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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> [<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’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>
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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> [<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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