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-<a name="Transforms"></a>
-<div class="header">
-<p>
-Next: <a href="Tweens.html#Tweens" accesskey="n" rel="next">Tweens</a>, Previous: <a href="Rectangles.html#Rectangles" accesskey="p" rel="prev">Rectangles</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> &nbsp; [<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="Transforms-1"></a>
-<h4 class="subsection">4.2.3 Transforms</h4>
-
-<div class="example">
-<pre class="example">(use-modules (sly math transform))
-</pre></div>
-
-<p>Transforms are 4x4 transformation matrices.  Matrices are the
-fundamental structure for modeling affine transformations such as
-translation, rotation, and scaling.  Complex transformations are
-created by composing many simpler ones with the <code>transform*</code>
-procedure.
-</p>
-<p>It&rsquo;s a good idea to use transforms in a functional manner by treating
-them as immutable.  This is made easy because almost every procedure
-in this module returns a new transform rather than mutating an
-existing one.  However, in some cases it is necessary to use mutable
-transforms via <code>transform*!</code> for performance reasons.
-</p>
-<dl>
-<dt><a name="index-make_002dtransform"></a>Scheme Procedure: <strong>make-transform</strong> <em><var>aa</var> <var>ab</var> <var>ac</var> <var>ad</var> <var>ba</var> <var>bb</var> <var>bc</var> <var>bd</var> <var>ca</var> <var>cb</var> <var>cc</var> <var>cd</var> <var>da</var> <var>db</var> <var>dc</var> <var>dd</var></em></dt>
-<dd><p>Create a new transform initialized with the given 16 values in
-column-major format.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-null_002dtransform"></a>Scheme Variable: <strong>null-transform</strong></dt>
-<dd><p>A transform composed entirely of zeroes.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-identity_002dtransform"></a>Scheme Variable: <strong>identity-transform</strong></dt>
-<dd><p>The multiplicative identity transform.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_003f"></a>Scheme Syntax: <strong>transform?</strong> <em><var>obj</var></em></dt>
-<dd><p>Return <code>#t</code> if <var>obj</var> is a transform.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002dmatrix"></a>Scheme Syntax: <strong>transform-matrix</strong> <em><var>transform</var></em></dt>
-<dd><p>Return the underlying 4x4 floating point array for <var>transform</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transpose"></a>Scheme Procedure: <strong>transpose</strong> <em><var>transform</var></em></dt>
-<dd><p>Return a transform that is the transpose of <var>transform</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002dvector2"></a>Scheme Procedure: <strong>transform-vector2</strong> <em><var>transform</var> <var>v</var></em></dt>
-<dd><p>Apply <var>transform</var> to the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002dposition"></a>Scheme Procedure: <strong>transform-position</strong> <em><var>transform</var></em></dt>
-<dd><p>Return a 3D vector containing the positional data stored in
-<var>transform</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002b"></a>Scheme Procedure: <strong>transform+</strong> <em>. <var>transforms</var></em></dt>
-<dd><p>Return the sum of <var>transforms</var>.  Return <code>null-transform</code> if
-called without any arguments.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002a"></a>Scheme Procedure: <strong>transform*</strong> <em>. <var>transforms</var></em></dt>
-<dd><p>Return the product of <var>transforms</var>.  Return identity-transform if
-called without any arguments.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-transform_002a_0021"></a>Scheme Procedure: <strong>transform*!</strong> <em><var>dest</var> <var>a</var> <var>b</var></em></dt>
-<dd><p>Multiply <var>a</var> and <var>b</var>, storing the result in <var>dest</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-translate"></a>Scheme Procedure: <strong>translate</strong> <em><var>v</var></em></dt>
-<dd><p>Create a new transform that translates by the 2D or 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-scale"></a>Scheme Procedure: <strong>scale</strong> <em><var>v</var></em></dt>
-<dt><a name="index-scale-1"></a>Scheme Procedure: <strong>scale</strong> <em><var>scalar</var></em></dt>
-<dd><p>Create a new transform that scales by the 2D or 3D vector <var>v</var>, or
-by <var>scalar</var> to scale evenly in all dimensions.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-rotate_002dx"></a>Scheme Procedure: <strong>rotate-x</strong> <em><var>angle</var></em></dt>
-<dd><p>Create a new transform that rotates the x axis by <var>angle</var> radians.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-rotate_002dy"></a>Scheme Procedure: <strong>rotate-y</strong> <em><var>angle</var></em></dt>
-<dd><p>Create a new transform that rotates the y axis by <var>angle</var> radians.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-rotate_002dz"></a>Scheme Procedure: <strong>rotate-z</strong> <em><var>angle</var></em></dt>
-<dd><p>Create a new transform that rotates the z axis by <var>angle</var> radians.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-rotate"></a>Scheme Procedure: <strong>rotate</strong> <em><var>q</var></em></dt>
-<dd><p>Convert the quaternion <var>q</var> into a rotation transform.
-See <a href="Quaternions.html#Quaternions">Quaternions</a> for more information.
-</p></dd></dl>
-
-<p>One of the most common composite transformations is a translation
-multiplied by a scale multiplied by a rotation.  The
-<code>build-transform</code> procedure is a convenience procedure for this
-case.
-</p>
-<dl>
-<dt><a name="index-build_002dtransform"></a>Scheme Procedure: <strong>build-transform</strong> <em><var>[#:position=(vector3 0 0 0)] [#:scale=1] [#:rotation=null-quaternion]</var></em></dt>
-<dd><p>Build a transform by multiplying the following transforms:
-</p>
-<ul>
-<li> translation by <var>position</var>
-</li><li> rotation by <var>rotation</var>
-</li><li> scaling by <var>scale</var>
-</li></ul>
-
-</dd></dl>
-
-<p>The procedures below are useful for creating projection and view
-matrices for cameras. See <a href="Cameras.html#Cameras">Cameras</a> for more details.
-</p>
-<dl>
-<dt><a name="index-orthographic_002dprojection"></a>Scheme Procedure: <strong>orthographic-projection</strong> <em>left right top bottom near far</em></dt>
-<dd><p>Create a new transform that represents an orthographic projection for
-the vertical clipping plane <var>left</var> and <var>right</var>, the horizontal
-clipping plane <var>top</var> and <var>bottom</var>, and the depth clipping
-plane <var>near</var> and <var>far</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-perspective_002dprojection"></a>Scheme Procedure: <strong>perspective-projection</strong> <em><var>field-of-vision</var> <var>aspect-ratio</var> <var>near</var> <var>far</var></em></dt>
-<dd><p>Create a new transform that represents a perspective projection with a
-<var>field-of-vision</var> in degrees, the desired <var>aspect-ratio</var>, and
-the depth clipping plane <var>near</var> and <var>far</var>.
-</p></dd></dl>
-
-<dl>
-<dt><a name="index-look_002dat"></a>Scheme Procedure: <strong>look-at</strong> <em><var>eye</var> <var>center</var> [<var>up=(vector3 0 1 0)</var>]</em></dt>
-<dd><p>Create a view transform that looks from 3D vector <var>eye</var> at the 3D
-vector <var>center</var>, with the 3D vector <var>up</var> indicating which
-direction points up.
-</p></dd></dl>
-
-<hr>
-<div class="header">
-<p>
-Next: <a href="Tweens.html#Tweens" accesskey="n" rel="next">Tweens</a>, Previous: <a href="Rectangles.html#Rectangles" accesskey="p" rel="prev">Rectangles</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> &nbsp; [<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>
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