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<h2><span class="refentrytitle"><a name="mialm-MiaQuaternion.top_of_page"></a>Quaternions</span></h2>
<p>Quaternions — Quaternions to describe rotations in 3D space</p>
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<div class="refsynopsisdiv">
<a name="mialm-MiaQuaternion.synopsis"></a><h2>Synopsis</h2>
<pre class="synopsis"> <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion">MiaQuaternion</a>;
typedef <a class="link" href="mialm-MiaQuaternion.html#RotMatrix" title="RotMatrix">RotMatrix</a>;
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-copy" title="mia_quaternion_copy ()">mia_quaternion_copy</a> (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *dest</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *src</code></em>);
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-dup" title="mia_quaternion_dup ()">mia_quaternion_dup</a> (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *org</code></em>);
<a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-equal" title="mia_quaternion_equal ()">mia_quaternion_equal</a> (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *a</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *b</code></em>);
<span class="returnvalue">void</span> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-get-rotation" title="mia_quaternion_get_rotation ()">mia_quaternion_get_rotation</a> (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>,
<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#RotMatrix" title="RotMatrix"><span class="type">RotMatrix</span></a> m</code></em>);
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-multby" title="mia_quaternion_multby ()">mia_quaternion_multby</a> (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>,
<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *other</code></em>);
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-new" title="mia_quaternion_new ()">mia_quaternion_new</a> (<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> x</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> y</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> z</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> w</code></em>);
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-new-from-eulerrot" title="mia_quaternion_new_from_eulerrot ()">mia_quaternion_new_from_eulerrot</a> (<em class="parameter"><code>const <a class="link" href="mialm-MiaVector3d.html#MiaVector3d" title="MiaVector3d"><span class="type">MiaVector3d</span></a> *axis</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> angle</code></em>);
<a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="returnvalue">gfloat</span></a> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-norm" title="mia_quaternion_norm ()">mia_quaternion_norm</a> (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>);
<span class="returnvalue">void</span> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-normalize" title="mia_quaternion_normalize ()">mia_quaternion_normalize</a> (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>);
<a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-test" title="mia_quaternion_test ()">mia_quaternion_test</a> (<em class="parameter"><code><span class="type">void</span></code></em>);
<span class="returnvalue">void</span> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-xmlio-read" title="mia_quaternion_xmlio_read ()">mia_quaternion_xmlio_read</a> (<em class="parameter"><code><a class="link" href="mialm-XML-manipulation-of-landmarks.html#ParserState" title="struct ParserState"><span class="type">ParserState</span></a> *state</code></em>,
<em class="parameter"><code>const <a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gchar"><span class="type">gchar</span></a> *property</code></em>);
<a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> <a class="link" href="mialm-MiaQuaternion.html#mia-quaternion-xmlio-write" title="mia_quaternion_xmlio_write ()">mia_quaternion_xmlio_write</a> (<em class="parameter"><code><span class="type">xmlNodePtr</span> root</code></em>,
<em class="parameter"><code><span class="type">xmlNsPtr</span> ns</code></em>,
<em class="parameter"><code>const <a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gchar"><span class="type">gchar</span></a> *tag</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *q</code></em>);
</pre>
</div>
<div class="refsect1">
<a name="mialm-MiaQuaternion.description"></a><h2>Description</h2>
<p>
<a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> and the related functions describe and handle rotations in 3D space that
are specifically suited for visualization.
</p>
</div>
<div class="refsect1">
<a name="mialm-MiaQuaternion.details"></a><h2>Details</h2>
<div class="refsect2">
<a name="MiaQuaternion"></a><h3>MiaQuaternion</h3>
<pre class="programlisting">typedef struct _MiaQuaternion MiaQuaternion;</pre>
<p>
This defines a Quaternion and is used to describe a rotation in 3D space.
</p>
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<hr>
<div class="refsect2">
<a name="RotMatrix"></a><h3>RotMatrix</h3>
<pre class="programlisting">typedef float RotMatrix[4][4];
</pre>
<p>
A 4x4 matrix used for rotations.
</p>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-copy"></a><h3>mia_quaternion_copy ()</h3>
<pre class="programlisting"><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * mia_quaternion_copy (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *dest</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *src</code></em>);</pre>
<p>
Copy one quaternion into another one. The destination quaternion
must already be properly created.
</p>
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<td><p><span class="term"><em class="parameter"><code>dest</code></em> :</span></p></td>
<td>destination quaternion to copy to</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>src</code></em> :</span></p></td>
<td>source quaternion to copy from</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>the destination quaternion</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-dup"></a><h3>mia_quaternion_dup ()</h3>
<pre class="programlisting"><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * mia_quaternion_dup (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *org</code></em>);</pre>
<p>
Create a duplicate of a quaternion. It must be destroyed by calling
calling <a href="http://library.gnome.org/devel/gobject/unstable/gobject-The-Base-Object-Type.html#g-object-unref"><code class="function">g_object_unref()</code></a>
</p>
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<td><p><span class="term"><em class="parameter"><code>org</code></em> :</span></p></td>
<td>a quaterion</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>a newly created copy of the quaternion.</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-equal"></a><h3>mia_quaternion_equal ()</h3>
<pre class="programlisting"><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> mia_quaternion_equal (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *a</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *b</code></em>);</pre>
<p>
Test if two quaternions are exactly equal.
</p>
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<td><p><span class="term"><em class="parameter"><code>a</code></em> :</span></p></td>
<td>left hand value for comparison</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>b</code></em> :</span></p></td>
<td>right hand value for comparison</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>TRUE if equal, FALSE otherwise</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-get-rotation"></a><h3>mia_quaternion_get_rotation ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span> mia_quaternion_get_rotation (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>,
<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#RotMatrix" title="RotMatrix"><span class="type">RotMatrix</span></a> m</code></em>);</pre>
<p>
Evaluate the 4x4 Matrix corresponding to the 3D rotation.
</p>
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<td><p><span class="term"><em class="parameter"><code>self</code></em> :</span></p></td>
<td>the quaternion desctibing the rotation</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>m</code></em> :</span></p></td>
<td>The result will be stored in this matrix.</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-multby"></a><h3>mia_quaternion_multby ()</h3>
<pre class="programlisting"><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * mia_quaternion_multby (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>,
<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *other</code></em>);</pre>
<p>
Multiply the quaternion dest by a quaternion other as in dest *= other
</p>
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<td><p><span class="term"><em class="parameter"><code>self</code></em> :</span></p></td>
<td>destination quaternion</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>other</code></em> :</span></p></td>
<td>other quaternion to multiply by</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>the quaternion self</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-new"></a><h3>mia_quaternion_new ()</h3>
<pre class="programlisting"><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * mia_quaternion_new (<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> x</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> y</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> z</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> w</code></em>);</pre>
<p>
Create a quaternion q = w + x *i + y * j + z * k.
</p>
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<td><p><span class="term"><em class="parameter"><code>x</code></em> :</span></p></td>
<td>x-component of rotation axis</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>y</code></em> :</span></p></td>
<td>y-component of rotation axis</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>z</code></em> :</span></p></td>
<td>z-component of rotation axis</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>w</code></em> :</span></p></td>
<td>scalar part of the quaternion</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>a newly created quaternion representing the rotation</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-new-from-eulerrot"></a><h3>mia_quaternion_new_from_eulerrot ()</h3>
<pre class="programlisting"><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="returnvalue">MiaQuaternion</span></a> * mia_quaternion_new_from_eulerrot (<em class="parameter"><code>const <a class="link" href="mialm-MiaVector3d.html#MiaVector3d" title="MiaVector3d"><span class="type">MiaVector3d</span></a> *axis</code></em>,
<em class="parameter"><code><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="type">gfloat</span></a> angle</code></em>);</pre>
<p>
Create a quaternion that represents a rotation around the given axis
by the given angle. The returned quaternion must be destroyed by
calling <a href="http://library.gnome.org/devel/gobject/unstable/gobject-The-Base-Object-Type.html#g-object-unref"><code class="function">g_object_unref()</code></a>
</p>
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<td><p><span class="term"><em class="parameter"><code>axis</code></em> :</span></p></td>
<td>the rotation axis</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>angle</code></em> :</span></p></td>
<td>the rotation angle</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>a newly created quaternion</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2">
<a name="mia-quaternion-norm"></a><h3>mia_quaternion_norm ()</h3>
<pre class="programlisting"><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gfloat"><span class="returnvalue">gfloat</span></a> mia_quaternion_norm (<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>);</pre>
<p>
Evaluate the quaternions norm.
</p>
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<td><p><span class="term"><em class="parameter"><code>self</code></em> :</span></p></td>
<td>the quaternion</td>
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<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>the Euclidian norm</td>
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<div class="refsect2">
<a name="mia-quaternion-normalize"></a><h3>mia_quaternion_normalize ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span> mia_quaternion_normalize (<em class="parameter"><code><a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *self</code></em>);</pre>
<p>
Normalize a quaternion if it's norm is not zero.
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<td><p><span class="term"><em class="parameter"><code>self</code></em> :</span></p></td>
<td>the quaternion to be normalized</td>
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<a name="mia-quaternion-test"></a><h3>mia_quaternion_test ()</h3>
<pre class="programlisting"><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> mia_quaternion_test (<em class="parameter"><code><span class="type">void</span></code></em>);</pre>
<p>
Test the quaternion implementation
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<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>
<a href="http://library.gnome.org/devel/glib/unstable/glib-Standard-Macros.html#TRUE:CAPS"><code class="literal">TRUE</code></a> if all tests pass, <a href="http://library.gnome.org/devel/glib/unstable/glib-Standard-Macros.html#FALSE:CAPS"><code class="literal">FALSE</code></a> otherwise.</td>
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<div class="refsect2">
<a name="mia-quaternion-xmlio-read"></a><h3>mia_quaternion_xmlio_read ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span> mia_quaternion_xmlio_read (<em class="parameter"><code><a class="link" href="mialm-XML-manipulation-of-landmarks.html#ParserState" title="struct ParserState"><span class="type">ParserState</span></a> *state</code></em>,
<em class="parameter"><code>const <a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gchar"><span class="type">gchar</span></a> *property</code></em>);</pre>
<p>
Helper function to read a quaternion from a XML file
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<td><p><span class="term"><em class="parameter"><code>state</code></em> :</span></p></td>
<td>XML parser state holding the parent object and the values</td>
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<td><p><span class="term"><em class="parameter"><code>property</code></em> :</span></p></td>
<td>property name the quaternion has in the parent class</td>
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<div class="refsect2">
<a name="mia-quaternion-xmlio-write"></a><h3>mia_quaternion_xmlio_write ()</h3>
<pre class="programlisting"><a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gboolean"><span class="returnvalue">gboolean</span></a> mia_quaternion_xmlio_write (<em class="parameter"><code><span class="type">xmlNodePtr</span> root</code></em>,
<em class="parameter"><code><span class="type">xmlNsPtr</span> ns</code></em>,
<em class="parameter"><code>const <a href="http://library.gnome.org/devel/glib/unstable/glib-Basic-Types.html#gchar"><span class="type">gchar</span></a> *tag</code></em>,
<em class="parameter"><code>const <a class="link" href="mialm-MiaQuaternion.html#MiaQuaternion" title="MiaQuaternion"><span class="type">MiaQuaternion</span></a> *q</code></em>);</pre>
<p>
Helper function to write a quaternion to a XML file
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<td><p><span class="term"><em class="parameter"><code>root</code></em> :</span></p></td>
<td>xml node this quaternion will be attached to</td>
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<td><p><span class="term"><em class="parameter"><code>ns</code></em> :</span></p></td>
<td>name space</td>
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<td><p><span class="term"><em class="parameter"><code>tag</code></em> :</span></p></td>
<td>the xml tag to store this quaternion under</td>
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<td><p><span class="term"><em class="parameter"><code>q</code></em> :</span></p></td>
<td>the quaternion</td>
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<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td>true if the node creation was successfu, otherwise false.</td>
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