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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/Vectors.html
parent: 5b2e467a7e5e2ffbb0cbbf2557283be891d8206b (diff)
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-<title>Vectors (The Chickadee Game Toolkit)</title>
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-<body lang="en">
-<span id="Vectors"></span><div class="header">
-<p>
-Next: <a href="Rectangles.html" accesskey="n" rel="next">Rectangles</a>, Previous: <a href="Basics.html" accesskey="p" rel="prev">Basics</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="Vectors-1"></span><h4 class="subsection">5.2.2 Vectors</h4>
-
-<p>Unlike Scheme&rsquo;s vector data type, which is a sequence of arbitrary
-Scheme objects, Chickadee&rsquo;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&rsquo;s a quick example of adding two vectors:
-</p>
-<div class="lisp">
-<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">v</span> <span class="syntax-open">(</span><span class="syntax-symbol">vec2+</span> <span class="syntax-open">(</span><span class="syntax-symbol">vec2</span> <span class="syntax-symbol">1</span> <span class="syntax-symbol">2</span><span class="syntax-close">)</span> <span class="syntax-open">(</span><span class="syntax-symbol">vec2</span> <span class="syntax-symbol">3</span> <span class="syntax-symbol">4</span><span class="syntax-close">)</span><span class="syntax-close">)</span><span class="syntax-close">)</span>
-</pre></div>
-
-<p><em>A Note About Performance</em>
-</p>
-<p>A lot of time has been spent making Chickadee&rsquo;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&rsquo;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>
-<span id="g_t2D-Vectors"></span><h4 class="subsubsection">5.2.2.1 2D Vectors</h4>
-
-<dl>
-<dt id="index-vec2">Procedure: <strong>vec2</strong> <em>x y</em></dt>
-<dd><p>Return a new 2D vector with coordinates (<var>x</var>, <var>y</var>).
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002fpolar">Procedure: <strong>vec2/polar</strong> <em>r theta</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 id="index-vec2_003f">Procedure: <strong>vec2?</strong> <em>obj</em></dt>
-<dd><p>Return <code>#t</code> if <var>obj</var> is a 2D vector.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dx">Procedure: <strong>vec2-x</strong> <em>v</em></dt>
-<dd><p>Return the X coordinate of the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dy">Procedure: <strong>vec2-y</strong> <em>v</em></dt>
-<dd><p>Return the Y coordinate of the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dcopy">Procedure: <strong>vec2-copy</strong> <em>v</em></dt>
-<dd><p>Return a fresh copy of the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dmagnitude">Procedure: <strong>vec2-magnitude</strong> <em>v</em></dt>
-<dd><p>Return the magnitude of the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002ddot">Procedure: <strong>vec2-dot</strong> <em>v1 v2</em></dt>
-<dd><p>Return the dot product of the 2D vectors <var>v1</var> and <var>v2</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dnormalize">Procedure: <strong>vec2-normalize</strong> <em>v</em></dt>
-<dd><p>Return the normalized form of the 2D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002b">Procedure: <strong>vec2+</strong> <em>v x</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 id="index-vec2_002d">Procedure: <strong>vec2-</strong> <em>v x</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 id="index-vec2_002a">Procedure: <strong>vec2*</strong> <em>v x</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 id="index-set_002dvec2_002dx_0021">Procedure: <strong>set-vec2-x!</strong> <em>v x</em></dt>
-<dd><p>Set the X coordinate of the 2D vector <var>v</var> to <var>x</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-set_002dvec2_002dy_0021">Procedure: <strong>set-vec2-y!</strong> <em>v y</em></dt>
-<dd><p>Set the Y coordinate of the 2D vector <var>v</var> to <var>y</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-set_002dvec2_0021">Procedure: <strong>set-vec2!</strong> <em>v x y</em></dt>
-<dd><p>Set the X and Y coordinates of the 2D vector <var>v</var> to <var>x</var> and
-<var>y</var>, respectively.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dcopy_0021">Procedure: <strong>vec2-copy!</strong> <em>source target</em></dt>
-<dd><p>Copy the 2D vector <var>source</var> into the 2D vector <var>target</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec2_002dadd_0021">Procedure: <strong>vec2-add!</strong> <em>v x</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 id="index-vec2_002dsub_0021">Procedure: <strong>vec2-sub!</strong> <em>v x</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 id="index-vec2_002dmult_0021">Procedure: <strong>vec2-mult!</strong> <em>v x</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>
-
-<span id="g_t3D-Vectors"></span><h4 class="subsubsection">5.2.2.2 3D Vectors</h4>
-
-<dl>
-<dt id="index-vec3">Procedure: <strong>vec3</strong> <em>x y</em></dt>
-<dd><p>Return a new 2D vector with coordinates (<var>x</var>, <var>y</var>).
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_003f">Procedure: <strong>vec3?</strong> <em>obj</em></dt>
-<dd><p>Return <code>#t</code> if <var>obj</var> is a 3D vector.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dx">Procedure: <strong>vec3-x</strong> <em>v</em></dt>
-<dd><p>Return the X coordinate of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dy">Procedure: <strong>vec3-y</strong> <em>v</em></dt>
-<dd><p>Return the Y coordinate of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dz">Procedure: <strong>vec3-z</strong> <em>v</em></dt>
-<dd><p>Return the Z coordinate of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dcopy">Procedure: <strong>vec3-copy</strong> <em>v</em></dt>
-<dd><p>Return a fresh copy of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dmagnitude">Procedure: <strong>vec3-magnitude</strong> <em>v</em></dt>
-<dd><p>Return the magnitude of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002ddot">Procedure: <strong>vec3-dot</strong> <em>v1 v2</em></dt>
-<dd><p>Return the dot product of the 3D vectors <var>v1</var> and <var>v2</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dcross">Procedure: <strong>vec3-cross</strong> <em>v1 v2</em></dt>
-<dd><p>Return a new 3D vector containing the cross product of <var>v1</var> and
-<var>v2</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dnormalize">Procedure: <strong>vec3-normalize</strong> <em>v</em></dt>
-<dd><p>Return the normalized form of the 3D vector <var>v</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002b">Procedure: <strong>vec3+</strong> <em>v x</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 id="index-vec3_002d">Procedure: <strong>vec3-</strong> <em>v x</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 id="index-vec3_002a">Procedure: <strong>vec3*</strong> <em>v x</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 id="index-set_002dvec3_002dx_0021">Procedure: <strong>set-vec3-x!</strong> <em>v x</em></dt>
-<dd><p>Set the X coordinate of the 3D vector <var>v</var> to <var>x</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-set_002dvec3_002dy_0021">Procedure: <strong>set-vec3-y!</strong> <em>v y</em></dt>
-<dd><p>Set the Y coordinate of the 3D vector <var>v</var> to <var>y</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-set_002dvec3_002dz_0021">Procedure: <strong>set-vec3-z!</strong> <em>v z</em></dt>
-<dd><p>Set the Z coordinate of the 3D vector <var>v</var> to <var>z</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-set_002dvec3_0021">Procedure: <strong>set-vec3!</strong> <em>v x y z</em></dt>
-<dd><p>Set the X, Y, and Z coordinates of the 3D vector <var>v</var> to <var>x</var>,
-<var>y</var>, and <var>z</var>, respectively.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dcopy_0021">Procedure: <strong>vec3-copy!</strong> <em>source target</em></dt>
-<dd><p>Copy the 3D vector <var>source</var> into the 3D vector <var>target</var>.
-</p></dd></dl>
-
-<dl>
-<dt id="index-vec3_002dadd_0021">Procedure: <strong>vec3-add!</strong> <em>v x</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 id="index-vec3_002dsub_0021">Procedure: <strong>vec3-sub!</strong> <em>v x</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 id="index-vec3_002dmult_0021">Procedure: <strong>vec3-mult!</strong> <em>v x</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>
-
-<dl>
-<dt id="index-vec3_002dcross_0021">Procedure: <strong>vec3-cross!</strong> <em>dest v1 v2</em></dt>
-<dd><p>Compute the cross product of the 3D vectors <var>v1</var> and <var>v2</var> and
-store the result in <var>dest</var>.
-</p></dd></dl>
-
-<hr />
-<div class="header">
-<p>
-Next: <a href="Rectangles.html" accesskey="n" rel="next">Rectangles</a>, Previous: <a href="Basics.html" accesskey="p" rel="prev">Basics</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/Vectors.html
parent	5b2e467a7e5e2ffbb0cbbf2557283be891d8206b (diff)