little_helpers/tikz/sketch-0.2.161/Doc/sketch/Object-transforms.html

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  56 <h3 class="section">2.5 Transforms</h3>
  57
  58 <p><a name="index-transform-58"></a>Now let's add a second copy of the pierced tetrahedron.  We'll rotate
  59 the copy 90 degrees about the x-axis with the origin as
  60 <dfn>center of rotation</dfn>
  61 <a name="index-center-of-rotation-59"></a><a name="index-rotation_002c-center-of-60"></a>so we can see the back,
  62 then translate it to the right&mdash;in the positive
  63 x-direction&mdash;so it doesn't collide with the original. To help
  64 us see what's going on, make the back side gray.
  65 <a name="index-def-61"></a><a name="index-put-62"></a><a name="index-line-63"></a><a name="index-polygon-64"></a><a name="index-linecolor-65"></a><a name="index-fillcolor-66"></a><a name="index-rotate-67"></a><a name="index-translate-68"></a><a name="index-then-69"></a>
  66 <pre class="verbatim">
  67   def pierced_tetrahedron {
  68     def p1 (0,0,1) def p2 (1,0,0)
  69     def p3 (0,1,0) def p4 (-.3,-.5,-.8)
  70     polygon(p1)(p2)(p3)                      % original
  71     polygon(p1)(p4)(p2)                      % bottom
  72     polygon(p1)(p3)(p4)                      % left
  73     polygon[fillcolor=lightgray](p3)(p2)(p4) % rear
  74     line[linecolor=red](-1,-1,-1)(2,2,2)
  75   }
  76   {pierced_tetrahedron}  % tetrahedron in original position
  77   put { rotate(90, (0,0,0), [1,0,0]) % copy in new position
  78         then translate([2.5,0,0]) } {pierced_tetrahedron}
  79 </pre>
  80 Here the entire code of the previous example has been wrapped in a
  81 definition by forming a <dfn>block</dfn>
  82 <a name="index-block-70"></a><a name="index-_0040_007b-_0040_007d_0040r_007b_002c-block-drawable_007d-71"></a>with braces (a single item would not need them).  The point
  83 definitions nested inside the braces are <dfn>lexically scoped</dfn>.
  84 <a name="index-lexical-scope-72"></a><a name="index-scope_002c-identifier-73"></a>Their meaning extends only to the end of the block.  The outer
  85 <tt>def</tt> is called a <dfn>drawable</dfn>
  86 <a name="index-drawable-74"></a>definition
  87 <a name="index-definition_002c-drawable-75"></a><a name="index-drawable-definition-76"></a>because it describes something that can be drawn.
  88
  89    <p>A drawable definition by itself causes nothing to happen until its
  90 name is referenced.  Drawable references must be enclosed in curly
  91 braces, e.g. <tt>{foo}</tt>, with no intervening
  92 <a name="index-white-space-77"></a>white space.  In the code
  93 above, the first reference
  94 <a name="index-reference_002c-drawable-78"></a><tt>{pierced_tetrahedron}</tt>
  95 <a name="index-_0040_007bfoo_0040_007d_0040r_007b_002c-drawable-reference_007d-79"></a>is a plain
  96 one. Its effect is merely to duplicate the earlier drawing.  Almost
  97 any series of <code>sketch</code> commands <tt>stuff</tt> may be replaced
  98 with <tt>def foo { stuff } {foo}</tt> without changing its meaning.
  99
 100    <p>The <tt>put</tt> command supplies a second reference, this time with
 101 a <dfn>transform</dfn> applied first.  The <tt>rotate</tt>
 102 <a name="index-rotate-80"></a><a name="index-rotation-81"></a>transform turns the tetrahedron 90 degrees about the origin.  The
 103 axis of rotation
 104 <a name="index-axis_002c-rotation-82"></a>is the vector [1,0,0].  By the <dfn>right
 105 hand rule</dfn>,
 106 <a name="index-right-hand-rule-83"></a>this causes the top of the tetrahedron to rotate toward
 107 the viewer and the bottom away.  The rule receives its name from the
 108 following definition:
 109 <blockquote>
 110 <a name="Right-hand-rule"></a>
 111 <strong>Right hand rule.</strong>  If the right hand is wrapped around any
 112 axis with the thumb pointing in the axis direction, then the fingers
 113 curl in the direction of positive rotation about that axis.
 114 </blockquote>
 115    The <tt>translate</tt>
 116 <a name="index-translate-84"></a><a name="index-translation-transform-85"></a><a name="index-transform_002c-translation-86"></a>transform moves the pyramid laterally to
 117 the right by adding the vector
 118 <a name="index-vector-87"></a>[2.5,0,0] to each vertex
 119 coordinate.  The result is shown here.
 120
 121 <div align="center"><img src="ex050.png" alt="ex050.png"></div>
 122
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 124