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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Geometry-module.html">Package Geometry</a> ::
<a href="Scientific.Geometry.Transformation-module.html">Module Transformation</a> ::
Class Rotation
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Rotation</h1><p class="nomargin-top"></p>
<pre class="base-tree">
<a href="Scientific.Geometry.Transformation.Transformation-class.html">Transformation</a> --+
|
<a href="Scientific.Geometry.Transformation.RigidBodyTransformation-class.html">RigidBodyTransformation</a> --+
|
<strong class="uidshort">Rotation</strong>
</pre>
<hr />
<p>Rotational transformation</p>
<!-- ==================== INSTANCE METHODS ==================== -->
<a name="section-InstanceMethods"></a>
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<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Instance Methods</span></td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#__call__" class="summary-sig-name">__call__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span><br />
Returns:
the transformed vector</td>
<td align="right" valign="top">
</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">*args</span>)</span><br />
There are two calling patterns:</td>
<td align="right" valign="top">
</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__mul__"></a><span class="summary-sig-name">__mul__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a name="asLinearTransformation"></a><span class="summary-sig-name">asLinearTransformation</span>(<span class="summary-sig-arg">self</span>)</span></td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Geometry.Quaternion.Quaternion-class.html"
class="link">Scientific.Geometry.Quaternion.Quaternion</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#asQuaternion" class="summary-sig-name">asQuaternion</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
a quaternion representing the same rotation</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">(<a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>, <code>float</code>)</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#axisAndAngle" class="summary-sig-name">axisAndAngle</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the axis (a normalized vector) and angle (in radians).</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a
href="Scientific.Geometry.Transformation.Transformation-class.html"
class="link">Transformation</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#inverse" class="summary-sig-name">inverse</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the inverse transformation</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Geometry.Transformation.Rotation-class.html"
class="link">Rotation</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#rotation" class="summary-sig-name">rotation</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the rotational component</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#screwMotion" class="summary-sig-name">screwMotion</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the four parameters (reference, direction, angle, distance) of a
screw-like motion that is equivalent to the transformation.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>list</code> of <code>N.array</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#threeAngles" class="summary-sig-name">threeAngles</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">e1</span>,
<span class="summary-sig-arg">e2</span>,
<span class="summary-sig-arg">e3</span>,
<span class="summary-sig-arg">tolerance</span>=<span class="summary-sig-default">1e-07</span>)</span><br />
Find three angles a1, a2, a3 such that
Rotation(a1*e1)*Rotation(a2*e2)*Rotation(a3*e3) is equal to the
rotation object.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><a href="Scientific.Geometry.Transformation.Translation-class.html"
class="link">Translation</a></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Geometry.Transformation.Rotation-class.html#translation" class="summary-sig-name">translation</a>(<span class="summary-sig-arg">self</span>)</span><br />
Returns:
the translational component.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- ==================== CLASS VARIABLES ==================== -->
<a name="section-ClassVariables"></a>
<table class="summary" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
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<span class="table-header">Class Variables</span></td>
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<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<a name="is_rotation"></a><span class="summary-name">is_rotation</span> = <code title="1">1</code>
</td>
</tr>
</table>
<!-- ==================== METHOD DETAILS ==================== -->
<a name="section-MethodDetails"></a>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Method Details</span></td>
</tr>
</table>
<a name="__call__"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">__call__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">other</span>)</span>
<br /><em class="fname">(Call operator)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>vector</code></strong> - the input vector</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a></dt>
<dd>the transformed vector</dd>
<dt>Overrides:
<a href="Scientific.Geometry.Transformation.Transformation-class.html#__call__">Transformation.__call__</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
<a name="__init__"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">*args</span>)</span>
<br /><em class="fname">(Constructor)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>There are two calling patterns:</p>
<ul>
<li>
Rotation(tensor), where tensor is a <a
href="Scientific.Geometry.Tensor-class.html"
class="link">Scientific.Geometry.Tensor</a> of rank 2 containing the
rotation matrix.
</li>
<li>
Rotation(axis, angle), where axis is a <a
href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a> and angle a number (the
angle in radians).
</li>
</ul>
<dl class="fields">
</dl>
</td></tr></table>
</div>
<a name="asQuaternion"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">asQuaternion</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Quaternion.Quaternion-class.html"
class="link">Scientific.Geometry.Quaternion.Quaternion</a></dt>
<dd>a quaternion representing the same rotation</dd>
</dl>
</td></tr></table>
</div>
<a name="axisAndAngle"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">axisAndAngle</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: (<a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>, <code>float</code>)</dt>
<dd>the axis (a normalized vector) and angle (in radians). The angle
is in the interval (-pi, pi]</dd>
</dl>
</td></tr></table>
</div>
<a name="inverse"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">inverse</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a
href="Scientific.Geometry.Transformation.Transformation-class.html"
class="link">Transformation</a></dt>
<dd>the inverse transformation</dd>
<dt>Overrides:
<a href="Scientific.Geometry.Transformation.Transformation-class.html#inverse">Transformation.inverse</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
<a name="rotation"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">rotation</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Transformation.Rotation-class.html"
class="link">Rotation</a></dt>
<dd>the rotational component</dd>
<dt>Overrides:
<a href="Scientific.Geometry.Transformation.RigidBodyTransformation-class.html#rotation">RigidBodyTransformation.rotation</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
<a name="screwMotion"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">screwMotion</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns:</dt>
<dd>the four parameters (reference, direction, angle, distance) of a
screw-like motion that is equivalent to the transformation. The
screw motion consists of a displacement of distance (a
<code>float</code>) along direction (a normalized <a
href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>) plus a rotation of
angle radians around an axis pointing along direction and passing
through the point reference (a <a
href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>).</dd>
<dt>Overrides:
<a href="Scientific.Geometry.Transformation.RigidBodyTransformation-class.html#screwMotion">RigidBodyTransformation.screwMotion</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
<a name="threeAngles"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">threeAngles</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">e1</span>,
<span class="sig-arg">e2</span>,
<span class="sig-arg">e3</span>,
<span class="sig-arg">tolerance</span>=<span class="sig-default">1e-07</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Find three angles a1, a2, a3 such that
Rotation(a1*e1)*Rotation(a2*e2)*Rotation(a3*e3) is equal to the rotation
object. e1, e2, and e3 are non-zero vectors. There are two solutions,
both of which are computed.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>e1</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>) - a rotation axis</li>
<li><strong class="pname"><code>e2</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>) - a rotation axis</li>
<li><strong class="pname"><code>e3</code></strong> (<a href="Scientific.Geometry.Vector-class.html"
class="link">Scientific.Geometry.Vector</a>) - a rotation axis</li>
</ul></dd>
<dt>Returns: <code>list</code> of <code>N.array</code></dt>
<dd>a list containing two arrays of shape (3,), each containing the
three angles of one solution</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if two consecutive axes are parallel</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="translation"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">translation</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Returns: <a href="Scientific.Geometry.Transformation.Translation-class.html"
class="link">Translation</a></dt>
<dd>the translational component. In the case of a mixed
rotation/translation, this translation is executed <b>after</b>
the rotation.</dd>
<dt>Overrides:
<a href="Scientific.Geometry.Transformation.RigidBodyTransformation-class.html#translation">RigidBodyTransformation.translation</a>
<dd><em class="note">(inherited documentation)</em></dd>
</dt>
</dl>
</td></tr></table>
</div>
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