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<h1 >Namespace Paths
</h1> <div class="doc"></div>
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<div class="summary">
<div class="heading">Class templates Summary:</div>
<div class="item"><div class="synopsis"><div class="template">template <size_t <span class="variable">Order</span>></div> class <a href="Paths/Bezier.html" >Bezier</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc">
The Bezier class.</div></div>
<div class="item"><div class="synopsis"><div class="template">template <size_t <span class="variable">Order</span>></div> class <a href="Paths/Nurbs.html" >Nurbs</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc"><p>The Nurbs class.</p>
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<div class="summary">
<div class="heading">Classes Summary:</div>
<div class="item"><div class="synopsis">class <a href="Paths/Polyline.html" >Polyline</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc">The Polyline class.</div></div>
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<div class="detail">
<div class="heading">Class templates Details:</div>
<div class="item"><div class="synopsis"><div class="template">template <size_t <span class="variable">Order</span>></div> class <a href="Paths/Bezier.html" >Bezier</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc">
The Bezier class. It implements a Bezier curve
for the given order.</div></div>
<div class="item"><div class="synopsis"><div class="template">template <size_t <span class="variable">Order</span>></div> class <a href="Paths/Nurbs.html" >Nurbs</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc"><p>The Nurbs class. It implements a nurbs curve
for the given order. It is a very powerful
and flexible curve representation. For simpler
cases you may prefer to use a <a class="reference" href="Paths/Bezier.html">Bezier</a> curve.</p>
<p>While non-rational curves are not sufficient to represent a circle,
this is one of many sets of NURBS control points for an almost uniformly
parameterized circle:</p>
<table border="1" class="docutils">
<colgroup>
<col width="11%" />
<col width="21%" />
<col width="68%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">x</th>
<th class="head">y</th>
<th class="head">weight</th>
</tr>
</thead>
<tbody valign="top">
<tr><td>1</td>
<td>0</td>
<td>1</td>
</tr>
<tr><td>1</td>
<td>1</td>
<td><em>sqrt(2)/2</em></td>
</tr>
<tr><td>0</td>
<td>1</td>
<td>1</td>
</tr>
<tr><td>-1</td>
<td>1</td>
<td><em>sqrt(2)/2</em></td>
</tr>
<tr><td>-1</td>
<td>0</td>
<td>1</td>
</tr>
<tr><td>-1</td>
<td>-1</td>
<td><em>sqrt(2)/2</em></td>
</tr>
<tr><td>0</td>
<td>-1</td>
<td>1</td>
</tr>
<tr><td>1</td>
<td>-1</td>
<td><em>sqrt(2)/2</em></td>
</tr>
<tr><td>1</td>
<td>0</td>
<td>1</td>
</tr>
</tbody>
</table>
<p>The order is three, the knot vector is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4}.
It should be noted that the circle is composed of four quarter circles,
tied together with double knots. Although double knots in a third order NURBS
curve would normally result in loss of continuity in the first derivative,
the control points are positioned in such a way that the first derivative is continuous.
(From <a class="reference" href="http://en.wikipedia.org/wiki/NURBS">Wikipedia</a> )</p>
<p>Example:</p>
<pre class="literal-block">
Nurbs<3> circle;
circle.insert_control_point(0, Vertex(1., 0.), 1.);
circle.insert_control_point(0, Vertex(1., 1.), sqrt(2.)/2.);
...
</pre>
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<div class="detail">
<div class="heading">Classes Details:</div>
<div class="item"><div class="synopsis">class <a href="Paths/Polyline.html" >Polyline</a></div> <div class="xref"></div> <div class="source"></div> <div class="doc">The Polyline class. It is an ordered set of
connected line segments.</div></div>
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<div class="logo">Generated on Fri Apr 17 08:48:05 2009 by
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<a href="http://synopsis.fresco.org" target="_blank"><img src="../synopsis.png" alt="logo"/> synopsis</a> (version devel)</div>
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