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author: David Thompson <dthompson2@worcester.edu> 2023-12-28 11:23:49 -0500
committer: David Thompson <dthompson2@worcester.edu> 2023-12-28 11:23:49 -0500
commit: 25c5eac5e6ca1035db1eddd7bea9ac78531da57e (patch)
tree: 96377006bbfee75bcf0ce208c1ef89cbdfa5b803 /manuals/chickadee/Matrices.html
parent: 5b2e467a7e5e2ffbb0cbbf2557283be891d8206b (diff)
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-<title>Matrices (The Chickadee Game Toolkit)</title>
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-<link href="Math.html" rel="up" title="Math" />
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-</head>
-
-<body lang="en">
-<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> &nbsp; [<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> &nbsp; [<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>
-
-
-
-</body>
-</html>
author	David Thompson <dthompson2@worcester.edu>	2023-12-28 11:23:49 -0500
committer	David Thompson <dthompson2@worcester.edu>	2023-12-28 11:23:49 -0500
commit	25c5eac5e6ca1035db1eddd7bea9ac78531da57e (patch)
tree	96377006bbfee75bcf0ce208c1ef89cbdfa5b803 /manuals/chickadee/Matrices.html
parent	5b2e467a7e5e2ffbb0cbbf2557283be891d8206b (diff)