little_helpers/tikz/sketch-0.2.161/Doc/sketch/Sweeps.html

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  56 <h4 class="subsection">3.2.6 Sweeps</h4>
  57
  58 <p><a name="index-sweep-278"></a><strong>Syntax:</strong>
  59 <pre class="example">     sweep { <var>n</var>, <var>T_1</var>, <var>T_2</var>, ..., <var>T_r</var> }[<var>options</var>] <var>swept_object</var>
  60      sweep { <var>n</var>&lt;&gt;, <var>T_1</var>, <var>T_2</var>, ..., <var>T_r</var> }[<var>options</var>] <var>swept_object</var>
  61 </pre>
  62    <p class="noindent">The sweep connects <var>n</var> (or perhaps <var>n</var>+1) copies of
  63 <var>swept_object</var>
  64 <a name="index-swept-object-279"></a>in order to create a new object of higher
  65 dimension.  The <var>T_i</var> (for i between 1 and
  66 r) are transforms.
  67 <a name="index-transform-280"></a>The k'th copy of <var>swept_object</var> is produced by applying the
  68 following transform to the original.
  69 <pre class="example">     <var>T_1</var>^k then <var>T_2</var>^k then ... then <var>T_r</var>^k
  70 </pre>
  71    <p class="noindent">Here <var>T</var>^k means &ldquo;transform <var>T</var> applied k
  72 times.&rdquo;  The original object is the zero'th copy, with k=0 and
  73 effectively no transform applied (T^0=I, the identity
  74 transform).
  75
  76    <p>The method of connecting the copies depends on the type of
  77 <var>swept_object</var> and on whether the closure tag
  78 <a name="index-_003c_003e_0040r_007b_002c-closure-tag_007d-281"></a><a name="index-closure-tag_002c-_0040code_007b_003c_003e_007d-282"></a><span class="samp">&lt;&gt;</span> is present
  79 or not.
  80
  81    <p>An example of a sweep where r=2 is the Mobius figure at
  82 <a href="More-to-learn.html#More-to-learn">More to learn</a>.
  83
  84 <ul class="menu">
  85 <li><a accesskey="1" href="Swept-points.html#Swept-points">Swept points</a>:                 Swept points make lines or polygons.
  86 <li><a accesskey="2" href="Swept-lines.html#Swept-lines">Swept lines</a>:                  Swept lines make open or closed surfaces.
  87 <li><a accesskey="3" href="Swept-polygons.html#Swept-polygons">Swept polygons</a>:               Swept polygons make closed surfaces.
  88 <li><a accesskey="4" href="Swept-blocks.html#Swept-blocks">Swept blocks</a>:                 Swept block == block of sweeps.
  89 <li><a accesskey="5" href="Sweep-face-splitting.html#Sweep-face-splitting">Sweep face splitting</a>:         Fixing warped faces with triangles.
  90 </ul>
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