a ready-made <a class="reference external" href="http://tinyurl.com/oou9lp7/mov-tut/vehicle0.html">movie</a>.</p>
    517. 

  517. </div>
    518. 

  518. <div class="section" id="animation-rolling-the-wheels">
    519. 

  519. <span id="sketcher-vehicle1-anim"></span><h4>Animation: rolling the wheels<a class="headerlink" href="#animation-rolling-the-wheels" title="Permalink to this headline">¶</a></h4>
    520. 

  520. <p>It is time to show rolling wheels. To this end, we add spokes to the
    521. 

  521. wheels, formed by two crossing lines, see Figure <a class="reference internal" href="#sketcher-fig-vehicle1"><span class="std std-ref">Wheels with spokes to illustrate rolling</span></a>.
    522. 

  522. The construction of the wheels will now involve a circle and two lines:</p>
    523. 

  523. <div class="highlight-python"><div class="highlight"><pre><span class="n">wheel1</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span>
    524. 

  524.     <span class="s">&#39;wheel&#39;</span><span class="p">:</span> <span class="n">Circle</span><span class="p">(</span><span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">),</span> <span class="n">radius</span><span class="o">=</span><span class="n">R</span><span class="p">),</span>
    525. 

  525.     <span class="s">&#39;cross&#39;</span><span class="p">:</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;cross1&#39;</span><span class="p">:</span> <span class="n">Line</span><span class="p">((</span><span class="n">w_1</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span>   <span class="p">(</span><span class="n">w_1</span><span class="p">,</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">)),</span>
    526. 

  526.                           <span class="s">&#39;cross2&#39;</span><span class="p">:</span> <span class="n">Line</span><span class="p">((</span><span class="n">w_1</span><span class="o">-</span><span class="n">R</span><span class="p">,</span><span class="n">R</span><span class="p">),</span> <span class="p">(</span><span class="n">w_1</span><span class="o">+</span><span class="n">R</span><span class="p">,</span><span class="n">R</span><span class="p">))})})</span>
    527. 

  527. <span class="n">wheel2</span> <span class="o">=</span> <span class="n">wheel1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
    528. 

  528. <span class="n">wheel2</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">L</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span>
    529. 

  529. </pre></div>
    530. 

  530. </div>
    531. 

  531. <p>Observe that <code class="docutils literal"><span class="pre">wheel1.copy()</span></code> copies all the objects that make
    532. 

  532. up the first wheel, and <code class="docutils literal"><span class="pre">wheel2.translate</span></code> translates all
    533. 

  533. the copied objects.</p>
    534. 

  534. <div class="figure" id="id8">
    535. 

  535. <span id="sketcher-fig-vehicle1"></span><a class="reference internal image-reference" href="_images/vehicle1.png"><img alt="_images/vehicle1.png" src="_images/vehicle1.png" style="width: 400px;" /></a>
    536. 

  536. <p class="caption"><span class="caption-text"><em>Wheels with spokes to illustrate rolling</em></span></p>
    537. 

  537. </div>
    538. 

  538. <p>The <code class="docutils literal"><span class="pre">move</span></code> function now needs to displace all the objects in the
    539. 

  539. entire vehicle and also rotate the <code class="docutils literal"><span class="pre">cross1</span></code> and <code class="docutils literal"><span class="pre">cross2</span></code>
    540. 

  540. objects in both wheels.
    541. 

  541. The rotation angle follows from the fact that the arc length
    542. 

  542. of a rolling wheel equals the displacement of the center of
    543. 

  543. the wheel, leading to a rotation angle</p>
    544. 

  544. <div class="highlight-python"><div class="highlight"><pre><span class="n">angle</span> <span class="o">=</span> <span class="o">-</span> <span class="n">x_displacement</span><span class="o">/</span><span class="n">R</span>
    545. 

  545. </pre></div>
    546. 

  546. </div>
    547. 

  547. <p>With <code class="docutils literal"><span class="pre">w_1</span></code> tracking the <span class="math">\(x\)</span> coordinate of the center
    548. 

  548. of the front wheel, we can rotate that wheel by</p>
    549. 

  549. <div class="highlight-python"><div class="highlight"><pre><span class="n">w1</span> <span class="o">=</span> <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel1&#39;</span><span class="p">]</span>
    550. 

  550. <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">degrees</span>
    551. 

  551. <span class="n">w1</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">degrees</span><span class="p">(</span><span class="n">angle</span><span class="p">),</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">))</span>
    552. 

  552. </pre></div>
    553. 

  553. </div>
    554. 

  554. <p>The <code class="docutils literal"><span class="pre">rotate</span></code> function takes two parameters: the rotation angle
    555. 

  555. (in degrees) and the center point of the rotation, which is the
    556. 

  556. center of the wheel in this case. The other wheel is rotated by</p>
    557. 

  557. <div class="highlight-python"><div class="highlight"><pre><span class="n">w2</span> <span class="o">=</span> <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">]</span>
    558. 

  558. <span class="n">w2</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">degrees</span><span class="p">(</span><span class="n">angle</span><span class="p">),</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span> <span class="o">+</span> <span class="n">L</span><span class="p">,</span> <span class="n">R</span><span class="p">))</span>
    559. 

  559. </pre></div>
    560. 

  560. </div>
    561. 

  561. <p>That is, the angle is the same, but the rotation point is different.
    562. 

  562. The update of the center point is done by <code class="docutils literal"><span class="pre">w_1</span> <span class="pre">+=</span> <span class="pre">x_displacement</span></code>.
    563. 

  563. The complete <code class="docutils literal"><span class="pre">move</span></code> function with translation of the entire
    564. 

  564. vehicle and rotation of the wheels then becomes</p>
    565. 

  565. <div class="highlight-python"><div class="highlight"><pre><span class="n">w_1</span> <span class="o">=</span> <span class="n">w_1</span> <span class="o">+</span> <span class="n">L</span>   <span class="c"># start position</span>
    566. 

  566. 

  567. <span class="k">def</span> <span class="nf">move</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">fig</span><span class="p">):</span>
    568. 

  568.     <span class="n">x_displacement</span> <span class="o">=</span> <span class="n">dt</span><span class="o">*</span><span class="n">v</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    569. 

  569.     <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">x_displacement</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
    570. 

  570. 

  571.     <span class="c"># Rotate wheels</span>
    572. 

  572.     <span class="k">global</span> <span class="n">w_1</span>
    573. 

  573.     <span class="n">w_1</span> <span class="o">+=</span> <span class="n">x_displacement</span>
    574. 

  574.     <span class="c"># R*angle = -x_displacement</span>
    575. 

  575.     <span class="n">angle</span> <span class="o">=</span> <span class="o">-</span> <span class="n">x_displacement</span><span class="o">/</span><span class="n">R</span>
    576. 

  576.     <span class="n">w1</span> <span class="o">=</span> <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel1&#39;</span><span class="p">]</span>
    577. 

  577.     <span class="n">w1</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">degrees</span><span class="p">(</span><span class="n">angle</span><span class="p">),</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">))</span>
    578. 

  578.     <span class="n">w2</span> <span class="o">=</span> <span class="n">fig</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">][</span><span class="s">&#39;wheel2&#39;</span><span class="p">]</span>
    579. 

  579.     <span class="n">w2</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">degrees</span><span class="p">(</span><span class="n">angle</span><span class="p">),</span> <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span> <span class="o">+</span> <span class="n">L</span><span class="p">,</span> <span class="n">R</span><span class="p">))</span>
    580. 

  580. </pre></div>
    581. 

  581. </div>
    582. 

  582. <p>The complete example is found in the file
    583. 

  583. <a class="reference external" href="http://tinyurl.com/ot733jn/vehicle1.py">vehicle1.py</a>. You may run this file or watch a <a class="reference external" href="http://tinyurl.com/oou9lp7/mov-tut/vehicle1.html">ready-made movie</a>.</p>
    584. 

  584. <p>The advantages with making figures this way, through programming
    585. 

  585. rather than using interactive drawing programs, are numerous.  For
    586. 

  586. example, the objects are parameterized by variables so that various
    587. 

  587. dimensions can easily be changed.  Subparts of the figure, possible
    588. 

  588. involving a lot of figure objects, can change color, linetype, filling
    589. 

  589. or other properties through a <em>single</em> function call.  Subparts of the
    590. 

  590. figure can be rotated, translated, or scaled.  Subparts of the figure
    591. 

  591. can also be copied and moved to other parts of the drawing
    592. 

  592. area. However, the single most important feature is probably the
    593. 

  593. ability to make animations governed by mathematical formulas or data
    594. 

  594. coming from physics simulations of the problem, as shown in the example above.</p>
    595. 

  595. </div>
    596. 

  596. </div>
    597. 

  597. </div>
    598. 

  598. <div class="section" id="basic-shapes">
    599. 

  599. <h2>Basic shapes<a class="headerlink" href="#basic-shapes" title="Permalink to this headline">¶</a></h2>
    600. 

  600. <p>This section presents many of the basic shapes in Pysketcher:
    601. 

  601. <code class="docutils literal"><span class="pre">Axis</span></code>, <code class="docutils literal"><span class="pre">Distance_wText</span></code>, <code class="docutils literal"><span class="pre">Rectangle</span></code>,    <code class="docutils literal"><span class="pre">Triangle</span></code>, <code class="docutils literal"><span class="pre">Arc</span></code>,
    602. 

  602. <code class="docutils literal"><span class="pre">Spring</span></code>, <code class="docutils literal"><span class="pre">Dashpot</span></code>, and <code class="docutils literal"><span class="pre">Wavy</span></code>.
    603. 

  603. Each shape is demonstrated with a figure and a
    604. 

  604. unit test that shows how the figure is constructed in Python code.
    605. 

  605. These demos rely heavily on the method <code class="docutils literal"><span class="pre">draw_dimensions</span></code> in
    606. 

  606. the shape classes, which annotates the basic drawing of the shape
    607. 

  607. with the various geometric parameters that govern the shape.</p>
    608. 

  608. <div class="section" id="axis">
    609. 

  609. <h3>Axis<a class="headerlink" href="#axis" title="Permalink to this headline">¶</a></h3>
    610. 

  610. <p>The <code class="docutils literal"><span class="pre">Axis</span></code> object gives the possibility draw a single axis to
    611. 

  611. notify a coordinate system. Here is an example where we
    612. 

  612. draw <span class="math">\(x\)</span> and <span class="math">\(y\)</span> axis of three coordinate systems of different
    613. 

  613. rotation:</p>
    614. 

  614. <div class="line-block">
    615. 

  615. <div class="line"><br /></div>
    616. 

  616. <div class="line"><br /></div>
    617. 

  617. </div>
    618. 

  618. <div class="figure">
    619. 

  619. <a class="reference internal image-reference" href="_images/Axis.png"><img alt="_images/Axis.png" src="_images/Axis.png" style="width: 500px;" /></a>
    620. 

  620. </div>
    621. 

  621. <div class="line-block">
    622. 

  622. <div class="line"><br /></div>
    623. 

  623. <div class="line"><br /></div>
    624. 

  624. </div>
    625. 

  625. <p>The corresponding code looks like this:</p>
    626. 

  626. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Axis</span><span class="p">():</span>
    627. 

  627.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    628. 

  628.         <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="mi">7</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
    629. 

  629.         <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Axis.py&#39;</span><span class="p">)</span>
    630. 

  630.     <span class="c"># Draw normal x and y axis with origin at (7.5, 2)</span>
    631. 

  631.     <span class="c"># in the coordinate system of the sketch: [0,15]x[-7,8]</span>
    632. 

  632.     <span class="n">x_axis</span> <span class="o">=</span> <span class="n">Axis</span><span class="p">((</span><span class="mf">7.5</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="mi">5</span><span class="p">,</span> <span class="s">&#39;x&#39;</span><span class="p">,</span> <span class="n">rotation_angle</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
    633. 

  633.     <span class="n">y_axis</span> <span class="o">=</span> <span class="n">Axis</span><span class="p">((</span><span class="mf">7.5</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="mi">5</span><span class="p">,</span> <span class="s">&#39;y&#39;</span><span class="p">,</span> <span class="n">rotation_angle</span><span class="o">=</span><span class="mi">90</span><span class="p">)</span>
    634. 

  634.     <span class="n">system</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;x axis&#39;</span><span class="p">:</span> <span class="n">x_axis</span><span class="p">,</span> <span class="s">&#39;y axis&#39;</span><span class="p">:</span> <span class="n">y_axis</span><span class="p">})</span>
    635. 

  635.     <span class="n">system</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    636. 

  636.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    637. 

  637. 

  638.     <span class="c"># Rotate this system 40 degrees counter clockwise</span>
    639. 

  639.     <span class="c"># and draw it with dashed lines</span>
    640. 

  640.     <span class="n">system</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;dashed&#39;</span><span class="p">)</span>
    641. 

  641.     <span class="n">system</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">40</span><span class="p">,</span> <span class="p">(</span><span class="mf">7.5</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
    642. 

  642.     <span class="n">system</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    643. 

  643.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    644. 

  644. 

  645.     <span class="c"># Rotate this system another 220 degrees and show</span>
    646. 

  646.     <span class="c"># with dotted lines</span>
    647. 

  647.     <span class="n">system</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;dotted&#39;</span><span class="p">)</span>
    648. 

  648.     <span class="n">system</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">220</span><span class="p">,</span> <span class="p">(</span><span class="mf">7.5</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
    649. 

  649.     <span class="n">system</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    650. 

  650.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    651. 

  651. 

  652.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Axis&#39;</span><span class="p">)</span>
    653. 

  653. </pre></div>
    654. 

  654. </div>
    655. 

  655. </div>
    656. 

  656. <div class="section" id="distance-with-text">
    657. 

  657. <h3>Distance with text<a class="headerlink" href="#distance-with-text" title="Permalink to this headline">¶</a></h3>
    658. 

  658. <p>The object <code class="docutils literal"><span class="pre">Distance_wText</span></code> is used to display an arrow, to indicate
    659. 

  659. a distance in a sketch, with an additional text in the middle of the arrow.</p>
    660. 

  660. <p>The figure</p>
    661. 

  661. <div class="line-block">
    662. 

  662. <div class="line"><br /></div>
    663. 

  663. <div class="line"><br /></div>
    664. 

  664. </div>
    665. 

  665. <div class="figure">
    666. 

  666. <a class="reference internal image-reference" href="_images/Distance_wText.png"><img alt="_images/Distance_wText.png" src="_images/Distance_wText.png" style="width: 500px;" /></a>
    667. 

  667. </div>
    668. 

  668. <div class="line-block">
    669. 

  669. <div class="line"><br /></div>
    670. 

  670. <div class="line"><br /></div>
    671. 

  671. </div>
    672. 

  672. <p>was produced by this code:</p>
    673. 

  673. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Distance_wText</span><span class="p">():</span>
    674. 

  674.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    675. 

  675.         <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span>
    676. 

  676.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Distance_wText.py&#39;</span><span class="p">)</span>
    677. 

  677. 

  678.     <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span>
    679. 

  679.     <span class="n">t</span> <span class="o">=</span> <span class="s">r&#39;$ 2\pi R^2 $&#39;</span>  <span class="c"># sample text</span>
    680. 

  680.     <span class="n">examples</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span>
    681. 

  681.         <span class="s">&#39;a0&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">),</span>
    682. 

  682.         <span class="s">&#39;a6&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">),</span>
    683. 

  683.         <span class="s">&#39;a1&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mf">4.5</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">),</span>
    684. 

  684.         <span class="s">&#39;a2&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">),</span>
    685. 

  685.         <span class="s">&#39;a3&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mf">4.5</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">5.5</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">),</span>
    686. 

  686.         <span class="s">&#39;a4&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">8</span><span class="p">,</span><span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">,</span>
    687. 

  687.                              <span class="n">text_spacing</span><span class="o">=-</span><span class="mf">1.</span><span class="o">/</span><span class="mi">60</span><span class="p">),</span>
    688. 

  688.         <span class="s">&#39;a5&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">((</span><span class="mi">8</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">t</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">,</span>
    689. 

  689.                              <span class="n">text_spacing</span><span class="o">=-</span><span class="mf">1.</span><span class="o">/</span><span class="mi">40</span><span class="p">,</span> <span class="n">alignment</span><span class="o">=</span><span class="s">&#39;right&#39;</span><span class="p">),</span>
    690. 

  690.         <span class="s">&#39;c1&#39;</span><span class="p">:</span> <span class="n">Text_wArrow</span><span class="p">(</span><span class="s">&#39;text_spacing=-1./60&#39;</span><span class="p">,</span>
    691. 

  691.                           <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mf">3.5</span><span class="p">),</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mf">3.2</span><span class="p">),</span>
    692. 

  692.                           <span class="n">fontsize</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">alignment</span><span class="o">=</span><span class="s">&#39;left&#39;</span><span class="p">),</span>
    693. 

  693.         <span class="s">&#39;c2&#39;</span><span class="p">:</span> <span class="n">Text_wArrow</span><span class="p">(</span><span class="s">&#39;text_spacing=-1./40, alignment=&quot;right&quot;&#39;</span><span class="p">,</span>
    694. 

  694.                           <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">),</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">),</span>
    695. 

  695.                           <span class="n">fontsize</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">alignment</span><span class="o">=</span><span class="s">&#39;left&#39;</span><span class="p">),</span>
    696. 

  696.         <span class="p">})</span>
    697. 

  697.     <span class="n">examples</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    698. 

  698.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Distance_wText and text positioning&#39;</span><span class="p">)</span>
    699. 

  699. </pre></div>
    700. 

  700. </div>
    701. 

  701. <p>Note the use of <code class="docutils literal"><span class="pre">Text_wArrow</span></code> to write an explaining text with an
    702. 

  702. associated arrow, here used to explain how
    703. 

  703. the <code class="docutils literal"><span class="pre">text_spacing</span></code> and <code class="docutils literal"><span class="pre">alignment</span></code> arguments can be used to adjust
    704. 

  704. the appearance of the text that goes with the distance arrow.</p>
    705. 

  705. </div>
    706. 

  706. <div class="section" id="rectangle">
    707. 

  707. <h3>Rectangle<a class="headerlink" href="#rectangle" title="Permalink to this headline">¶</a></h3>
    708. 

  708. <div class="figure">
    709. 

  709. <a class="reference internal image-reference" href="_images/Rectangle.png"><img alt="_images/Rectangle.png" src="_images/Rectangle.png" style="width: 500px;" /></a>
    710. 

  710. </div>
    711. 

  711. <div class="line-block">
    712. 

  712. <div class="line"><br /></div>
    713. 

  713. <div class="line"><br /></div>
    714. 

  714. </div>
    715. 

  715. <p>The above figure can be produced by the following code.</p>
    716. 

  716. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Rectangle</span><span class="p">():</span>
    717. 

  717.     <span class="n">L</span> <span class="o">=</span> <span class="mf">3.0</span>
    718. 

  718.     <span class="n">W</span> <span class="o">=</span> <span class="mf">4.0</span>
    719. 

  719. 

  720.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    721. 

  721.         <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">W</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">L</span><span class="p">,</span>
    722. 

  722.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Rectangle.py&#39;</span><span class="p">)</span>
    723. 

  723.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    724. 

  724.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_grid</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
    725. 

  725. 

  726.     <span class="n">xpos</span> <span class="o">=</span> <span class="n">W</span><span class="o">/</span><span class="mi">2</span>
    727. 

  727.     <span class="n">r</span> <span class="o">=</span> <span class="n">Rectangle</span><span class="p">(</span><span class="n">lower_left_corner</span><span class="o">=</span><span class="p">(</span><span class="n">xpos</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">width</span><span class="o">=</span><span class="n">W</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="n">L</span><span class="p">)</span>
    728. 

  728.     <span class="n">r</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    729. 

  729.     <span class="n">r</span><span class="o">.</span><span class="n">draw_dimensions</span><span class="p">()</span>
    730. 

  730.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Rectangle&#39;</span><span class="p">)</span>
    731. 

  731. </pre></div>
    732. 

  732. </div>
    733. 

  733. <p>Note that the <code class="docutils literal"><span class="pre">draw_dimension</span></code> method adds explanation of dimensions and various
    734. 

  734. important argument in the construction of a shape. It adapts the annotations
    735. 

  735. to the geometry of the current shape.</p>
    736. 

  736. </div>
    737. 

  737. <div class="section" id="triangle">
    738. 

  738. <h3>Triangle<a class="headerlink" href="#triangle" title="Permalink to this headline">¶</a></h3>
    739. 

  739. <div class="figure">
    740. 

  740. <a class="reference internal image-reference" href="_images/Triangle.png"><img alt="_images/Triangle.png" src="_images/Triangle.png" style="width: 500px;" /></a>
    741. 

  741. </div>
    742. 

  742. <div class="line-block">
    743. 

  743. <div class="line"><br /></div>
    744. 

  744. <div class="line"><br /></div>
    745. 

  745. </div>
    746. 

  746. <p>The code below produces the figure.</p>
    747. 

  747. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Triangle</span><span class="p">():</span>
    748. 

  748.     <span class="n">L</span> <span class="o">=</span> <span class="mf">3.0</span>
    749. 

  749.     <span class="n">W</span> <span class="o">=</span> <span class="mf">4.0</span>
    750. 

  750. 

  751.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    752. 

  752.         <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">W</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mf">1.2</span><span class="o">*</span><span class="n">L</span><span class="p">,</span>
    753. 

  753.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Triangle.py&#39;</span><span class="p">)</span>
    754. 

  754.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    755. 

  755.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_grid</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
    756. 

  756. 

  757.     <span class="n">xpos</span> <span class="o">=</span> <span class="mi">1</span>
    758. 

  758.     <span class="n">t</span> <span class="o">=</span> <span class="n">Triangle</span><span class="p">(</span><span class="n">p1</span><span class="o">=</span><span class="p">(</span><span class="n">W</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">p2</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">W</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">W</span><span class="o">/</span><span class="mi">2</span><span class="p">),</span> <span class="n">p3</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">W</span><span class="o">/</span><span class="mf">5.</span><span class="p">,</span><span class="n">L</span><span class="p">))</span>
    759. 

  759.     <span class="n">t</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    760. 

  760.     <span class="n">t</span><span class="o">.</span><span class="n">draw_dimensions</span><span class="p">()</span>
    761. 

  761.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Triangle&#39;</span><span class="p">)</span>
    762. 

  762. </pre></div>
    763. 

  763. </div>
    764. 

  764. <p>Here, the <code class="docutils literal"><span class="pre">draw_dimension</span></code> method writes the name of the corners at the
    765. 

  765. position of the corners, which does not always look nice (the present figure
    766. 

  766. is an example). For a high-quality sketch one would add some spacing
    767. 

  767. to the location of the p1, p2, and even p3 texts.</p>
    768. 

  768. </div>
    769. 

  769. <div class="section" id="arc">
    770. 

  770. <h3>Arc<a class="headerlink" href="#arc" title="Permalink to this headline">¶</a></h3>
    771. 

  771. <div class="figure">
    772. 

  772. <a class="reference internal image-reference" href="_images/Arc.png"><img alt="_images/Arc.png" src="_images/Arc.png" style="width: 400px;" /></a>
    773. 

  773. </div>
    774. 

  774. <div class="line-block">
    775. 

  775. <div class="line"><br /></div>
    776. 

  776. <div class="line"><br /></div>
    777. 

  777. </div>
    778. 

  778. <p>An arc like the one above is produced by</p>
    779. 

  779. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Arc</span><span class="p">():</span>
    780. 

  780.     <span class="n">L</span> <span class="o">=</span> <span class="mf">4.0</span>
    781. 

  781.     <span class="n">W</span> <span class="o">=</span> <span class="mf">4.0</span>
    782. 

  782. 

  783.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    784. 

  784.         <span class="n">xmin</span><span class="o">=-</span><span class="n">W</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="n">W</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mf">1.5</span><span class="o">*</span><span class="n">L</span><span class="p">,</span>
    785. 

  785.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Arc.py&#39;</span><span class="p">)</span>
    786. 

  786.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    787. 

  787.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_grid</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
    788. 

  788. 

  789.     <span class="n">center</span> <span class="o">=</span> <span class="n">point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
    790. 

  790.     <span class="n">radius</span> <span class="o">=</span> <span class="n">L</span><span class="o">/</span><span class="mi">2</span>
    791. 

  791.     <span class="n">start_angle</span> <span class="o">=</span> <span class="mi">60</span>
    792. 

  792.     <span class="n">arc_angle</span> <span class="o">=</span> <span class="mi">45</span>
    793. 

  793.     <span class="n">a</span> <span class="o">=</span> <span class="n">Arc</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">start_angle</span><span class="p">,</span> <span class="n">arc_angle</span><span class="p">)</span>
    794. 

  794.     <span class="n">a</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    795. 

  795. 

  796.     <span class="n">R1</span> <span class="o">=</span> <span class="mf">1.25</span><span class="o">*</span><span class="n">radius</span>
    797. 

  797.     <span class="n">R2</span> <span class="o">=</span> <span class="mf">1.5</span><span class="o">*</span><span class="n">radius</span>
    798. 

  798.     <span class="n">R</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">radius</span>
    799. 

  799.     <span class="n">a</span><span class="o">.</span><span class="n">dimensions</span> <span class="o">=</span> <span class="p">{</span>
    800. 

  800.         <span class="s">&#39;start_angle&#39;</span><span class="p">:</span>
    801. 

  801.         <span class="n">Arc_wText</span><span class="p">(</span>
    802. 

  802.             <span class="s">&#39;start_angle&#39;</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">R1</span><span class="p">,</span> <span class="n">start_angle</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
    803. 

  803.             <span class="n">arc_angle</span><span class="o">=</span><span class="n">start_angle</span><span class="p">,</span> <span class="n">text_spacing</span><span class="o">=</span><span class="mi">1</span><span class="o">/</span><span class="mf">10.</span><span class="p">),</span>
    804. 

  804.         <span class="s">&#39;arc_angle&#39;</span><span class="p">:</span>
    805. 

  805.         <span class="n">Arc_wText</span><span class="p">(</span>
    806. 

  806.             <span class="s">&#39;arc_angle&#39;</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">R2</span><span class="p">,</span> <span class="n">start_angle</span><span class="o">=</span><span class="n">start_angle</span><span class="p">,</span>
    807. 

  807.             <span class="n">arc_angle</span><span class="o">=</span><span class="n">arc_angle</span><span class="p">,</span> <span class="n">text_spacing</span><span class="o">=</span><span class="mi">1</span><span class="o">/</span><span class="mf">20.</span><span class="p">),</span>
    808. 

  808.         <span class="s">&#39;r=0&#39;</span><span class="p">:</span>
    809. 

  809.         <span class="n">Line</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span>
    810. 

  810.              <span class="n">point</span><span class="p">(</span><span class="n">R</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">radians</span><span class="p">(</span><span class="n">start_angle</span><span class="p">)),</span>
    811. 

  811.                    <span class="n">R</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">radians</span><span class="p">(</span><span class="n">start_angle</span><span class="p">)))),</span>
    812. 

  812.         <span class="s">&#39;r=start_angle&#39;</span><span class="p">:</span>
    813. 

  813.         <span class="n">Line</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span>
    814. 

  814.              <span class="n">point</span><span class="p">(</span><span class="n">R</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">radians</span><span class="p">(</span><span class="n">start_angle</span><span class="o">+</span><span class="n">arc_angle</span><span class="p">)),</span>
    815. 

  815.                    <span class="n">R</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">radians</span><span class="p">(</span><span class="n">start_angle</span><span class="o">+</span><span class="n">arc_angle</span><span class="p">)))),</span>
    816. 

  816.         <span class="s">&#39;r=start+arc_angle&#39;</span><span class="p">:</span>
    817. 

  817.         <span class="n">Line</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span>
    818. 

  818.              <span class="n">point</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;dashed&#39;</span><span class="p">),</span>
    819. 

  819.         <span class="s">&#39;radius&#39;</span><span class="p">:</span> <span class="n">Distance_wText</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">a</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="s">&#39;radius&#39;</span><span class="p">,</span> <span class="n">text_spacing</span><span class="o">=</span><span class="mi">1</span><span class="o">/</span><span class="mf">40.</span><span class="p">),</span>
    820. 

  820.         <span class="s">&#39;center&#39;</span><span class="p">:</span> <span class="n">Text</span><span class="p">(</span><span class="s">&#39;center&#39;</span><span class="p">,</span> <span class="n">center</span><span class="o">-</span><span class="n">point</span><span class="p">(</span><span class="n">radius</span><span class="o">/</span><span class="mf">10.</span><span class="p">,</span> <span class="n">radius</span><span class="o">/</span><span class="mf">10.</span><span class="p">)),</span>
    821. 

  821.         <span class="p">}</span>
    822. 

  822.     <span class="k">for</span> <span class="n">dimension</span> <span class="ow">in</span> <span class="n">a</span><span class="o">.</span><span class="n">dimensions</span><span class="p">:</span>
    823. 

  823.         <span class="k">if</span> <span class="n">dimension</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s">&#39;r=&#39;</span><span class="p">):</span>
    824. 

  824.             <span class="n">dim</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">dimensions</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
    825. 

  825.             <span class="n">dim</span><span class="o">.</span><span class="n">set_linestyle</span><span class="p">(</span><span class="s">&#39;dashed&#39;</span><span class="p">)</span>
    826. 

  826.             <span class="n">dim</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
    827. 

  827.             <span class="n">dim</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;black&#39;</span><span class="p">)</span>
    828. 

  828. 

  829.     <span class="n">a</span><span class="o">.</span><span class="n">draw_dimensions</span><span class="p">()</span>
    830. 

  830.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Arc&#39;</span><span class="p">)</span>
    831. 

  831. </pre></div>
    832. 

  832. </div>
    833. 

  833. </div>
    834. 

  834. <div class="section" id="spring">
    835. 

  835. <h3>Spring<a class="headerlink" href="#spring" title="Permalink to this headline">¶</a></h3>
    836. 

  836. <div class="figure">
    837. 

  837. <a class="reference internal image-reference" href="_images/Spring.png"><img alt="_images/Spring.png" src="_images/Spring.png" style="width: 800px;" /></a>
    838. 

  838. </div>
    839. 

  839. <div class="line-block">
    840. 

  840. <div class="line"><br /></div>
    841. 

  841. <div class="line"><br /></div>
    842. 

  842. </div>
    843. 

  843. <p>The code for making these two springs goes like this:</p>
    844. 

  844. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Spring</span><span class="p">():</span>
    845. 

  845.     <span class="n">L</span> <span class="o">=</span> <span class="mf">5.0</span>
    846. 

  846.     <span class="n">W</span> <span class="o">=</span> <span class="mf">2.0</span>
    847. 

  847. 

  848.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    849. 

  849.         <span class="n">xmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="mi">7</span><span class="o">*</span><span class="n">W</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mf">1.5</span><span class="o">*</span><span class="n">L</span><span class="p">,</span>
    850. 

  850.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Spring.py&#39;</span><span class="p">)</span>
    851. 

  851.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    852. 

  852.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_grid</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
    853. 

  853. 

  854.     <span class="n">xpos</span> <span class="o">=</span> <span class="n">W</span>
    855. 

  855.     <span class="n">s1</span> <span class="o">=</span> <span class="n">Spring</span><span class="p">((</span><span class="n">W</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">L</span><span class="p">,</span> <span class="n">teeth</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
    856. 

  856.     <span class="n">s1_title</span> <span class="o">=</span> <span class="n">Text</span><span class="p">(</span><span class="s">&#39;Default Spring&#39;</span><span class="p">,</span>
    857. 

  857.                     <span class="n">s1</span><span class="o">.</span><span class="n">geometric_features</span><span class="p">()[</span><span class="s">&#39;end&#39;</span><span class="p">]</span> <span class="o">+</span> <span class="n">point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">L</span><span class="o">/</span><span class="mi">10</span><span class="p">))</span>
    858. 

  858.     <span class="n">s1</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    859. 

  859.     <span class="n">s1_title</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    860. 

  860.     <span class="c">#s1.draw_dimensions()</span>
    861. 

  861.     <span class="n">xpos</span> <span class="o">+=</span> <span class="mi">3</span><span class="o">*</span><span class="n">W</span>
    862. 

  862.     <span class="n">s2</span> <span class="o">=</span> <span class="n">Spring</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="p">(</span><span class="n">xpos</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">length</span><span class="o">=</span><span class="n">L</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="n">W</span><span class="o">/</span><span class="mf">2.</span><span class="p">,</span>
    863. 

  863.                 <span class="n">bar_length</span><span class="o">=</span><span class="n">L</span><span class="o">/</span><span class="mf">6.</span><span class="p">,</span> <span class="n">teeth</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
    864. 

  864.     <span class="n">s2</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    865. 

  865.     <span class="n">s2</span><span class="o">.</span><span class="n">draw_dimensions</span><span class="p">()</span>
    866. 

  866.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Spring&#39;</span><span class="p">)</span>
    867. 

  867. </pre></div>
    868. 

  868. </div>
    869. 

  869. </div>
    870. 

  870. <div class="section" id="dashpot">
    871. 

  871. <h3>Dashpot<a class="headerlink" href="#dashpot" title="Permalink to this headline">¶</a></h3>
    872. 

  872. <div class="figure">
    873. 

  873. <a class="reference internal image-reference" href="_images/Dashpot.png"><img alt="_images/Dashpot.png" src="_images/Dashpot.png" style="width: 600px;" /></a>
    874. 

  874. </div>
    875. 

  875. <div class="line-block">
    876. 

  876. <div class="line"><br /></div>
    877. 

  877. <div class="line"><br /></div>
    878. 

  878. </div>
    879. 

  879. <p>This dashpot is produced by</p>
    880. 

  880. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">test_Dashpot</span><span class="p">():</span>
    881. 

  881.     <span class="n">L</span> <span class="o">=</span> <span class="mf">5.0</span>
    882. 

  882.     <span class="n">W</span> <span class="o">=</span> <span class="mf">2.0</span>
    883. 

  883.     <span class="n">xpos</span> <span class="o">=</span> <span class="mi">0</span>
    884. 

  884. 

  885.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_coordinate_system</span><span class="p">(</span>
    886. 

  886.         <span class="n">xmin</span><span class="o">=</span><span class="n">xpos</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="n">xpos</span><span class="o">+</span><span class="mf">5.5</span><span class="o">*</span><span class="n">W</span><span class="p">,</span> <span class="n">ymin</span><span class="o">=-</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ymax</span><span class="o">=</span><span class="mf">1.5</span><span class="o">*</span><span class="n">L</span><span class="p">,</span>
    887. 

  887.         <span class="n">axis</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">instruction_file</span><span class="o">=</span><span class="s">&#39;tmp_Dashpot.py&#39;</span><span class="p">)</span>
    888. 

  888.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    889. 

  889.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">set_grid</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
    890. 

  890. 

  891.     <span class="c"># Default (simple) dashpot</span>
    892. 

  892.     <span class="n">xpos</span> <span class="o">=</span> <span class="mf">1.5</span>
    893. 

  893.     <span class="n">d1</span> <span class="o">=</span> <span class="n">Dashpot</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="p">(</span><span class="n">xpos</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">total_length</span><span class="o">=</span><span class="n">L</span><span class="p">)</span>
    894. 

  894.     <span class="n">d1_title</span> <span class="o">=</span> <span class="n">Text</span><span class="p">(</span><span class="s">&#39;Dashpot (default)&#39;</span><span class="p">,</span>
    895. 

  895.                     <span class="n">d1</span><span class="o">.</span><span class="n">geometric_features</span><span class="p">()[</span><span class="s">&#39;end&#39;</span><span class="p">]</span> <span class="o">+</span> <span class="n">point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">L</span><span class="o">/</span><span class="mi">10</span><span class="p">))</span>
    896. 

  896.     <span class="n">d1</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    897. 

  897.     <span class="n">d1_title</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    898. 

  898. 

  899.     <span class="c"># Dashpot for animation with fixed bar_length, dashpot_length and</span>
    900. 

  900.     <span class="c"># prescribed piston_pos</span>
    901. 

  901.     <span class="n">xpos</span> <span class="o">+=</span> <span class="mf">2.5</span><span class="o">*</span><span class="n">W</span>
    902. 

  902.     <span class="n">d2</span> <span class="o">=</span> <span class="n">Dashpot</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="p">(</span><span class="n">xpos</span><span class="p">,</span><span class="mi">0</span><span class="p">),</span> <span class="n">total_length</span><span class="o">=</span><span class="mf">1.2</span><span class="o">*</span><span class="n">L</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="n">W</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span>
    903. 

  903.                  <span class="n">bar_length</span><span class="o">=</span><span class="n">W</span><span class="p">,</span> <span class="n">dashpot_length</span><span class="o">=</span><span class="n">L</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">piston_pos</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">W</span><span class="p">)</span>
    904. 

  904.     <span class="n">d2</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    905. 

  905.     <span class="n">d2</span><span class="o">.</span><span class="n">draw_dimensions</span><span class="p">()</span>
    906. 

  906. 

  907.     <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">(</span><span class="s">&#39;Dashpot&#39;</span><span class="p">)</span>
    908. 

  908. </pre></div>
    909. 

  909. </div>
    910. 

  910. </div>
    911. 

  911. <div class="section" id="wavy">
    912. 

  912. <h3>Wavy<a class="headerlink" href="#wavy" title="Permalink to this headline">¶</a></h3>
    913. 

  913. <p>Looks strange. Fix x axis.</p>
    914. 

  914. </div>
    915. 

  915. <div class="section" id="stochastic-curves">
    916. 

  916. <h3>Stochastic curves<a class="headerlink" href="#stochastic-curves" title="Permalink to this headline">¶</a></h3>
    917. 

  917. <p>The <code class="docutils literal"><span class="pre">StochasticWavyCurve</span></code> object offers three precomputed
    918. 

  918. graphics that have a random variation:</p>
    919. 

  919. <div class="line-block">
    920. 

  920. <div class="line"><br /></div>
    921. 

  921. <div class="line"><br /></div>
    922. 

  922. </div>
    923. 

  923. <div class="figure">
    924. 

  924. <a class="reference internal image-reference" href="_images/StochasticWavyCurve.png"><img alt="_images/StochasticWavyCurve.png" src="_images/StochasticWavyCurve.png" style="width: 600px;" /></a>
    925. 

  925. </div>
    926. 

  926. <div class="line-block">
    927. 

  927. <div class="line"><br /></div>
    928. 

  928. <div class="line"><br /></div>
    929. 

  929. </div>
    930. 

  930. <p>The usage is simple. The construction</p>
    931. 

  931. <div class="highlight-python"><div class="highlight"><pre><span class="n">curve</span> <span class="o">=</span> <span class="n">StochasticWavyCurve</span><span class="p">(</span><span class="n">curve_no</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">percentage</span><span class="o">=</span><span class="mi">40</span><span class="p">)</span>
    932. 

  932. </pre></div>
    933. 

  933. </div>
    934. 

  934. <p>picks the second curve (the three are numbered 0, 1, and 2),
    935. 

  935. and the first 40% of that curve. In case one desires another extent
    936. 

  936. of the axis, one can just scale the coordinates directly as these
    937. 

  937. are stored in the arrays <code class="docutils literal"><span class="pre">curve.x[curve_no]</span></code> and
    938. 

  938. <code class="docutils literal"><span class="pre">curve.y[curve_no]</span></code>.</p>
    939. 

  939. </div>
    940. 

  940. </div>
    941. 

  941. <div class="section" id="inner-workings-of-the-pysketcher-tool">
    942. 

  942. <h2>Inner workings of the Pysketcher tool<a class="headerlink" href="#inner-workings-of-the-pysketcher-tool" title="Permalink to this headline">¶</a></h2>
    943. 

  943. <p>We shall now explain how we can, quite easily, realize software with
    944. 

  944. the capabilities demonstrated in the previous examples. Each object in
    945. 

  945. the figure is represented as a class in a class hierarchy. Using
    946. 

  946. inheritance, classes can inherit properties from parent classes and
    947. 

  947. add new geometric features.</p>
    948. 

  948. <p id="index-0">Class programming is a key technology for realizing Pysketcher.
    949. 

  949. As soon as some classes are established, more are easily
    950. 

  950. added. Enhanced functionality for all the classes is also easy to
    951. 

  951. implement in common, generic code that can immediately be shared by
    952. 

  952. all present and future classes. The fundamental data structure
    953. 

  953. involved in the <code class="docutils literal"><span class="pre">pysketcher</span></code> package is a hierarchical tree, and much
    954. 

  954. of the material on implementation issues targets how to traverse tree
    955. 

  955. structures with recursive function calls in object hierarchies. This
    956. 

  956. topic is of key relevance in a wide range of other applications as
    957. 

  957. well. In total, the inner workings of Pysketcher constitute an
    958. 

  958. excellent example on the power of class programming.</p>
    959. 

  959. <div class="section" id="example-of-classes-for-geometric-objects">
    960. 

  960. <h3>Example of classes for geometric objects<a class="headerlink" href="#example-of-classes-for-geometric-objects" title="Permalink to this headline">¶</a></h3>
    961. 

  961. <p>We introduce class <code class="docutils literal"><span class="pre">Shape</span></code> as superclass for all specialized objects
    962. 

  962. in a figure. This class does not store any data, but provides a
    963. 

  963. series of functions that add functionality to all the subclasses.
    964. 

  964. This will be shown later.</p>
    965. 

  965. <div class="section" id="simple-geometric-objects">
    966. 

  966. <h4>Simple geometric objects<a class="headerlink" href="#simple-geometric-objects" title="Permalink to this headline">¶</a></h4>
    967. 

  967. <p>One simple subclass is <code class="docutils literal"><span class="pre">Rectangle</span></code>, specified by the coordinates of
    968. 

  968. the lower left corner and its width and height:</p>
    969. 

  969. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Rectangle</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    970. 

  970.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">lower_left_corner</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
    971. 

  971.         <span class="n">p</span> <span class="o">=</span> <span class="n">lower_left_corner</span>  <span class="c"># short form</span>
    972. 

  972.         <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">width</span><span class="p">,</span>
    973. 

  973.              <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">width</span><span class="p">,</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
    974. 

  974.         <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">height</span><span class="p">,</span>
    975. 

  975.              <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">height</span><span class="p">,</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
    976. 

  976.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;rectangle&#39;</span><span class="p">:</span> <span class="n">Curve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)}</span>
    977. 

  977. </pre></div>
    978. 

  978. </div>
    979. 

  979. <p>Any subclass of <code class="docutils literal"><span class="pre">Shape</span></code> will have a constructor that takes geometric
    980. 

  980. information about the shape of the object and creates a dictionary
    981. 

  981. <code class="docutils literal"><span class="pre">self.shapes</span></code> with the shape built of simpler shapes. The most
    982. 

  982. fundamental shape is <code class="docutils literal"><span class="pre">Curve</span></code>, which is just a collection of <span class="math">\((x,y)\)</span>
    983. 

  983. coordinates in two arrays <code class="docutils literal"><span class="pre">x</span></code> and <code class="docutils literal"><span class="pre">y</span></code>.  Drawing the <code class="docutils literal"><span class="pre">Curve</span></code> object is
    984. 

  984. a matter of plotting <code class="docutils literal"><span class="pre">y</span></code> versus <code class="docutils literal"><span class="pre">x</span></code>.  For class <code class="docutils literal"><span class="pre">Rectangle</span></code> the <code class="docutils literal"><span class="pre">x</span></code>
    985. 

  985. and <code class="docutils literal"><span class="pre">y</span></code> arrays contain the corner points of the rectangle in
    986. 

  986. counterclockwise direction, starting and ending with in the lower left
    987. 

  987. corner.</p>
    988. 

  988. <p>Class <code class="docutils literal"><span class="pre">Line</span></code> is also a simple class:</p>
    989. 

  989. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Line</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    990. 

  990.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">end</span><span class="p">):</span>
    991. 

  991.         <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">start</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">end</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
    992. 

  992.         <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">start</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">end</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
    993. 

  993.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;line&#39;</span><span class="p">:</span> <span class="n">Curve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)}</span>
    994. 

  994. </pre></div>
    995. 

  995. </div>
    996. 

  996. <p>Here we only need two points, the start and end point on the line.
    997. 

  997. However, we may want to add some useful functionality, e.g., the ability
    998. 

  998. to give an <span class="math">\(x\)</span> coordinate and have the class calculate the
    999. 

  999. corresponding <span class="math">\(y\)</span> coordinate:</p>
    1000. 

  1000. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
    1001. 

  1001.     <span class="sd">&quot;&quot;&quot;Given x, return y on the line.&quot;&quot;&quot;</span>
    1002. 

  1002.     <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;line&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;line&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">y</span>
    1003. 

  1003.     <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">/</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
    1004. 

  1004.     <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    1005. 

  1005.     <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span>
    1006. 

  1006. </pre></div>
    1007. 

  1007. </div>
    1008. 

  1008. <p>Unfortunately, this is too simplistic because vertical lines cannot be
    1009. 

  1009. handled (infinite <code class="docutils literal"><span class="pre">self.a</span></code>). The true source code of <code class="docutils literal"><span class="pre">Line</span></code> therefore
    1010. 

  1010. provides a more general solution at the cost of significantly longer
    1011. 

  1011. code with more tests.</p>
    1012. 

  1012. <p>A circle implies a somewhat increased complexity. Again we represent
    1013. 

  1013. the geometric object by a <code class="docutils literal"><span class="pre">Curve</span></code> object, but this time the <code class="docutils literal"><span class="pre">Curve</span></code>
    1014. 

  1014. object needs to store a large number of points on the curve such that
    1015. 

  1015. a plotting program produces a visually smooth curve.  The points on
    1016. 

  1016. the circle must be calculated manually in the constructor of class
    1017. 

  1017. <code class="docutils literal"><span class="pre">Circle</span></code>. The formulas for points <span class="math">\((x,y)\)</span> on a curve with radius <span class="math">\(R\)</span>
    1018. 

  1018. and center at <span class="math">\((x_0, y_0)\)</span> are given by</p>
    1019. 

  1019. <div class="math">
    1020. 

  1020. \[\begin{split}x &amp;= x_0 + R\cos (t),\\
    1021. 

  1021. y &amp;= y_0 + R\sin (t),\end{split}\]</div>
    1022. 

  1022. <p>where <span class="math">\(t\in [0, 2\pi]\)</span>. A discrete set of <span class="math">\(t\)</span> values in this
    1023. 

  1023. interval gives the corresponding set of <span class="math">\((x,y)\)</span> coordinates on
    1024. 

  1024. the circle. The user must specify the resolution as the number
    1025. 

  1025. of <span class="math">\(t\)</span> values. The circle&#8217;s radius and center must of course
    1026. 

  1026. also be specified.</p>
    1027. 

  1027. <p>We can write the <code class="docutils literal"><span class="pre">Circle</span></code> class as</p>
    1028. 

  1028. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Circle</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    1029. 

  1029.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">resolution</span><span class="o">=</span><span class="mi">180</span><span class="p">):</span>
    1030. 

  1030.         <span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">center</span><span class="p">,</span> <span class="n">radius</span>
    1031. 

  1031.         <span class="bp">self</span><span class="o">.</span><span class="n">resolution</span> <span class="o">=</span> <span class="n">resolution</span>
    1032. 

  1032. 

  1033.         <span class="n">t</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">,</span> <span class="n">resolution</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
    1034. 

  1034.         <span class="n">x0</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>  <span class="n">y0</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
    1035. 

  1035.         <span class="n">R</span> <span class="o">=</span> <span class="n">radius</span>
    1036. 

  1036.         <span class="n">x</span> <span class="o">=</span> <span class="n">x0</span> <span class="o">+</span> <span class="n">R</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    1037. 

  1037.         <span class="n">y</span> <span class="o">=</span> <span class="n">y0</span> <span class="o">+</span> <span class="n">R</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    1038. 

  1038.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;circle&#39;</span><span class="p">:</span> <span class="n">Curve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)}</span>
    1039. 

  1039. </pre></div>
    1040. 

  1040. </div>
    1041. 

  1041. <p>As in class <code class="docutils literal"><span class="pre">Line</span></code> we can offer the possibility to give an angle
    1042. 

  1042. <span class="math">\(\theta\)</span> (equivalent to <span class="math">\(t\)</span> in the formulas above)
    1043. 

  1043. and then get the corresponding <span class="math">\(x\)</span> and <span class="math">\(y\)</span> coordinates:</p>
    1044. 

  1044. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
    1045. 

  1045.     <span class="sd">&quot;&quot;&quot;Return (x, y) point corresponding to angle theta.&quot;&quot;&quot;</span>
    1046. 

  1046.     <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> \
    1047. 

  1047.            <span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
    1048. 

  1048. </pre></div>
    1049. 

  1049. </div>
    1050. 

  1050. <p>There is one flaw with this method: it yields illegal values after
    1051. 

  1051. a translation, scaling, or rotation of the circle.</p>
    1052. 

  1052. <p>A part of a circle, an arc, is a frequent geometric object when
    1053. 

  1053. drawing mechanical systems. The arc is constructed much like
    1054. 

  1054. a circle, but <span class="math">\(t\)</span> runs in <span class="math">\([\theta_s, \theta_s + \theta_a]\)</span>. Giving
    1055. 

  1055. <span class="math">\(\theta_s\)</span> and <span class="math">\(\theta_a\)</span> the slightly more descriptive names
    1056. 

  1056. <code class="docutils literal"><span class="pre">start_angle</span></code> and <code class="docutils literal"><span class="pre">arc_angle</span></code>, the code looks like this:</p>
    1057. 

  1057. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Arc</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    1058. 

  1058.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span>
    1059. 

  1059.                  <span class="n">start_angle</span><span class="p">,</span> <span class="n">arc_angle</span><span class="p">,</span>
    1060. 

  1060.                  <span class="n">resolution</span><span class="o">=</span><span class="mi">180</span><span class="p">):</span>
    1061. 

  1061.         <span class="bp">self</span><span class="o">.</span><span class="n">start_angle</span> <span class="o">=</span> <span class="n">radians</span><span class="p">(</span><span class="n">start_angle</span><span class="p">)</span>
    1062. 

  1062.         <span class="bp">self</span><span class="o">.</span><span class="n">arc_angle</span> <span class="o">=</span> <span class="n">radians</span><span class="p">(</span><span class="n">arc_angle</span><span class="p">)</span>
    1063. 

  1063. 

  1064.         <span class="n">t</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">start_angle</span><span class="p">,</span>
    1065. 

  1065.                      <span class="bp">self</span><span class="o">.</span><span class="n">start_angle</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">arc_angle</span><span class="p">,</span>
    1066. 

  1066.                      <span class="n">resolution</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
    1067. 

  1067.         <span class="n">x0</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>  <span class="n">y0</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
    1068. 

  1068.         <span class="n">R</span> <span class="o">=</span> <span class="n">radius</span>
    1069. 

  1069.         <span class="n">x</span> <span class="o">=</span> <span class="n">x0</span> <span class="o">+</span> <span class="n">R</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    1070. 

  1070.         <span class="n">y</span> <span class="o">=</span> <span class="n">y0</span> <span class="o">+</span> <span class="n">R</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
    1071. 

  1071.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;arc&#39;</span><span class="p">:</span> <span class="n">Curve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)}</span>
    1072. 

  1072. </pre></div>
    1073. 

  1073. </div>
    1074. 

  1074. <p>Having the <code class="docutils literal"><span class="pre">Arc</span></code> class, a <code class="docutils literal"><span class="pre">Circle</span></code> can alternatively be defined as
    1075. 

  1075. a subclass specializing the arc to a circle:</p>
    1076. 

  1076. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Circle</span><span class="p">(</span><span class="n">Arc</span><span class="p">):</span>
    1077. 

  1077.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">resolution</span><span class="o">=</span><span class="mi">180</span><span class="p">):</span>
    1078. 

  1078.         <span class="n">Arc</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">360</span><span class="p">,</span> <span class="n">resolution</span><span class="p">)</span>
    1079. 

  1079. </pre></div>
    1080. 

  1080. </div>
    1081. 

  1081. </div>
    1082. 

  1082. <div class="section" id="class-curve">
    1083. 

  1083. <h4>Class curve<a class="headerlink" href="#class-curve" title="Permalink to this headline">¶</a></h4>
    1084. 

  1084. <p>Class <code class="docutils literal"><span class="pre">Curve</span></code> sits on the coordinates to be drawn, but how is that
    1085. 

  1085. done? The constructor of class <code class="docutils literal"><span class="pre">Curve</span></code> just stores the coordinates,
    1086. 

  1086. while a method <code class="docutils literal"><span class="pre">draw</span></code> sends the coordinates to the plotting program to
    1087. 

  1087. make a graph.  Or more precisely, to avoid a lot of (e.g.)
    1088. 

  1088. Matplotlib-specific plotting commands in class <code class="docutils literal"><span class="pre">Curve</span></code> we have created
    1089. 

  1089. a small layer with a simple programming interface to plotting
    1090. 

  1090. programs. This makes it straightforward to change from Matplotlib to
    1091. 

  1091. another plotting program. The programming interface is represented by
    1092. 

  1092. the <code class="docutils literal"><span class="pre">drawing_tool</span></code> object and has a few functions:</p>
    1093. 

  1093. <blockquote>
    1094. 

  1094. <div><ul class="simple">
    1095. 

  1095. <li><code class="docutils literal"><span class="pre">plot_curve</span></code> for sending a curve in terms of <span class="math">\(x\)</span> and <span class="math">\(y\)</span> coordinates
    1096. 

  1096. to the plotting program,</li>
    1097. 

  1097. <li><code class="docutils literal"><span class="pre">set_coordinate_system</span></code> for specifying the graphics area,</li>
    1098. 

  1098. <li><code class="docutils literal"><span class="pre">erase</span></code> for deleting all elements of the graph,</li>
    1099. 

  1099. <li><code class="docutils literal"><span class="pre">set_grid</span></code> for turning on a grid (convenient while constructing the figure),</li>
    1100. 

  1100. <li><code class="docutils literal"><span class="pre">set_instruction_file</span></code> for creating a separate file with all
    1101. 

  1101. plotting commands (Matplotlib commands in our case),</li>
    1102. 

  1102. <li>a series of <code class="docutils literal"><span class="pre">set_X</span></code> functions where <code class="docutils literal"><span class="pre">X</span></code> is some property like
    1103. 

  1103. <code class="docutils literal"><span class="pre">linecolor</span></code>, <code class="docutils literal"><span class="pre">linestyle</span></code>, <code class="docutils literal"><span class="pre">linewidth</span></code>, <code class="docutils literal"><span class="pre">filled_curves</span></code>.</li>
    1104. 

  1104. </ul>
    1105. 

  1105. </div></blockquote>
    1106. 

  1106. <p>This is basically all we need to communicate to a plotting program.</p>
    1107. 

  1107. <p>Any class in the <code class="docutils literal"><span class="pre">Shape</span></code> hierarchy inherits <code class="docutils literal"><span class="pre">set_X</span></code> functions for
    1108. 

  1108. setting properties of curves. This information is propagated to
    1109. 

  1109. all other shape objects in the <code class="docutils literal"><span class="pre">self.shapes</span></code> dictionary. Class
    1110. 

  1110. <code class="docutils literal"><span class="pre">Curve</span></code> stores the line properties together with the coordinates
    1111. 

  1111. of its curve and propagates this information to the plotting program.
    1112. 

  1112. When saying <code class="docutils literal"><span class="pre">vehicle.set_linewidth(10)</span></code>, all objects that make
    1113. 

  1113. up the <code class="docutils literal"><span class="pre">vehicle</span></code> object will get a <code class="docutils literal"><span class="pre">set_linewidth(10)</span></code> call,
    1114. 

  1114. but only the <code class="docutils literal"><span class="pre">Curve</span></code> object at the end of the chain will actually
    1115. 

  1115. store the information and send it to the plotting program.</p>
    1116. 

  1116. <p>A rough sketch of class <code class="docutils literal"><span class="pre">Curve</span></code> reads</p>
    1117. 

  1117. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Curve</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    1118. 

  1118.     <span class="sd">&quot;&quot;&quot;General curve as a sequence of (x,y) coordintes.&quot;&quot;&quot;</span>
    1119. 

  1119.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    1120. 

  1120.         <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">asarray</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
    1121. 

  1121.         <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">asarray</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
    1122. 

  1122. 

  1123.     <span class="k">def</span> <span class="nf">draw</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
    1124. 

  1124.         <span class="n">drawing_tool</span><span class="o">.</span><span class="n">plot_curve</span><span class="p">(</span>
    1125. 

  1125.             <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">,</span>
    1126. 

  1126.             <span class="bp">self</span><span class="o">.</span><span class="n">linestyle</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">linewidth</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">linecolor</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
    1127. 

  1127. 

  1128.     <span class="k">def</span> <span class="nf">set_linewidth</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">width</span><span class="p">):</span>
    1129. 

  1129.         <span class="bp">self</span><span class="o">.</span><span class="n">linewidth</span> <span class="o">=</span> <span class="n">width</span>
    1130. 

  1130. 

  1131.     <span class="n">det</span> <span class="n">set_linestyle</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">style</span><span class="p">):</span>
    1132. 

  1132.         <span class="bp">self</span><span class="o">.</span><span class="n">linestyle</span> <span class="o">=</span> <span class="n">style</span>
    1133. 

  1133.     <span class="o">...</span>
    1134. 

  1134. </pre></div>
    1135. 

  1135. </div>
    1136. 

  1136. </div>
    1137. 

  1137. <div class="section" id="compound-geometric-objects">
    1138. 

  1138. <h4>Compound geometric objects<a class="headerlink" href="#compound-geometric-objects" title="Permalink to this headline">¶</a></h4>
    1139. 

  1139. <p>The simple classes <code class="docutils literal"><span class="pre">Line</span></code>, <code class="docutils literal"><span class="pre">Arc</span></code>, and <code class="docutils literal"><span class="pre">Circle</span></code> could can the geometric
    1140. 

  1140. shape through just one <code class="docutils literal"><span class="pre">Curve</span></code> object. More complicated shapes are
    1141. 

  1141. built from instances of various subclasses of <code class="docutils literal"><span class="pre">Shape</span></code>. Classes used
    1142. 

  1142. for professional drawings soon get quite complex in composition and
    1143. 

  1143. have a lot of geometric details, so here we prefer to make a very
    1144. 

  1144. simple composition: the already drawn vehicle from Figure
    1145. 

  1145. <a class="reference internal" href="#sketcher-fig-vehicle0"><span class="std std-ref">Sketch of a simple figure</span></a>.  That is, instead of composing the drawing
    1146. 

  1146. in a Python program as shown above, we make a subclass <code class="docutils literal"><span class="pre">Vehicle0</span></code> in
    1147. 

  1147. the <code class="docutils literal"><span class="pre">Shape</span></code> hierarchy for doing the same thing.</p>
    1148. 

  1148. <p>The <code class="docutils literal"><span class="pre">Shape</span></code> hierarchy is found in the <code class="docutils literal"><span class="pre">pysketcher</span></code> package, so to use these
    1149. 

  1149. classes or derive a new one, we need to import <code class="docutils literal"><span class="pre">pysketcher</span></code>. The constructor
    1150. 

  1150. of class <code class="docutils literal"><span class="pre">Vehicle0</span></code> performs approximately the same statements as
    1151. 

  1151. in the example program we developed for making the drawing in
    1152. 

  1152. Figure <a class="reference internal" href="#sketcher-fig-vehicle0"><span class="std std-ref">Sketch of a simple figure</span></a>.</p>
    1153. 

  1153. <div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">pysketcher</span> <span class="kn">import</span> <span class="o">*</span>
    1154. 

  1154. 

  1155. <span class="k">class</span> <span class="nc">Vehicle0</span><span class="p">(</span><span class="n">Shape</span><span class="p">):</span>
    1156. 

  1156.     <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">H</span><span class="p">):</span>
    1157. 

  1157.         <span class="n">wheel1</span> <span class="o">=</span> <span class="n">Circle</span><span class="p">(</span><span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">),</span> <span class="n">radius</span><span class="o">=</span><span class="n">R</span><span class="p">)</span>
    1158. 

  1158.         <span class="n">wheel2</span> <span class="o">=</span> <span class="n">wheel1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
    1159. 

  1159.         <span class="n">wheel2</span><span class="o">.</span><span class="n">translate</span><span class="p">((</span><span class="n">L</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span>
    1160. 

  1160. 

  1161.         <span class="n">under</span> <span class="o">=</span> <span class="n">Rectangle</span><span class="p">(</span><span class="n">lower_left_corner</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">),</span>
    1162. 

  1162.                           <span class="n">width</span><span class="o">=</span><span class="mi">2</span><span class="o">*</span><span class="n">R</span> <span class="o">+</span> <span class="n">L</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="n">H</span><span class="p">)</span>
    1163. 

  1163.         <span class="n">over</span>  <span class="o">=</span> <span class="n">Rectangle</span><span class="p">(</span><span class="n">lower_left_corner</span><span class="o">=</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">R</span> <span class="o">+</span> <span class="n">H</span><span class="p">),</span>
    1164. 

  1164.                           <span class="n">width</span><span class="o">=</span><span class="mf">2.5</span><span class="o">*</span><span class="n">R</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="mf">1.25</span><span class="o">*</span><span class="n">H</span><span class="p">)</span>
    1165. 

  1165. 

  1166.         <span class="n">wheels</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">(</span>
    1167. 

  1167.             <span class="p">{</span><span class="s">&#39;wheel1&#39;</span><span class="p">:</span> <span class="n">wheel1</span><span class="p">,</span> <span class="s">&#39;wheel2&#39;</span><span class="p">:</span> <span class="n">wheel2</span><span class="p">})</span>
    1168. 

  1168.         <span class="n">body</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">(</span>
    1169. 

  1169.             <span class="p">{</span><span class="s">&#39;under&#39;</span><span class="p">:</span> <span class="n">under</span><span class="p">,</span> <span class="s">&#39;over&#39;</span><span class="p">:</span> <span class="n">over</span><span class="p">})</span>
    1170. 

  1170. 

  1171.         <span class="n">vehicle</span> <span class="o">=</span> <span class="n">Composition</span><span class="p">({</span><span class="s">&#39;wheels&#39;</span><span class="p">:</span> <span class="n">wheels</span><span class="p">,</span> <span class="s">&#39;body&#39;</span><span class="p">:</span> <span class="n">body</span><span class="p">})</span>
    1172. 

  1172.         <span class="n">xmax</span> <span class="o">=</span> <span class="n">w_1</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">L</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">R</span>
    1173. 

  1173.         <span class="n">ground</span> <span class="o">=</span> <span class="n">Wall</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="n">R</span><span class="p">,</span> <span class="n">xmax</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">thickness</span><span class="o">=-</span><span class="mf">0.3</span><span class="o">*</span><span class="n">R</span><span class="p">)</span>
    1174. 

  1174. 

  1175.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;vehicle&#39;</span><span class="p">:</span> <span class="n">vehicle</span><span class="p">,</span> <span class="s">&#39;ground&#39;</span><span class="p">:</span> <span class="n">ground</span><span class="p">}</span>
    1176. 

  1176. </pre></div>
    1177. 

  1177. </div>
    1178. 

  1178. <p>Any subclass of <code class="docutils literal"><span class="pre">Shape</span></code> <em>must</em> define the <code class="docutils literal"><span class="pre">shapes</span></code> attribute, otherwise
    1179. 

  1179. the inherited <code class="docutils literal"><span class="pre">draw</span></code> method (and a lot of other methods too) will
    1180. 

  1180. not work.</p>
    1181. 

  1181. <p>The painting of the vehicle, as shown in the right part of
    1182. 

  1182. Figure <a class="reference internal" href="#sketcher-fig-vehicle0-v2"><span class="std std-ref">Left: Basic line-based drawing. Right: Thicker lines and filled parts</span></a>, could in class <code class="docutils literal"><span class="pre">Vehicle0</span></code>
    1183. 

  1183. be offered by a method:</p>
    1184. 

  1184. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">colorful</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
    1185. 

  1185.     <span class="n">wheels</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;wheels&#39;</span><span class="p">]</span>
    1186. 

  1186.     <span class="n">wheels</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="s">&#39;blue&#39;</span><span class="p">)</span>
    1187. 

  1187.     <span class="n">wheels</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
    1188. 

  1188.     <span class="n">wheels</span><span class="o">.</span><span class="n">set_linecolor</span><span class="p">(</span><span class="s">&#39;black&#39;</span><span class="p">)</span>
    1189. 

  1189.     <span class="n">under</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;under&#39;</span><span class="p">]</span>
    1190. 

  1190.     <span class="n">under</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="s">&#39;red&#39;</span><span class="p">)</span>
    1191. 

  1191.     <span class="n">over</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">][</span><span class="s">&#39;body&#39;</span><span class="p">][</span><span class="s">&#39;over&#39;</span><span class="p">]</span>
    1192. 

  1192.     <span class="n">over</span><span class="o">.</span><span class="n">set_filled_curves</span><span class="p">(</span><span class="n">pattern</span><span class="o">=</span><span class="s">&#39;/&#39;</span><span class="p">)</span>
    1193. 

  1193.     <span class="n">over</span><span class="o">.</span><span class="n">set_linewidth</span><span class="p">(</span><span class="mi">14</span><span class="p">)</span>
    1194. 

  1194. </pre></div>
    1195. 

  1195. </div>
    1196. 

  1196. <p>The usage of the class is simple: after having set up an appropriate
    1197. 

  1197. coordinate system as previously shown, we can do</p>
    1198. 

  1198. <div class="highlight-python"><div class="highlight"><pre><span class="n">vehicle</span> <span class="o">=</span> <span class="n">Vehicle0</span><span class="p">(</span><span class="n">w_1</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">H</span><span class="p">)</span>
    1199. 

  1199. <span class="n">vehicle</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    1200. 

  1200. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    1201. 

  1201. </pre></div>
    1202. 

  1202. </div>
    1203. 

  1203. <p>and go on the make a painted version by</p>
    1204. 

  1204. <div class="highlight-python"><div class="highlight"><pre><span class="n">drawing_tool</span><span class="o">.</span><span class="n">erase</span><span class="p">()</span>
    1205. 

  1205. <span class="n">vehicle</span><span class="o">.</span><span class="n">colorful</span><span class="p">()</span>
    1206. 

  1206. <span class="n">vehicle</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    1207. 

  1207. <span class="n">drawing_tool</span><span class="o">.</span><span class="n">display</span><span class="p">()</span>
    1208. 

  1208. </pre></div>
    1209. 

  1209. </div>
    1210. 

  1210. <p>A complete code defining and using class <code class="docutils literal"><span class="pre">Vehicle0</span></code> is found in the file
    1211. 

  1211. <a class="reference external" href="http://tinyurl.com/ot733jn/vehicle2.py">vehicle2.py</a>.</p>
    1212. 

  1212. <p>The <code class="docutils literal"><span class="pre">pysketcher</span></code> package contains a wide range of classes for various
    1213. 

  1213. geometrical objects, particularly those that are frequently used in
    1214. 

  1214. drawings of mechanical systems.</p>
    1215. 

  1215. </div>
    1216. 

  1216. </div>
    1217. 

  1217. <div class="section" id="adding-functionality-via-recursion">
    1218. 

  1218. <h3>Adding functionality via recursion<a class="headerlink" href="#adding-functionality-via-recursion" title="Permalink to this headline">¶</a></h3>
    1219. 

  1219. <p id="index-1">The really powerful feature of our class hierarchy is that we can add
    1220. 

  1220. much functionality to the superclass <code class="docutils literal"><span class="pre">Shape</span></code> and to the &#8220;bottom&#8221; class
    1221. 

  1221. <code class="docutils literal"><span class="pre">Curve</span></code>, and then all other classes for various types of geometrical shapes
    1222. 

  1222. immediately get the new functionality. To explain the idea we may
    1223. 

  1223. look at the <code class="docutils literal"><span class="pre">draw</span></code> method, which all classes in the <code class="docutils literal"><span class="pre">Shape</span></code>
    1224. 

  1224. hierarchy must have. The inner workings of the <code class="docutils literal"><span class="pre">draw</span></code> method explain
    1225. 

  1225. the secrets of how a series of other useful operations on figures
    1226. 

  1226. can be implemented.</p>
    1227. 

  1227. <div class="section" id="basic-principles-of-recursion">
    1228. 

  1228. <h4>Basic principles of recursion<a class="headerlink" href="#basic-principles-of-recursion" title="Permalink to this headline">¶</a></h4>
    1229. 

  1229. <p>Note that we work with two types of hierarchies in the
    1230. 

  1230. present documentation: one Python <em>class hierarchy</em>,
    1231. 

  1231. with <code class="docutils literal"><span class="pre">Shape</span></code> as superclass, and one <em>object hierarchy</em> of figure elements
    1232. 

  1232. in a specific figure. A subclass of <code class="docutils literal"><span class="pre">Shape</span></code> stores its figure in the
    1233. 

  1233. <code class="docutils literal"><span class="pre">self.shapes</span></code> dictionary. This dictionary represents the object hierarchy
    1234. 

  1234. of figure elements for that class. We want to make one <code class="docutils literal"><span class="pre">draw</span></code> call
    1235. 

  1235. for an instance, say our class <code class="docutils literal"><span class="pre">Vehicle0</span></code>, and then we want this call
    1236. 

  1236. to be propagated to <em>all</em> objects that are contained in
    1237. 

  1237. <code class="docutils literal"><span class="pre">self.shapes</span></code> and all is nested subdictionaries. How is this done?</p>
    1238. 

  1238. <p>The natural starting point is to call <code class="docutils literal"><span class="pre">draw</span></code> for each <code class="docutils literal"><span class="pre">Shape</span></code> object
    1239. 

  1239. in the <code class="docutils literal"><span class="pre">self.shapes</span></code> dictionary:</p>
    1240. 

  1240. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">draw</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
    1241. 

  1241.     <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">:</span>
    1242. 

  1242.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="n">shape</span><span class="p">]</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    1243. 

  1243. </pre></div>
    1244. 

  1244. </div>
    1245. 

  1245. <p>This general method can be provided by class <code class="docutils literal"><span class="pre">Shape</span></code> and inherited in
    1246. 

  1246. subclasses like <code class="docutils literal"><span class="pre">Vehicle0</span></code>. Let <code class="docutils literal"><span class="pre">v</span></code> be a <code class="docutils literal"><span class="pre">Vehicle0</span></code> instance.
    1247. 

  1247. Seemingly, a call <code class="docutils literal"><span class="pre">v.draw()</span></code> just calls</p>
    1248. 

  1248. <div class="highlight-python"><div class="highlight"><pre><span class="n">v</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;vehicle&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    1249. 

  1249. <span class="n">v</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="s">&#39;ground&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
    1250. 

  1250. </pre></div>
    1251. 

  1251. </div>
    1252. 

  1252. <p>However, in the former call we call the <code class="docutils literal"><span class="pre">draw</span></code> method of a <code class="docutils literal"><span class="pre">Composition</span></code> object
    1253. 

  1253. whose <code class="docutils literal"><span class="pre">self.shapes</span></code> attributed has two elements: <code class="docutils literal"><span class="pre">wheels</span></code> and <code class="docutils literal"><span class="pre">body</span></code>.
    1254. 

  1254. Since class <code class="docutils literal"><span class="pre">Composition</span></code> inherits the same <code class="docutils literal"><span class="pre">draw</span></code> method, this method will
    1255. 

  1255. run through <code class="docutils literal"><span class="pre">self.shapes</span></code> and call <code class="docutils literal"><span class="pre">wheels.draw()</span></code> and <code class="docutils literal"><span class="pre">body.draw()</span></code>.
    1256. 

  1256. Now, the <code class="docutils literal"><span class="pre">wheels</span></code> object is also a <code class="docutils literal"><span class="pre">Composition</span></code> with the same <code class="docutils literal"><span class="pre">draw</span></code>
    1257. 

  1257. method, which will run through <code class="docutils literal"><span class="pre">self.shapes</span></code>, now containing
    1258. 

  1258. the <code class="docutils literal"><span class="pre">wheel1</span></code> and <code class="docutils literal"><span class="pre">wheel2</span></code> objects. The <code class="docutils literal"><span class="pre">wheel1</span></code> object is a <code class="docutils literal"><span class="pre">Circle</span></code>,
    1259. 

  1259. so calling <code class="docutils literal"><span class="pre">wheel1.draw()</span></code> calls the <code class="docutils literal"><span class="pre">draw</span></code> method in class <code class="docutils literal"><span class="pre">Circle</span></code>,
    1260. 

  1260. but this is the same <code class="docutils literal"><span class="pre">draw</span></code> method as shown above. This method will
    1261. 

  1261. therefore traverse the circle&#8217;s <code class="docutils literal"><span class="pre">shapes</span></code> dictionary, which we have seen
    1262. 

  1262. consists of one <code class="docutils literal"><span class="pre">Curve</span></code> element.</p>
    1263. 

  1263. <p>The <code class="docutils literal"><span class="pre">Curve</span></code> object holds the coordinates to be plotted so here <code class="docutils literal"><span class="pre">draw</span></code>
    1264. 

  1264. really needs to do something &#8220;physical&#8221;, namely send the coordinates to
    1265. 

  1265. the plotting program. The <code class="docutils literal"><span class="pre">draw</span></code> method is outlined in the short listing
    1266. 

  1266. of class <code class="docutils literal"><span class="pre">Curve</span></code> shown previously.</p>
    1267. 

  1267. <p>We can go to any of the other shape objects that appear in the figure
    1268. 

  1268. hierarchy and follow their <code class="docutils literal"><span class="pre">draw</span></code> calls in the similar way. Every time,
    1269. 

  1269. a <code class="docutils literal"><span class="pre">draw</span></code> call will invoke a new <code class="docutils literal"><span class="pre">draw</span></code> call, until we eventually hit
    1270. 

  1270. a <code class="docutils literal"><span class="pre">Curve</span></code> object at the &#8220;bottom&#8221; of the figure hierarchy, and then that part
    1271. 

  1271. of the figure is really plotted (or more precisely, the coordinates
    1272. 

  1272. are sent to a plotting program).</p>
    1273. 

  1273. <p>When a method calls itself, such as <code class="docutils literal"><span class="pre">draw</span></code> does, the calls are known as
    1274. 

  1274. <em>recursive</em> and the programming principle is referred to as
    1275. 

  1275. <em>recursion</em>. This technique is very often used to traverse hierarchical
    1276. 

  1276. structures like the figure structures we work with here. Even though the
    1277. 

  1277. hierarchy of objects building up a figure are of different types, they
    1278. 

  1278. all inherit the same <code class="docutils literal"><span class="pre">draw</span></code> method and therefore exhibit the same
    1279. 

  1279. behavior with respect to drawing. Only the <code class="docutils literal"><span class="pre">Curve</span></code> object has a different
    1280. 

  1280. <code class="docutils literal"><span class="pre">draw</span></code> method, which does not lead to more recursion.</p>
    1281. 

  1281. </div>
    1282. 

  1282. <div class="section" id="explaining-recursion">
    1283. 

  1283. <h4>Explaining recursion<a class="headerlink" href="#explaining-recursion" title="Permalink to this headline">¶</a></h4>
    1284. 

  1284. <p>Understanding recursion is usually a challenge. To get a better idea of
    1285. 

  1285. how recursion works, we have equipped class <code class="docutils literal"><span class="pre">Shape</span></code> with a method <code class="docutils literal"><span class="pre">recurse</span></code>
    1286. 

  1286. that just visits all the objects in the <code class="docutils literal"><span class="pre">shapes</span></code> dictionary and prints
    1287. 

  1287. out a message for each object.
    1288. 

  1288. This feature allows us to trace the execution and see exactly where
    1289. 

  1289. we are in the hierarchy and which objects that are visited.</p>
    1290. 

  1290. <p>The <code class="docutils literal"><span class="pre">recurse</span></code> method is very similar to <code class="docutils literal"><span class="pre">draw</span></code>:</p>
    1291. 

  1291. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">recurse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    1292. 

  1292.     <span class="c"># print message where we are (name is where we come from)</span>
    1293. 

  1293.     <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">:</span>
    1294. 

  1294.         <span class="c"># print message about which object to visit</span>
    1295. 

  1295.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="n">shape</span><span class="p">]</span><span class="o">.</span><span class="n">recurse</span><span class="p">(</span><span class="n">indent</span><span class="o">+</span><span class="mi">2</span><span class="p">,</span> <span class="n">shape</span><span class="p">)</span>
    1296. 

  1296. </pre></div>
    1297. 

  1297. </div>
    1298. 

  1298. <p>The <code class="docutils literal"><span class="pre">indent</span></code> parameter governs how much the message from this
    1299. 

  1299. <code class="docutils literal"><span class="pre">recurse</span></code> method is intended. We increase <code class="docutils literal"><span class="pre">indent</span></code> by 2 for every
    1300. 

  1300. level in the hierarchy, i.e., every row of objects in Figure
    1301. 

  1301. <span class="xref std std-ref">sketcher:fig:Vehicle0:hier2</span>. This indentation makes it easy to
    1302. 

  1302. see on the printout how far down in the hierarchy we are.</p>
    1303. 

  1303. <p>A typical message written by <code class="docutils literal"><span class="pre">recurse</span></code> when <code class="docutils literal"><span class="pre">name</span></code> is <code class="docutils literal"><span class="pre">'body'</span></code> and
    1304. 

  1304. the <code class="docutils literal"><span class="pre">shapes</span></code> dictionary has the keys <code class="docutils literal"><span class="pre">'over'</span></code> and <code class="docutils literal"><span class="pre">'under'</span></code>,
    1305. 

  1305. will be</p>
    1306. 

  1306. <div class="highlight-text"><div class="highlight"><pre>Composition: body.shapes has entries &#39;over&#39;, &#39;under&#39;
    1307. 

  1307. call body.shapes[&quot;over&quot;].recurse(&quot;over&quot;, 6)
    1308. 

  1308. </pre></div>
    1309. 

  1309. </div>
    1310. 

  1310. <p>The number of leading blanks on each line corresponds to the value of
    1311. 

  1311. <code class="docutils literal"><span class="pre">indent</span></code>. The code printing out such messages looks like</p>
    1312. 

  1312. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">recurse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    1313. 

  1313.     <span class="n">space</span> <span class="o">=</span> <span class="s">&#39; &#39;</span><span class="o">*</span><span class="n">indent</span>
    1314. 

  1314.     <span class="k">print</span> <span class="n">space</span><span class="p">,</span> <span class="s">&#39;</span><span class="si">%s</span><span class="s">: </span><span class="si">%s</span><span class="s">.shapes has entries&#39;</span> <span class="o">%</span> \
    1315. 

  1315.           <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__class__</span><span class="o">.</span><span class="n">__name__</span><span class="p">,</span> <span class="n">name</span><span class="p">),</span> \
    1316. 

  1316.           <span class="nb">str</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="o">.</span><span class="n">keys</span><span class="p">()))[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
    1317. 

  1317. 

  1318.     <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">:</span>
    1319. 

  1319.         <span class="k">print</span> <span class="n">space</span><span class="p">,</span>
    1320. 

  1320.         <span class="k">print</span> <span class="s">&#39;call </span><span class="si">%s</span><span class="s">.shapes[&quot;</span><span class="si">%s</span><span class="s">&quot;].recurse(&quot;</span><span class="si">%s</span><span class="s">&quot;, </span><span class="si">%d</span><span class="s">)&#39;</span> <span class="o">%</span> \
    1321. 

  1321.               <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">indent</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
    1322. 

  1322.         <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="n">shape</span><span class="p">]</span><span class="o">.</span><span class="n">recurse</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="n">indent</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
    1323. 

  1323. </pre></div>
    1324. 

  1324. </div>
    1325. 

  1325. <p>Let us follow a <code class="docutils literal"><span class="pre">v.recurse('vehicle')</span></code> call in detail, <code class="docutils literal"><span class="pre">v</span></code> being
    1326. 

  1326. a <code class="docutils literal"><span class="pre">Vehicle0</span></code> instance. Before looking into the output from <code class="docutils literal"><span class="pre">recurse</span></code>,
    1327. 

  1327. let us get an overview of the figure hierarchy in the <code class="docutils literal"><span class="pre">v</span></code> object
    1328. 

  1328. (as produced by <code class="docutils literal"><span class="pre">print</span> <span class="pre">v</span></code>)</p>
    1329. 

  1329. <div class="highlight-text"><div class="highlight"><pre>ground
    1330. 

  1330.     wall
    1331. 

  1331. vehicle
    1332. 

  1332.     body
    1333. 

  1333.         over
    1334. 

  1334.             rectangle
    1335. 

  1335.         under
    1336. 

  1336.             rectangle
    1337. 

  1337.     wheels
    1338. 

  1338.         wheel1
    1339. 

  1339.             arc
    1340. 

  1340.         wheel2
    1341. 

  1341.             arc
    1342. 

  1342. </pre></div>
    1343. 

  1343. </div>
    1344. 

  1344. <p>The <code class="docutils literal"><span class="pre">recurse</span></code> method performs the same kind of traversal of the
    1345. 

  1345. hierarchy, but writes out and explains a lot more.</p>
    1346. 

  1346. <p>The data structure represented by <code class="docutils literal"><span class="pre">v.shapes</span></code> is known as a <em>tree</em>.
    1347. 

  1347. As in physical trees, there is a <em>root</em>, here the <code class="docutils literal"><span class="pre">v.shapes</span></code>
    1348. 

  1348. dictionary. A graphical illustration of the tree (upside down) is
    1349. 

  1349. shown in Figure <span class="xref std std-ref">sketcher:fig:Vehicle0:hier2</span>.
    1350. 

  1350. From the root there are one or more branches, here two:
    1351. 

  1351. <code class="docutils literal"><span class="pre">ground</span></code> and <code class="docutils literal"><span class="pre">vehicle</span></code>. Following the <code class="docutils literal"><span class="pre">vehicle</span></code> branch, it has two new
    1352. 

  1352. branches, <code class="docutils literal"><span class="pre">body</span></code> and <code class="docutils literal"><span class="pre">wheels</span></code>. Relationships as in family trees
    1353. 

  1353. are often used to describe the relations in object trees too: we say
    1354. 

  1354. that <code class="docutils literal"><span class="pre">vehicle</span></code> is the parent of <code class="docutils literal"><span class="pre">body</span></code> and that <code class="docutils literal"><span class="pre">body</span></code> is a child of
    1355. 

  1355. <code class="docutils literal"><span class="pre">vehicle</span></code>. The term <em>node</em> is also often used to describe an element
    1356. 

  1356. in a tree. A node may have several other nodes as <em>descendants</em>.</p>
    1357. 

  1357. <div class="figure" id="id9">
    1358. 

  1358. <span id="id1"></span><a class="reference internal image-reference" href="_images/Vehicle0_hier2.png"><img alt="_images/Vehicle0_hier2.png" src="_images/Vehicle0_hier2.png" style="width: 600px;" /></a>
    1359. 

  1359. <p class="caption"><span class="caption-text"><em>Hierarchy of figure elements in an instance of class `Vehicle0`</em></span></p>
    1360. 

  1360. </div>
    1361. 

  1361. <p>Recursion is the principal programming technique to traverse tree structures.
    1362. 

  1362. Any object in the tree can be viewed as a root of a subtree. For
    1363. 

  1363. example, <code class="docutils literal"><span class="pre">wheels</span></code> is the root of a subtree that branches into
    1364. 

  1364. <code class="docutils literal"><span class="pre">wheel1</span></code> and <code class="docutils literal"><span class="pre">wheel2</span></code>. So when processing an object in the tree,
    1365. 

  1365. we imagine we process the root and then recurse into a subtree, but the
    1366. 

  1366. first object we recurse into can be viewed as the root of the subtree, so the
    1367. 

  1367. processing procedure of the parent object can be repeated.</p>
    1368. 

  1368. <p>A recommended next step is to simulate the <code class="docutils literal"><span class="pre">recurse</span></code> method by hand and
    1369. 

  1369. carefully check that what happens in the visits to <code class="docutils literal"><span class="pre">recurse</span></code> is
    1370. 

  1370. consistent with the output listed below. Although tedious, this is
    1371. 

  1371. a major exercise that guaranteed will help to demystify recursion.</p>
    1372. 

  1372. <p>A part of the printout of <code class="docutils literal"><span class="pre">v.recurse('vehicle')</span></code> looks like</p>
    1373. 

  1373. <div class="highlight-text"><div class="highlight"><pre> Vehicle0: vehicle.shapes has entries &#39;ground&#39;, &#39;vehicle&#39;
    1374. 

  1374.  call vehicle.shapes[&quot;ground&quot;].recurse(&quot;ground&quot;, 2)
    1375. 

  1375.    Wall: ground.shapes has entries &#39;wall&#39;
    1376. 

  1376.    call ground.shapes[&quot;wall&quot;].recurse(&quot;wall&quot;, 4)
    1377. 

  1377.      reached &quot;bottom&quot; object Curve
    1378. 

  1378.  call vehicle.shapes[&quot;vehicle&quot;].recurse(&quot;vehicle&quot;, 2)
    1379. 

  1379.    Composition: vehicle.shapes has entries &#39;body&#39;, &#39;wheels&#39;
    1380. 

  1380.    call vehicle.shapes[&quot;body&quot;].recurse(&quot;body&quot;, 4)
    1381. 

  1381.      Composition: body.shapes has entries &#39;over&#39;, &#39;under&#39;
    1382. 

  1382.      call body.shapes[&quot;over&quot;].recurse(&quot;over&quot;, 6)
    1383. 

  1383.        Rectangle: over.shapes has entries &#39;rectangle&#39;
    1384. 

  1384.        call over.shapes[&quot;rectangle&quot;].recurse(&quot;rectangle&quot;, 8)
    1385. 

  1385.          reached &quot;bottom&quot; object Curve
    1386. 

  1386.      call body.shapes[&quot;under&quot;].recurse(&quot;under&quot;, 6)
    1387. 

  1387.        Rectangle: under.shapes has entries &#39;rectangle&#39;
    1388. 

  1388.        call under.shapes[&quot;rectangle&quot;].recurse(&quot;rectangle&quot;, 8)
    1389. 

  1389.          reached &quot;bottom&quot; object Curve
    1390. 

  1390. ...
    1391. 

  1391. </pre></div>
    1392. 

  1392. </div>
    1393. 

  1393. <p>This example should clearly demonstrate the principle that we
    1394. 

  1394. can start at any object in the tree and do a recursive set
    1395. 

  1395. of calls with that object as root.</p>
    1396. 

  1396. </div>
    1397. 

  1397. </div>
    1398. 

  1398. <div class="section" id="scaling-translating-and-rotating-a-figure">
    1399. 

  1399. <span id="sketcher-scaling"></span><h3>Scaling, translating, and rotating a figure<a class="headerlink" href="#scaling-translating-and-rotating-a-figure" title="Permalink to this headline">¶</a></h3>
    1400. 

  1400. <p>With recursion, as explained in the previous section, we can within
    1401. 

  1401. minutes equip <em>all</em> classes in the <code class="docutils literal"><span class="pre">Shape</span></code> hierarchy, both present and
    1402. 

  1402. future ones, with the ability to scale the figure, translate it,
    1403. 

  1403. or rotate it. This added functionality requires only a few lines
    1404. 

  1404. of code.</p>
    1405. 

  1405. <div class="section" id="scaling">
    1406. 

  1406. <h4>Scaling<a class="headerlink" href="#scaling" title="Permalink to this headline">¶</a></h4>
    1407. 

  1407. <p>We start with the simplest of the three geometric transformations,
    1408. 

  1408. namely scaling.  For a <code class="docutils literal"><span class="pre">Curve</span></code> instance containing a set of <span class="math">\(n\)</span>
    1409. 

  1409. coordinates <span class="math">\((x_i,y_i)\)</span> that make up a curve, scaling by a factor <span class="math">\(a\)</span>
    1410. 

  1410. means that we multiply all the <span class="math">\(x\)</span> and <span class="math">\(y\)</span> coordinates by <span class="math">\(a\)</span>:</p>
    1411. 

  1411. <div class="math">
    1412. 

  1412. \[x_i \leftarrow ax_i,\quad y_i\leftarrow ay_i,
    1413. 

  1413. \quad i=0,\ldots,n-1\thinspace .\]</div>
    1414. 

  1414. <p>Here we apply the arrow as an assignment operator.
    1415. 

  1415. The corresponding Python implementation in
    1416. 

  1416. class <code class="docutils literal"><span class="pre">Curve</span></code> reads</p>
    1417. 

  1417. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Curve</span><span class="p">:</span>
    1418. 

  1418.     <span class="o">...</span>
    1419. 

  1419.     <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
    1420. 

  1420.         <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">factor</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span>
    1421. 

  1421.         <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">factor</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span>
    1422. 

  1422. </pre></div>
    1423. 

  1423. </div>
    1424. 

  1424. <p>Note here that <code class="docutils literal"><span class="pre">self.x</span></code> and <code class="docutils literal"><span class="pre">self.y</span></code> are Numerical Python arrays,
    1425. 

  1425. so that multiplication by a scalar number <code class="docutils literal"><span class="pre">factor</span></code> is
    1426. 

  1426. a vectorized operation.</p>
    1427. 

  1427. <p>An even more efficient implementation is to make use of in-place
    1428. 

  1428. multiplication in the arrays,</p>
    1429. 

  1429. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Curve</span><span class="p">:</span>
    1430. 

  1430.     <span class="o">...</span>
    1431. 

  1431.     <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
    1432. 

  1432.         <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">*=</span> <span class="n">factor</span>
    1433. 

  1433.         <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">*=</span> <span class="n">factor</span>
    1434. 

  1434. </pre></div>
    1435. 

  1435. </div>
    1436. 

  1436. <p>as this saves the creation of temporary arrays like <code class="docutils literal"><span class="pre">factor*self.x</span></code>.</p>
    1437. 

  1437. <p>In an instance of a subclass of <code class="docutils literal"><span class="pre">Shape</span></code>, the meaning of a method
    1438. 

  1438. <code class="docutils literal"><span class="pre">scale</span></code> is to run through all objects in the dictionary <code class="docutils literal"><span class="pre">shapes</span></code> and
    1439. 

  1439. ask each object to scale itself. This is the same delegation of
    1440. 

  1440. actions to subclass instances as we do in the <code class="docutils literal"><span class="pre">draw</span></code> (or <code class="docutils literal"><span class="pre">recurse</span></code>)
    1441. 

  1441. method. All objects, except <code class="docutils literal"><span class="pre">Curve</span></code> instances, can share the same
    1442. 

  1442. implementation of the <code class="docutils literal"><span class="pre">scale</span></code> method. Therefore, we place the <code class="docutils literal"><span class="pre">scale</span></code>
    1443. 

  1443. method in the superclass <code class="docutils literal"><span class="pre">Shape</span></code> such that all subclasses inherit the
    1444. 

  1444. method.  Since <code class="docutils literal"><span class="pre">scale</span></code> and <code class="docutils literal"><span class="pre">draw</span></code> are so similar, we can easily
    1445. 

  1445. implement the <code class="docutils literal"><span class="pre">scale</span></code> method in class <code class="docutils literal"><span class="pre">Shape</span></code> by copying and editing
    1446. 

  1446. the <code class="docutils literal"><span class="pre">draw</span></code> method:</p>
    1447. 

  1447. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Shape</span><span class="p">:</span>
    1448. 

  1448.     <span class="o">...</span>
    1449. 

  1449.     <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
    1450. 

  1450.         <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">:</span>
    1451. 

  1451.             <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="n">shape</span><span class="p">]</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
    1452. 

  1452. </pre></div>
    1453. 

  1453. </div>
    1454. 

  1454. <p>This is all we have to do in order to equip all subclasses of
    1455. 

  1455. <code class="docutils literal"><span class="pre">Shape</span></code> with scaling functionality!
    1456. 

  1456. Any piece of the figure will scale itself, in the same manner
    1457. 

  1457. as it can draw itself.</p>
    1458. 

  1458. </div>
    1459. 

  1459. <div class="section" id="translation">
    1460. 

  1460. <h4>Translation<a class="headerlink" href="#translation" title="Permalink to this headline">¶</a></h4>
    1461. 

  1461. <p>A set of coordinates <span class="math">\((x_i, y_i)\)</span> can be translated <span class="math">\(v_0\)</span> units in
    1462. 

  1462. the <span class="math">\(x\)</span> direction and <span class="math">\(v_1\)</span> units in the <span class="math">\(y\)</span> direction using the formulas</p>
    1463. 

  1463. <div class="math">
    1464. 

  1464. \[x_i\leftarrow x_i+v_0,\quad y_i\leftarrow y_i+v_1,
    1465. 

  1465. \quad i=0,\ldots,n-1\thinspace .\]</div>
    1466. 

  1466. <p>The natural specification of the translation is in terms of the
    1467. 

  1467. vector <span class="math">\(v=(v_0,v_1)\)</span>.
    1468. 

  1468. The corresponding Python implementation in class <code class="docutils literal"><span class="pre">Curve</span></code> becomes</p>
    1469. 

  1469. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Curve</span><span class="p">:</span>
    1470. 

  1470.     <span class="o">...</span>
    1471. 

  1471.     <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
    1472. 

  1472.         <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">+=</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    1473. 

  1473.         <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">+=</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
    1474. 

  1474. </pre></div>
    1475. 

  1475. </div>
    1476. 

  1476. <p>The translation operation for a shape object is very similar to the
    1477. 

  1477. scaling and drawing operations. This means that we can implement a
    1478. 

  1478. common method <code class="docutils literal"><span class="pre">translate</span></code> in the superclass <code class="docutils literal"><span class="pre">Shape</span></code>. The code
    1479. 

  1479. is parallel to the <code class="docutils literal"><span class="pre">scale</span></code> method:</p>
    1480. 

  1480. <div class="highlight-python"><div class="highlight"><pre><span class="k">class</span> <span class="nc">Shape</span><span class="p">:</span>
    1481. 

  1481.     <span class="o">....</span>
    1482. 

  1482.     <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
    1483. 

  1483.         <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">:</span>
    1484. 

  1484.             <span class="bp">self</span><span class="o">.</span><span class="n">shapes</span><span class="p">[</span><span class="n">shape</span><span class="p">]</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
    1485. 

  1485. </pre></div>
    1486. 

  1486. </div>
    1487. 

  1487. </div>
    1488. 

  1488. <div class="section" id="rotation">
    1489. 

  1489. <h4>Rotation<a class="headerlink" href="#rotation" title="Permalink to this headline">¶</a></h4>
    1490. 

  1490. <p>Rotating a figure is more complicated than scaling and translating.
    1491. 

  1491. A counter clockwise rotation of <span class="math">\(\theta\)</span> degrees for a set of
    1492. 

  1492. coordinates <span class="math">\((x_i,y_i)\)</span> is given by</p>
    1493. 

  1493. <div class="math">
    1494. 

  1494. \[\begin{split}\bar x_i &amp;\leftarrow x_i\cos\theta - y_i\sin\theta,\\
    1495. 

  1495. \bar y_i &amp;\leftarrow x_i\sin\theta + y_i\cos\theta\thinspace .\end{split}\]</div>
    1496. 

  1496. <p>This rotation is performed around the origin. If we want the figure
    1497. 

  1497. to be rotated with respect to a general point <span class="math">\((x,y)\)</span>, we need to
    1498. 

  1498. extend the formulas above:</p>
    1499. 

  1499. <div class="math">
    1500. 

  1500. \[\begin{split}\bar x_i &amp;\leftarrow x + (x_i -x)\cos\theta - (y_i -y)\sin\theta,\\
    1501. 

  1501. \bar y_i &amp;\leftarrow y + (x_i -x)\sin\theta + (y_i -y)\cos\theta\thinspace .\end{split}\]</div>
    1502. 

  1502. <p>The Python implementation in class <code class="docutils literal"><span class="pre">Curve</span></code>, assuming that <span class="math">\(\theta\)</span>
    1503. 

  1503. is given in degrees and not in radians, becomes</p>
    1504. 

  1504. <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">center</span><span class="p">):</span>
    1505. 

  1505.     <span class="n">angle</span> <span class="o">=</span> <span class="n">radians</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span>
    1506. 

  1506.     <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">center</span>
    1507. 

  1507.     <span class="n">c</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">);</span>  <span class="n">s</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span>
    1508. 

  1508.     <span class="n">xnew</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="n">c</span> <span class="o">-</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">-</span> <span class="n">y</span><span class="p">)</span><span class="o">*</span><span class="n">s</span>
    1509. 

  1509.     <span class="n">ynew</span> <span class="o">=</span> <span class="n">y</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="n">s</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">-</span> <span class="n">y</span><span class="p">)</span><span class="o">*</span><span class="n">c</span>
    1510. 

  1510.     <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">xnew</span>
    1511. 

  1511.     <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">ynew</span>
    1512. 

  1512. </pre></div>
    1513. 

  1513. </div>
    1514. 

  1514. <p>The <code class="docutils literal"><span class="pre">rotate</span></code> method in class <code class="docutils literal"><span class="pre">Shape</span></code> follows the principle of the
    1515. 

  1515. <code class="docutils literal"><span class="pre">draw</span></code>, <code class="docutils literal"><span class="pre">scale</span></code>, and <code class="docutils literal"><span class="pre">translate</span></code> methods.</p>
    1516. 

  1516. <p>We have already seen the <code class="docutils literal"><span class="pre">rotate</span></code> method in action when animating the
    1517. 

  1517. rolling wheel at the end of the section <a class="reference internal" href="#sketcher-vehicle1-anim"><span class="std std-ref">Animation: rolling the wheels</span></a>.</p>
    1518. 

  1518. </div>
    1519. 

  1519. </div>
    1520. 

  1520. </div>
    1521. 

  1521. </div>
    1522. 

  1522. 

  1523. 

  1524.           </div>
    1525. 

  1525.         </div>
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  1527.       <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
    1528. 

  1528.         <div class="sphinxsidebarwrapper">
    1529. 

  1529.             <center>
    1530. 

  1530.             <p class="logo"><a href="http://cbc.simula.no/" title="Go to Center for Biomedical Computing">
    1531. 

  1531.               <img class="logo" src="_static/cbc_logo.png" alt="Logo"/>
    1532. 

  1532.             </a></p>
    1533. 

  1533.             </center>
    1534. 

  1534.   <h3><a href="index.html">Table Of Contents</a></h3>
    1535. 

  1535.   <ul>
    1536. 

  1536. <li><a class="reference internal" href="#">Pysketcher: Create Principal Sketches of Physics Problems</a><ul>
    1537. 

  1537. <li><a class="reference internal" href="#a-first-glimpse-of-pysketcher">A first glimpse of Pysketcher</a><ul>
    1538. 

  1538. <li><a class="reference internal" href="#basic-construction-of-sketches">Basic construction of sketches</a><ul>
    1539. 

  1539. <li><a class="reference internal" href="#basic-drawing">Basic drawing</a></li>
    1540. 

  1540. <li><a class="reference internal" href="#groups-of-objects">Groups of objects</a></li>
    1541. 

  1541. <li><a class="reference internal" href="#changing-line-styles-and-colors">Changing line styles and colors</a></li>
    1542. 

  1542. <li><a class="reference internal" href="#the-figure-composition-as-an-object-hierarchy">The figure composition as an object hierarchy</a></li>
    1543. 

  1543. <li><a class="reference internal" href="#animation-translating-the-vehicle">Animation: translating the vehicle</a></li>
    1544. 

  1544. <li><a class="reference internal" href="#animation-rolling-the-wheels">Animation: rolling the wheels</a></li>
    1545. 

  1545. </ul>
    1546. 

  1546. </li>
    1547. 

  1547. </ul>
    1548. 

  1548. </li>
    1549. 

  1549. <li><a class="reference internal" href="#basic-shapes">Basic shapes</a><ul>
    1550. 

  1550. <li><a class="reference internal" href="#axis">Axis</a></li>
    1551. 

  1551. <li><a class="reference internal" href="#distance-with-text">Distance with text</a></li>
    1552. 

  1552. <li><a class="reference internal" href="#rectangle">Rectangle</a></li>
    1553. 

  1553. <li><a class="reference internal" href="#triangle">Triangle</a></li>
    1554. 

  1554. <li><a class="reference internal" href="#arc">Arc</a></li>
    1555. 

  1555. <li><a class="reference internal" href="#spring">Spring</a></li>
    1556. 

  1556. <li><a class="reference internal" href="#dashpot">Dashpot</a></li>
    1557. 

  1557. <li><a class="reference internal" href="#wavy">Wavy</a></li>
    1558. 

  1558. <li><a class="reference internal" href="#stochastic-curves">Stochastic curves</a></li>
    1559. 

  1559. </ul>
    1560. 

  1560. </li>
    1561. 

  1561. <li><a class="reference internal" href="#inner-workings-of-the-pysketcher-tool">Inner workings of the Pysketcher tool</a><ul>
    1562. 

  1562. <li><a class="reference internal" href="#example-of-classes-for-geometric-objects">Example of classes for geometric objects</a><ul>
    1563. 

  1563. <li><a class="reference internal" href="#simple-geometric-objects">Simple geometric objects</a></li>
    1564. 

  1564. <li><a class="reference internal" href="#class-curve">Class curve</a></li>
    1565. 

  1565. <li><a class="reference internal" href="#compound-geometric-objects">Compound geometric objects</a></li>
    1566. 

  1566. </ul>
    1567. 

  1567. </li>
    1568. 

  1568. <li><a class="reference internal" href="#adding-functionality-via-recursion">Adding functionality via recursion</a><ul>
    1569. 

  1569. <li><a class="reference internal" href="#basic-principles-of-recursion">Basic principles of recursion</a></li>
    1570. 

  1570. <li><a class="reference internal" href="#explaining-recursion">Explaining recursion</a></li>
    1571. 

  1571. </ul>
    1572. 

  1572. </li>
    1573. 

  1573. <li><a class="reference internal" href="#scaling-translating-and-rotating-a-figure">Scaling, translating, and rotating a figure</a><ul>
    1574. 

  1574. <li><a class="reference internal" href="#scaling">Scaling</a></li>
    1575. 

  1575. <li><a class="reference internal" href="#translation">Translation</a></li>
    1576. 

  1576. <li><a class="reference internal" href="#rotation">Rotation</a></li>
    1577. 

  1577. </ul>
    1578. 

  1578. </li>
    1579. 

  1579. </ul>
    1580. 

  1580. </li>
    1581. 

  1581. </ul>
    1582. 

  1582. </li>
    1583. 

  1583. </ul>
    1584. 

  1584. 

  1585.   <h4>Previous topic</h4>
    1586. 

  1586.   <p class="topless"><a href="index.html"
    1587. 

  1587.                         title="previous chapter">Pysketcher: Create Principal Sketches of Physics Problems</a></p>
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