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<h4 class="subsection">3.2.6 Sweeps</h4>
<p><a name="index-sweep-281"></a><strong>Syntax:</strong>
<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>
sweep { <var>n</var><>, <var>T_1</var>, <var>T_2</var>, ..., <var>T_r</var> }[<var>options</var>] <var>swept_object</var>
</pre>
<p class="noindent">The sweep connects <var>n</var> (or perhaps <var>n</var>+1) copies of
<var>swept_object</var>
<a name="index-swept-object-282"></a>in order to create a new object of higher
dimension. The <var>T_i</var> (for i between 1 and
r) are transforms.
<a name="index-transform-283"></a>The k'th copy of <var>swept_object</var> is produced by applying the
following transform to the original.
<pre class="example"> <var>T_1</var>^k then <var>T_2</var>^k then ... then <var>T_r</var>^k
</pre>
<p class="noindent">Here <var>T</var>^k means “transform <var>T</var> applied k
times.” The original object is the zero'th copy, with k=0 and
effectively no transform applied (T^0=I, the identity
transform).
<p>The method of connecting the copies depends on the type of
<var>swept_object</var> and on whether the closure tag
<a name="index-g_t_003c_003e_0040r_007b_002c-closure-tag_007d-284"></a><a name="index-closure-tag_002c-_0040code_007b_003c_003e_007d-285"></a>‘<samp><span class="samp"><></span></samp>’ is present
or not.
<p>An example of a sweep where r=2 is the Mobius figure at
<a href="More-to-learn.html#More-to-learn">More to learn</a>.
<ul class="menu">
<li><a accesskey="1" href="Swept-points.html#Swept-points">Swept points</a>: Swept points make lines or polygons.
<li><a accesskey="2" href="Swept-lines.html#Swept-lines">Swept lines</a>: Swept lines make open or closed surfaces.
<li><a accesskey="3" href="Swept-polygons.html#Swept-polygons">Swept polygons</a>: Swept polygons make closed surfaces.
<li><a accesskey="4" href="Swept-blocks.html#Swept-blocks">Swept blocks</a>: Swept block == block of sweeps.
<li><a accesskey="5" href="Sweep-face-splitting.html#Sweep-face-splitting">Sweep face splitting</a>: Fixing warped faces with triangles.
</ul>
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