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diff --git a/manuals/chickadee/Vectors.html b/manuals/chickadee/Vectors.html index eb79149..4857f0a 100644 --- a/manuals/chickadee/Vectors.html +++ b/manuals/chickadee/Vectors.html @@ -16,22 +16,22 @@ Foundation Web site at http://www.gnu.org/licenses/fdl.html. The document was typeset with http://www.texinfo.org/ (GNU Texinfo). --> -<!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> +<!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ --> <head> -<title>The Chickadee Game Toolkit: Vectors</title> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> +<title>Vectors (The Chickadee Game Toolkit)</title> -<meta name="description" content="The Chickadee Game Toolkit: Vectors"> -<meta name="keywords" content="The Chickadee Game Toolkit: Vectors"> +<meta name="description" content="Vectors (The Chickadee Game Toolkit)"> +<meta name="keywords" content="Vectors (The Chickadee Game Toolkit)"> <meta name="resource-type" content="document"> <meta name="distribution" content="global"> <meta name="Generator" content="makeinfo"> -<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <link href="index.html#Top" rel="start" title="Top"> <link href="Index.html#Index" rel="index" title="Index"> <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> <link href="Math.html#Math" rel="up" title="Math"> -<link href="Matrices.html#Matrices" rel="next" title="Matrices"> -<link href="Math.html#Math" rel="prev" title="Math"> +<link href="Rectangles.html#Rectangles" rel="next" title="Rectangles"> +<link href="Basics.html#Basics" rel="prev" title="Basics"> <style type="text/css"> <!-- a.summary-letter {text-decoration: none} @@ -90,12 +90,255 @@ ul.no-bullet {list-style: none} <a name="Vectors"></a> <div class="header"> <p> -Next: <a href="Matrices.html#Matrices" accesskey="n" rel="next">Matrices</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> +Next: <a href="Rectangles.html#Rectangles" accesskey="n" rel="next">Rectangles</a>, Previous: <a href="Basics.html#Basics" accesskey="p" rel="prev">Basics</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="Vectors-1"></a> -<h4 class="subsection">2.3.1 Vectors</h4> +<h4 class="subsection">2.2.2 Vectors</h4> + +<p>Unlike Scheme’s vector data type, which is a sequence of arbitrary +Scheme objects, Chickadee’s <code>(chickadee math vector)</code> module +provides vectors in the linear algebra sense: Sequences of numbers +specialized for particular coordinate spaces. As of now, Chickadee +provides 2D and 3D vectors, with 4D vector support coming in a future +release. +</p> +<p>Here’s a quick example of adding two vectors: +</p> +<div class="example"> +<pre class="example">(define v (vec2+ (vec2 1 2) (vec2 3 4))) +</pre></div> + +<p>Since vectors are used so frequently, the reader macro <code>#v</code> is +used to cut down on typing: +</p> +<div class="example"> +<pre class="example">(define v (vec2+ #v(1 2) #v(3 4))) +</pre></div> + +<a name="A-Note-About-Performance"></a> +<h4 class="subsubsection">2.2.2.1 A Note About Performance</h4> + +<p>A lot of time has been spent making Chickadee’s vector operations +perform relatively efficiently in critical code paths where excessive +garbage generation will cause major performance issues. The general +rule is that procedures ending with <code>!</code> perform an in-place +modification of one of the arguments in order to avoid allocating a +new vector. These procedures are also inlined by Guile’s compiler in +order to take advantage of optimizations relating to floating point +math operations. The downside is that since these are not pure +functions, they do not compose well and create more verbose code. +</p> +<a name="g_t2D-Vectors"></a> +<h4 class="subsubsection">2.2.2.2 2D Vectors</h4> + +<dl> +<dt><a name="index-vec2"></a>Procedure: <strong>vec2</strong> <em><var>x</var> <var>y</var></em></dt> +<dd><p>Return a new 2D vector with coordinates (<var>x</var>, <var>y</var>). +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002fpolar"></a>Procedure: <strong>vec2/polar</strong> <em><var>r</var> <var>theta</var></em></dt> +<dd><p>Return a new 2D vector containing the Cartesian representation of the +polar coordinate (<var>r</var>, <var>theta</var>). The angle <var>theta</var> is +measured in radians. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_003f"></a>Procedure: <strong>vec2?</strong> <em><var>obj</var></em></dt> +<dd><p>Return <code>#t</code> if <var>obj</var> is a 2D vector. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dx"></a>Procedure: <strong>vec2-x</strong> <em><var>v</var></em></dt> +<dd><p>Return the X coordinate of the 2D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dy"></a>Procedure: <strong>vec2-y</strong> <em><var>v</var></em></dt> +<dd><p>Return the Y coordinate of the 2D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dcopy"></a>Procedure: <strong>vec2-copy</strong> <em><var>v</var></em></dt> +<dd><p>Return a fresh copy of the 2D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dmagnitude"></a>Procedure: <strong>vec2-magnitude</strong> <em><var>v</var></em></dt> +<dd><p>Return the magnitude of the 2D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002ddot_002dproduct"></a>Procedure: <strong>vec2-dot-product</strong> <em><var>v1</var> <var>v2</var></em></dt> +<dd><p>Return the dot product of the 2D vectors <var>v1</var> and <var>v2</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dnormalize"></a>Procedure: <strong>vec2-normalize</strong> <em><var>v</var></em></dt> +<dd><p>Return the normalized form of the 2D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002b"></a>Procedure: <strong>vec2+</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Add <var>x</var>, either a 2D vector or a scalar (i.e. a real number), to +the 2D vector <var>v</var> and return a new vector containing the sum. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002d"></a>Procedure: <strong>vec2-</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Subtract <var>x</var>, either a 2D vector or a scalar, from the 2D vector +<var>v</var> and return a new vector containing the difference. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002a"></a>Procedure: <strong>vec2*</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Multiply the 2D vector <var>v</var> by <var>x</var>, a 2D vector or a scalar, +and return a new vector containing the product. +</p></dd></dl> + +<dl> +<dt><a name="index-set_002dvec2_002dx_0021"></a>Procedure: <strong>set-vec2-x!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Set the X coordinate of the 2D vector <var>v</var> to <var>x</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-set_002dvec2_002dy_0021"></a>Procedure: <strong>set-vec2-y!</strong> <em><var>v</var> <var>y</var></em></dt> +<dd><p>Set the Y coordinate of the 2D vector <var>v</var> to <var>y</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dcopy_0021"></a>Procedure: <strong>vec2-copy!</strong> <em><var>source</var> <var>target</var></em></dt> +<dd><p>Copy the 2D vector <var>source</var> into the 2D vector <var>target</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dadd_0021"></a>Procedure: <strong>vec2-add!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 2D vector <var>v</var> by adding +<var>x</var>, a 2D vector or a scalar. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dsub_0021"></a>Procedure: <strong>vec2-sub!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 2D vector <var>v</var> by +subtracting <var>x</var>, a 2D vector or a scalar. +</p></dd></dl> + +<dl> +<dt><a name="index-vec2_002dmult_0021"></a>Procedure: <strong>vec2-mult!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 2D vector <var>v</var> by +multiplying it by <var>x</var>, a 2D vector or a scalar. +</p></dd></dl> +<a name="g_t3D-Vectors"></a> +<h4 class="subsubsection">2.2.2.3 3D Vectors</h4> + +<dl> +<dt><a name="index-vec3"></a>Procedure: <strong>vec3</strong> <em><var>x</var> <var>y</var></em></dt> +<dd><p>Return a new 2D vector with coordinates (<var>x</var>, <var>y</var>). +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_003f"></a>Procedure: <strong>vec3?</strong> <em><var>obj</var></em></dt> +<dd><p>Return <code>#t</code> if <var>obj</var> is a 3D vector. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dx"></a>Procedure: <strong>vec3-x</strong> <em><var>v</var></em></dt> +<dd><p>Return the X coordinate of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dy"></a>Procedure: <strong>vec3-y</strong> <em><var>v</var></em></dt> +<dd><p>Return the Y coordinate of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dz"></a>Procedure: <strong>vec3-z</strong> <em><var>v</var></em></dt> +<dd><p>Return the Z coordinate of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dcopy"></a>Procedure: <strong>vec3-copy</strong> <em><var>v</var></em></dt> +<dd><p>Return a fresh copy of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dmagnitude"></a>Procedure: <strong>vec3-magnitude</strong> <em><var>v</var></em></dt> +<dd><p>Return the magnitude of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002ddot_002dproduct"></a>Procedure: <strong>vec3-dot-product</strong> <em><var>v1</var> <var>v2</var></em></dt> +<dd><p>Return the dot product of the 3D vectors <var>v1</var> and <var>v2</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dnormalize"></a>Procedure: <strong>vec3-normalize</strong> <em><var>v</var></em></dt> +<dd><p>Return the normalized form of the 3D vector <var>v</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002b"></a>Procedure: <strong>vec3+</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Add <var>x</var>, either a 3D vector or a scalar (i.e. a real number), to +the 3D vector <var>v</var> and return a new vector containing the sum. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002d"></a>Procedure: <strong>vec3-</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Subtract <var>x</var>, either a 3D vector or a scalar, from the 3D vector +<var>v</var> and return a new vector containing the difference. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002a"></a>Procedure: <strong>vec3*</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Multiply the 3D vector <var>v</var> by <var>x</var>, a 3D vector or a scalar, +and return a new vector containing the product. +</p></dd></dl> + +<dl> +<dt><a name="index-set_002dvec3_002dx_0021"></a>Procedure: <strong>set-vec3-x!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Set the X coordinate of the 3D vector <var>v</var> to <var>x</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-set_002dvec3_002dy_0021"></a>Procedure: <strong>set-vec3-y!</strong> <em><var>v</var> <var>y</var></em></dt> +<dd><p>Set the Y coordinate of the 3D vector <var>v</var> to <var>y</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-set_002dvec3_002dz_0021"></a>Procedure: <strong>set-vec3-z!</strong> <em><var>v</var> <var>z</var></em></dt> +<dd><p>Set the Z coordinate of the 3D vector <var>v</var> to <var>z</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dcopy_0021"></a>Procedure: <strong>vec3-copy!</strong> <em><var>source</var> <var>target</var></em></dt> +<dd><p>Copy the 3D vector <var>source</var> into the 3D vector <var>target</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dadd_0021"></a>Procedure: <strong>vec3-add!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 3D vector <var>v</var> by adding +<var>x</var>, a 3D vector or a scalar. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dsub_0021"></a>Procedure: <strong>vec3-sub!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 3D vector <var>v</var> by +subtracting <var>x</var>, a 3D vector or a scalar. +</p></dd></dl> + +<dl> +<dt><a name="index-vec3_002dmult_0021"></a>Procedure: <strong>vec3-mult!</strong> <em><var>v</var> <var>x</var></em></dt> +<dd><p>Perform an in-place modification of the 3D vector <var>v</var> by +multiplying it by <var>x</var>, a 3D vector or a scalar. +</p></dd></dl> + +<hr> +<div class="header"> +<p> +Next: <a href="Rectangles.html#Rectangles" accesskey="n" rel="next">Rectangles</a>, Previous: <a href="Basics.html#Basics" accesskey="p" rel="prev">Basics</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> |