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<span id="Matrices"></span><div class="header">
<p>
Next: <a href="Quaternions.html" accesskey="n" rel="next">Quaternions</a>, Previous: <a href="Rectangles.html" accesskey="p" rel="prev">Rectangles</a>, Up: <a href="Math.html" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html" title="Index" rel="index">Index</a>]</p>
</div>
<hr />
<span id="Matrices-1"></span><h4 class="subsection">5.2.4 Matrices</h4>
<p>The <code>(chickadee math matrix)</code> module provides an interface for
working with the most common type of matrices in game development: 4x4
transformation matrices.
</p>
<p><em>Another Note About Performance</em>
</p>
<p>Much like the vector API, the matrix API is commonly used in
performance critical code paths. In order to reduce the amount of
garbage generated and improve matrix multiplication performance, there
are many procedures that perform in-place modifications of matrix
objects.
</p>
<span id="g_t3x3-Matrices"></span><h4 class="subsubsection">5.2.4.1 3x3 Matrices</h4>
<dl>
<dt id="index-make_002dmatrix3">Procedure: <strong>make-matrix3</strong> <em>aa ab ac ba bb bc ca cb cc</em></dt>
<dd><p>Return a new 3x3 initialized with the given 9 values in column-major
format.
</p></dd></dl>
<dl>
<dt id="index-make_002dnull_002dmatrix3">Procedure: <strong>make-null-matrix3</strong></dt>
<dd><p>Return a new 3x3 matrix with all values initialized to 0.
</p></dd></dl>
<dl>
<dt id="index-make_002didentity_002dmatrix3">Procedure: <strong>make-identity-matrix3</strong></dt>
<dd><p>Return a new 3x3 identity matrix. Any matrix multiplied by the
identity matrix yields the original matrix. This procedure is
equivalent to the following code:
</p>
<div class="lisp">
<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-symbol">make-matrix3</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span>
<span class="syntax-symbol">0</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">0</span>
<span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">1</span><span class="syntax-close">)</span>
</pre></div>
</dd></dl>
<dl>
<dt id="index-matrix3_003f">Procedure: <strong>matrix3?</strong> <em>obj</em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a 3x3 matrix.
</p></dd></dl>
<dl>
<dt id="index-matrix3_003d">Procedure: <strong>matrix3=</strong> <em>m1 m2</em></dt>
<dd><p>Return <code>#t</code> if <var>m1</var> is the same matrix as <var>m2</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dcopy">Procedure: <strong>matrix3-copy</strong> <em>matrix</em></dt>
<dd><p>Return a new 3x3 matrix that is a copy of <var>matrix</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002a">Procedure: <strong>matrix3*</strong> <em>. matrices</em></dt>
<dd><p>Return a new 3x3 matrix containing the product of multiplying all of
the given <var>matrices</var>.
</p>
<p>Note: Remember that matrix multiplication is <strong>not</strong> commutative!
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dtranslate">Procedure: <strong>matrix3-translate</strong> <em>v</em></dt>
<dd><p>Return a new 3x3 matrix that represents a translation by <var>v</var>, a 2D
vector.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dscale">Procedure: <strong>matrix3-scale</strong> <em>s</em></dt>
<dd><p>Return a new 3x3 matrix that represents a scaling along the x and y
axes by the scaling factor <var>s</var>, a number or 2D vector.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002drotate">Procedure: <strong>matrix3-rotate</strong> <em>angle</em></dt>
<dd><p>Return a new 3x3 matrix that represents a rotation by <var>angle</var>
radians.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dtransform">Procedure: <strong>matrix3-transform</strong> <em>matrix v</em></dt>
<dd><p>Return a new 2D vector that is <var>v</var> as transformed by the 3x3
matrix <var>matrix</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dinverse">Procedure: <strong>matrix3-inverse</strong> <em>matrix</em></dt>
<dd><p>Return the inverse of <var>matrix</var>.
</p></dd></dl>
<p>The following procedures perform in-place, destructive updates to 3x3
matrix objects:
</p>
<dl>
<dt id="index-matrix3_002dcopy_0021">Procedure: <strong>matrix3-copy!</strong> <em>src dest</em></dt>
<dd><p>Copy the contents of matrix <var>src</var> to <var>dest</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002didentity_0021">Procedure: <strong>matrix3-identity!</strong> <em>matrix</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain the identity matrix.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dmult_0021">Procedure: <strong>matrix3-mult!</strong> <em>dest a b</em></dt>
<dd><p>Multiply the 3x3 matrix <var>a</var> by the 3x3 matrix <var>b</var> and store
the result in the 3x3 matrix <var>dest</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dtranslate_0021">Procedure: <strong>matrix3-translate!</strong> <em>matrix v</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a translation by <var>v</var>, a 2D
vector.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dscale_0021">Procedure: <strong>matrix3-scale!</strong> <em>matrix s</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a scaling along the x and y
axes by the scaling factor <var>s</var>, a number or 2D vector.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002drotate_0021">Procedure: <strong>matrix3-rotate!</strong> <em>matrix angle</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a rotation by <var>angle</var>
radians.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dtransform_0021">Procedure: <strong>matrix3-transform!</strong> <em>matrix v</em></dt>
<dd><p>Modify the 2D vector <var>v</var> in-place to contain <var>v</var> as
transformed by the 3x3 matrix <var>matrix</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix3_002dinverse_0021">Procedure: <strong>matrix3-inverse!</strong> <em>matrix target</em></dt>
<dd><p>Compute the inverse of <var>matrix</var> and store the results in
<var>target</var>.
</p></dd></dl>
<span id="g_t4x4-Matrices"></span><h4 class="subsubsection">5.2.4.2 4x4 Matrices</h4>
<dl>
<dt id="index-make_002dmatrix4">Procedure: <strong>make-matrix4</strong> <em>aa ab ac ad ba bb bc bd ca cb cc cd da db dc dd</em></dt>
<dd>
<p>Return a new 4x4 matrix initialized with the given 16 values in
column-major format.
</p></dd></dl>
<dl>
<dt id="index-make_002dnull_002dmatrix4">Procedure: <strong>make-null-matrix4</strong></dt>
<dd><p>Return a new 4x4 matrix with all values initialized to 0.
</p></dd></dl>
<dl>
<dt id="index-make_002didentity_002dmatrix4">Procedure: <strong>make-identity-matrix4</strong></dt>
<dd><p>Return a new 4x4 identity matrix. Any matrix multiplied by the
identity matrix yields the original matrix. This procedure is
equivalent to the following code:
</p>
<div class="lisp">
<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-symbol">make-matrix4</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span>
<span class="syntax-symbol">0</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span>
<span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">0</span>
<span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">1</span><span class="syntax-close">)</span>
</pre></div>
</dd></dl>
<dl>
<dt id="index-matrix4_003f">Procedure: <strong>matrix4?</strong> <em>obj</em></dt>
<dd><p>Return <code>#t</code> if <var>obj</var> is a 4x4 matrix.
</p></dd></dl>
<dl>
<dt id="index-matrix4_003d">Procedure: <strong>matrix4=</strong> <em>m1 m2</em></dt>
<dd><p>Return <code>#t</code> if <var>m1</var> is the same matrix as <var>m2</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dcopy">Procedure: <strong>matrix4-copy</strong> <em>matrix</em></dt>
<dd><p>Return a new 4x4 matrix that is a copy of <var>matrix</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002a">Procedure: <strong>matrix4*</strong> <em>. matrices</em></dt>
<dd><p>Return a new 4x4 matrix containing the product of multiplying all of
the given <var>matrices</var>.
</p>
<p>Note: Remember that matrix multiplication is <strong>not</strong> commutative!
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dinverse">Procedure: <strong>matrix4-inverse</strong> <em>matrix</em></dt>
<dd><p>Return the inverse of <var>matrix</var>.
</p>
<p>A matrix multiplied by its inverse is the identity matrix, thought not
always exactly due to the nature of floating point numbers.
</p></dd></dl>
<dl>
<dt id="index-orthographic_002dprojection">Procedure: <strong>orthographic-projection</strong> <em>left right top bottom near far</em></dt>
<dd>
<p>Return a new 4x4 matrix that represents an orthographic (2D)
projection for the horizontal clipping plane <var>top</var> and
<var>bottom</var>, the vertical 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 id="index-perspective_002dprojection">Procedure: <strong>perspective-projection</strong> <em>fov aspect-ratio near far</em></dt>
<dd>
<p>Return a new 4x4 matrix that represents a perspective (3D) projection
with a field of vision of <var>fov</var> radians, an aspect ratio of
<var>aspect-ratio</var>, and a depth clipping plane defined by <var>near</var>
and <var>far</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dtranslate">Procedure: <strong>matrix4-translate</strong> <em>x</em></dt>
<dd><p>Return a new 4x4 matrix that represents a translation by <var>x</var>, a 2D
vector, a 3D vector, or a rectangle (in which case the bottom-left
corner of the rectangle is used).
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dscale">Procedure: <strong>matrix4-scale</strong> <em>s</em></dt>
<dd><p>Return a new 4x4 matrix that represents a scaling along the X, Y, and
Z axes by the scaling factor <var>s</var>, a real number.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002drotate">Procedure: <strong>matrix4-rotate</strong> <em>q</em></dt>
<dd><p>Return a new 4x4 matrix that represents a rotation about an arbitrary
axis defined by the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002drotate_002dz">Procedure: <strong>matrix4-rotate-z</strong> <em>theta</em></dt>
<dd><p>Return a new 4x4 matrix that represents a rotation about the Z axis by
<var>theta</var> radians.
</p></dd></dl>
<p>The following procedures perform in-place, destructive updates to 4x4
matrix objects:
</p>
<dl>
<dt id="index-matrix4_002dcopy_0021">Procedure: <strong>matrix4-copy!</strong> <em>src dest</em></dt>
<dd><p>Copy the contents of matrix <var>src</var> to <var>dest</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002didentity_0021">Procedure: <strong>matrix4-identity!</strong> <em>matrix</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain the identity matrix.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dmult_0021">Procedure: <strong>matrix4-mult!</strong> <em>dest a b</em></dt>
<dd><p>Multiply the 4x4 matrix <var>a</var> by the 4x4 matrix <var>b</var> and store
the result in the 4x4 matrix <var>dest</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dinverse_0021">Procedure: <strong>matrix4-inverse!</strong> <em>matrix target</em></dt>
<dd><p>Compute the inverse of <var>matrix</var> and store the result in
<var>target</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dtranslate_0021">Procedure: <strong>matrix4-translate!</strong> <em>matrix x</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a translation by <var>x</var>, a 2D
vector, a 3D vector, or a rectangle (in which case the bottom-left
corner of the rectangle is used).
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dscale_0021">Procedure: <strong>matrix4-scale!</strong> <em>matrix s</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a scaling along the X, Y, and
Z axes by the scaling factor <var>s</var>, a real number.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002drotate_0021">Procedure: <strong>matrix4-rotate!</strong> <em>matrix q</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a rotation about an arbitrary
axis defined by the quaternion <var>q</var>.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002drotate_002dz_0021">Procedure: <strong>matrix4-rotate-z!</strong> <em>matrix theta</em></dt>
<dd><p>Modify <var>matrix</var> in-place to contain a rotation about the Z axis by
<var>theta</var> radians.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002d2d_002dtransform_0021">Procedure: <strong>matrix4-2d-transform!</strong> <em>matrix [#:origin] [#:position] [#:rotation] [#:scale] [#:shear]</em></dt>
<dd>
<p>Modify <var>matrix</var> in-place to contain the transformation described
by <var>position</var>, a 2D vector or rectangle, <var>rotation</var>, a scalar
representing a rotation about the Z axis, <var>scale</var>, a 2D vector,
and <var>shear</var>, a 2D vector. The transformation happens with respect
to <var>origin</var>, a 2D vector. If an argument is not provided, that
particular transformation will not be included in the result.
</p></dd></dl>
<dl>
<dt id="index-matrix4_002dtransform_0021">Procedure: <strong>matrix4-transform!</strong> <em>matrix v</em></dt>
<dd><p>Modify the 2D vector <var>v</var> in-place by multiplying it by the 4x4
matrix <var>matrix</var>.
</p></dd></dl>
<hr />
<div class="header">
<p>
Next: <a href="Quaternions.html" accesskey="n" rel="next">Quaternions</a>, Previous: <a href="Rectangles.html" accesskey="p" rel="prev">Rectangles</a>, Up: <a href="Math.html" accesskey="u" rel="up">Math</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html" title="Index" rel="index">Index</a>]</p>
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