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diff --git a/manuals/chickadee/Matrices.html b/manuals/chickadee/Matrices.html deleted file mode 100644 index bf65917..0000000 --- a/manuals/chickadee/Matrices.html +++ /dev/null @@ -1,409 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> -<html> -<!-- Copyright (C) 2017-2023 David Thompson dthompson2@worcester.edu - -Permission is granted to copy, distribute and/or modify this document -under the terms of the GNU Free Documentation License, Version 1.3 -or any later version published by the Free Software Foundation; -with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. -A copy of the license is included in the section entitled "GNU -Free Documentation License". - -A copy of the license is also available from the Free Software -Foundation Web site at http://www.gnu.org/licenses/fdl.html. - - -* Chickadee: (chickadee). Game programming toolkit for Guile. - -The document was typeset with -http://www.texinfo.org/ (GNU Texinfo). - --> -<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ --> -<head> -<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> -<title>Matrices (The Chickadee Game Toolkit)</title> - -<meta name="description" content="Matrices (The Chickadee Game Toolkit)" /> -<meta name="keywords" content="Matrices (The Chickadee Game Toolkit)" /> -<meta name="resource-type" content="document" /> -<meta name="distribution" content="global" /> -<meta name="Generator" content="makeinfo" /> -<link href="index.html" rel="start" title="Top" /> -<link href="Index.html" rel="index" title="Index" /> -<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents" /> -<link href="Math.html" rel="up" title="Math" /> -<link href="Quaternions.html" rel="next" title="Quaternions" /> -<link href="Rectangles.html" rel="prev" title="Rectangles" /> -<style type="text/css"> -<!-- -a.summary-letter {text-decoration: none} -blockquote.indentedblock {margin-right: 0em} -div.display {margin-left: 3.2em} -div.example {margin-left: 3.2em} -div.lisp {margin-left: 3.2em} -kbd {font-style: oblique} -pre.display {font-family: inherit} -pre.format {font-family: inherit} -pre.menu-comment {font-family: serif} -pre.menu-preformatted {font-family: serif} -span.nolinebreak {white-space: nowrap} -span.roman {font-family: initial; font-weight: normal} -span.sansserif {font-family: sans-serif; font-weight: normal} -ul.no-bullet {list-style: none} -@media (min-width: 1140px) { - body { - margin-left: 14rem; - margin-right: 4rem; - max-width: 52rem; - } -} - -@media (min-width: 800px) and (max-width: 1140px) { - body { - margin-left: 6rem; - margin-right: 4rem; - max-width: 52rem; - } -} - -@media (max-width: 800px) { - body { - margin: 1rem; - } -} - ---> -</style> -<link rel="stylesheet" type="text/css" href="https://dthompson.us/css/dthompson.css" /> - - -</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> [<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> -</div> - - - -</body> -</html> |