little_helpers/tikz/sketch-0.2.161/Doc/sketch/Swept-polygons.html

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  56 <h5 class="subsubsection">3.2.6.3 Swept polygons</h5>
  57
  58 <p><a name="index-polygon-sweep-310"></a>If <var>swept_object</var> is a polygon, the <code>sweep</code> connects
  59 <var>n</var>+1 successive copies of the closed polyline border of
  60 the polygon to form body polygons exactly as though the border were a
  61 swept polyline as described in <a href="Swept-lines.html#Swept-lines">Swept lines</a>.
  62 <a name="index-body-polygon-311"></a><a name="index-polygon_002c-body-312"></a>If there are m points in the
  63 original polygon, then m<var>n</var> body polygons are formed by
  64 this sweep.  The body polygons form an <dfn>extrusion</dfn> of the boundary of the
  65 original polygon with two holes at the open ends.
  66
  67    <p>Finally, the sweep adds two copies of the original polygon to cover
  68 the holes.  We call these hole-filling polygons <dfn>ends</dfn>.
  69 <a name="index-end-polygon-313"></a><a name="index-polygon_002c-end-314"></a>In this manner, <code>sweep</code> forms the boundary of a three-dimensional
  70 object from a two-dimensional polygon.
  71
  72    <p>The order of vertices
  73 <a name="index-polygon-vertex-order-315"></a><a name="index-order_002c-polygon-vertex-316"></a>of end polygons is important for correct culling as described above.
  74 An exact copy of the original polygon with vertex order intact forms
  75 the first end polygon.  The other end polygon results from
  76 transforming and the reversing the order of vertices in the original.
  77 The transform places the original polygon at the uncovered hole;
  78 it is
  79 <pre class="example">     <var>T_1</var>^n then <var>T_2</var>^n then ... then <var>T_r</var>^n.
  80 </pre>
  81    <p class="noindent">If there are no options on the swept polygon, then the <span class="samp">sweep</span>
  82 options are copied to each output polygon.  If the swept polygon does
  83 have options, these are copied to the ends; the sweep options are
  84 copied to the body polygons.  In this manner, body and ends may be
  85 drawn with different characteristics such as <code>fillcolor</code>.
  86
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