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<title>Sly: Quaternions</title>
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<a name="Quaternions"></a>
<div class="header">
<p>
Next: <a href="Miscellaneous.html#Miscellaneous" accesskey="n" rel="next">Miscellaneous</a>, Previous: <a href="Tweens.html#Tweens" accesskey="p" rel="prev">Tweens</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html#Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Quaternions-1"></a>
<h4 class="subsection">4.2.5 Quaternions</h4>
<div class="example">
<pre class="example">(use-modules (sly math quaternion))
</pre></div>
<p>Quaternions are used to express rotations about an arbitrary axis in a
way that avoids “gimbal lock” and allows for useful interpolation,
unlike matrices or Euler angles.
</p>
<p>Quaternions can be used in rotation transformations
(see <a href="Transforms.html#Transforms">Transforms</a>), as well as converted to and from <a href="Vectors.html#Vectors">Vectors</a>.
</p>
<dl>
<dt><a name="index-_003cquaternion_003e"></a>Record Type: <strong><quaternion></strong></dt>
<dd><p>Data type with 4 fields: <code>w</code>, <code>x</code>, <code>y</code>, <code>z</code>, in
that order. This type descriptor has been exposed for destructuring
via Guile’s <code>(ice-9 match)</code> module.
</p></dd></dl>
<dl>
<dt><a name="index-make_002dquaternion"></a>Scheme Procedure: <strong>make-quaternion</strong> <em><var>v</var> <var>theta</var></em></dt>
<dt><a name="index-make_002dquaternion-1"></a>Scheme Procedure: <strong>make-quaternion</strong> <em><var>w</var> <var>x</var> <var>y</var> <var>z</var></em></dt>
<dd><p>Create a new quaternion from an axis angle (a 3D vector <var>v</var> plus
an angle <var>theta</var>) or from individual coordinates <var>w</var>, <var>x</var>,
<var>y</var>, and <var>z</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion"></a>Scheme Procedure: <strong>quaternion</strong> <em><var>v</var> <var>theta</var></em></dt>
<dt><a name="index-quaternion-1"></a>Scheme Procedure: <strong>quaternion</strong> <em><var>w</var> <var>x</var> <var>y</var> <var>z</var></em></dt>
<dd><p>Alternate spelling of <code>make-quaternion</code>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_003f"></a>Scheme Syntax: <strong>quaternion?</strong> <em><var>obj</var></em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a quaternion.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dw"></a>Scheme Syntax: <strong>quaternion-w</strong> <em><var>q</var></em></dt>
<dd><p>Return the w coordinate of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dx"></a>Scheme Syntax: <strong>quaternion-x</strong> <em><var>q</var></em></dt>
<dd><p>Return the x coordinate of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dy"></a>Scheme Syntax: <strong>quaternion-y</strong> <em><var>q</var></em></dt>
<dd><p>Return the y coordinate of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dz"></a>Scheme Syntax: <strong>quaternion-z</strong> <em><var>q</var></em></dt>
<dd><p>Return the z coordinate of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-identity_002dquaternion"></a>Scheme Variable: <strong>identity-quaternion</strong></dt>
<dd><p>The multiplicative identity quaternion.
</p></dd></dl>
<dl>
<dt><a name="index-null_002dquaternion"></a>Scheme Variable: <strong>null-quaternion</strong></dt>
<dd><p>A quaternion with all fields set to zero.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002a"></a>Scheme Procedure: <strong>quaternion*</strong> <em>. <var>quaternions</var></em></dt>
<dd><p>Return the product of all <var>quaternions</var>. Return
<code>identity-quaternion</code> if called without arguments.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dslerp"></a>Scheme Procedure: <strong>quaternion-slerp</strong> <em><var>q1</var> <var>q2</var> <var>delta</var></em></dt>
<dd><p>Perform a spherical linear interpolation of the quaternions <var>q1</var>
and <var>q2</var> and blending factor <var>delta</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dmagnitude"></a>Scheme Procedure: <strong>quaternion-magnitude</strong> <em><var>q</var></em></dt>
<dd><p>Return the magnitude of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002dnormalize"></a>Scheme Procedure: <strong>quaternion-normalize</strong> <em><var>q</var></em></dt>
<dd><p>Return the normalized form of the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vector_002d_003equaternion"></a>Scheme Procedure: <strong>vector->quaternion</strong> <em><var>v</var></em></dt>
<dd><p>Convert the 4D vector <var>v</var> to a quaternion.
</p></dd></dl>
<dl>
<dt><a name="index-quaternion_002d_003evector"></a>Scheme Procedure: <strong>quaternion->vector</strong> <em><var>q</var></em></dt>
<dd><p>Convert the quaternion <var>q</var> to a 4D vector.
</p></dd></dl>
<hr>
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