little_helpers/tikz/sketch-0.2.161/Doc/sketch/Drawing-a-solid.html

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  16 Tuesday, September 08, 2009, a program that converts descriptions of simple
  17 three-dimensional scenes into static drawings. This version generates
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  56 <h3 class="section">2.3 Drawing a solid</h3>
  57
  58 <p>Let's try something more exciting.  <code>Sketch</code> has no notion of a
  59 solid,
  60 <a name="index-solid-28"></a>but polygonal <dfn>faces</dfn>
  61 <a name="index-faces-29"></a>can be used to represent the
  62 boundary of a solid.  To the previous example, let's add three more
  63 triangular polygons to make the faces of an irregular tetrahedron.
  64 <a name="index-tetrahedron-30"></a><a name="index-def-31"></a><a name="index-polygon-32"></a>
  65 <pre class="verbatim">
  66   % vertices of the tetrahedron
  67   def p1 (0,0,1) def p2 (1,0,0)
  68   def p3 (0,1,0) def p4 (-.3,-.5,-.8)
  69
  70   % faces of the tetrahedron.
  71   polygon(p1)(p2)(p3) % original front polygon
  72   polygon(p1)(p4)(p2) % bottom
  73   polygon(p1)(p3)(p4) % left
  74   polygon(p3)(p2)(p4) % rear
  75
  76   % line to pierce the tetrahedron
  77   line[linecolor=red](-1,-1,-1)(2,2,2)
  78 </pre>
  79 This example uses <dfn>definitions</dfn>,
  80 <a name="index-definition-33"></a>which begin with
  81 <code>def</code>.
  82 <a name="index-def-34"></a>These <dfn>define</dfn> or give names to points,
  83 <a name="index-definition_002c-point-35"></a><a name="index-point-definition-36"></a>which are then available
  84 as <dfn>references</dfn>
  85 <a name="index-reference_002c-point-37"></a>by enclosing the names in parentheses,
  86 e.g. <tt>(foo)</tt>.
  87 <a name="index-_0028foo_0029_0040r_007b_002c-point-reference_007d-38"></a>The parentheses denote that the names refer to points; they are
  88 required.  There can be no
  89 <a name="index-white-space-39"></a>white space between them and the name.
  90
  91    <p>As you can see, comments
  92 <a name="index-comments-40"></a>start with <tt>%</tt> as in TeX and extend
  93 to the end of the line (though <tt>#</tt> will work as well).  White
  94 space,
  95 <a name="index-white-space-41"></a>including spaces, tabs and blank lines, has no effect in the <code>sketch</code>
  96 language.
  97
  98 <div align="center"><img src="ex040.png" alt="ex040.png"></div>
  99
 100 <p class="noindent">If we look inside the TeX file produced by <code>sketch</code>, there
 101 will be only three polygons.  The fourth has been
 102 <a name="index-culling-42"></a>culled because it is
 103 a &ldquo;back face&rdquo;
 104 <a name="index-back-face-43"></a>of the tetrahedron, invisible to our view.  It is
 105 unnecessary, and so it is removed.
 106
 107    <p>In some drawings, polygons act as zero-thickness solid surfaces with
 108 both sides visible rather than as the faces of solid objects, where
 109 back faces can be culled.  For zero-thickness solids, culling
 110 <a name="index-culling-44"></a>is a
 111 problem.  One solution is to use a pair of <code>sketch</code> polygons for
 112 each zero-thickness face, identical except with opposite vertex
 113 orders.  This is unwieldy and expensive.  A better way is to
 114 set the <code>sketch</code> internal option <code>cull</code> to <code>false</code> in
 115 the usual <code>PSTricks</code> manner.
 116 <a name="index-cull-45"></a>
 117 <pre class="verbatim">
 118   polygon[cull=false](p1)(p2)(p3)
 119 </pre>
 120 The following shows the same helix
 121 <a name="index-helix-46"></a>shape drawn first with
 122 <tt>cull=true</tt> (the default) and then <tt>cull=false</tt>.
 123
 124 <div align="center"><img src="ex045.png" alt="ex045.png"> <a name="Helix-with-cull-set-false-then-true"></a></div>
 125
 126 <p class="noindent">We'll soon see how to produce these helixes with a few lines
 127 of <code>sketch</code> language code.
 128
 129    <p>It may be tempting to turn culling off gratuitously so that vertex order
 130 can be ignored.  This is not a good idea because output file size and
 131 TeX and Postscript processing time both depend on the number of
 132 output polygons.  Culling usually improves performance by a factor of
 133 two.  On the other hand, globally setting <code>cull=false</code> is
 134 reasonable while debugging.  See <a href="Global-options.html#Global-options">Global options</a> and
 135 <a href="Limits-on-error-detection.html#Limits-on-error-detection">Limits on error detection</a>.
 136
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