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<title>Sly: Vectors</title>
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<a name="Vectors"></a>
<div class="header">
<p>
Next: <a href="Rectangles.html#Rectangles" accesskey="n" rel="next">Rectangles</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">4.2.1 Vectors</h4>
<div class="example">
<pre class="example">(use-modules (sly math vector))
</pre></div>
<p>Not to be confused with Guile’s vector data structure, Sly provides
dedicated data types for 2D, 3D, and 4D vectors in the mathematical
sense. Vector procedures are polymorphic, and will work with any
dimensionality that the operation supports. In some cases, such as
<code>v+</code>, <code>v-</code>, and <code>v*</code>, scalar values may be passed as
well.
</p>
<p>The <code><vector2></code>, <code><vector3></code>, and <code><vector4></code> type
descriptors have been exposed for use with Guile’s <code>(ice-9
match)</code> pattern matching module.
</p>
<dl>
<dt><a name="index-_003cvector2_003e"></a>Record Type: <strong><vector2></strong></dt>
<dd><p>2D vector data type with fields <code>x</code> and <code>y</code>, in that order.
</p></dd></dl>
<dl>
<dt><a name="index-_003cvector3_003e"></a>Record Type: <strong><vector3></strong></dt>
<dd><p>3D vector data type with fields <code>x</code>, <code>y</code>, and <code>z</code>, in
that order.
</p></dd></dl>
<dl>
<dt><a name="index-_003cvector4_003e"></a>Record Type: <strong><vector4></strong></dt>
<dd><p>4D vector data type with fields <code>x</code>, <code>y</code>, <code>z</code> and
<code>w</code>, in that order.
</p></dd></dl>
<dl>
<dt><a name="index-vector2"></a>Scheme Syntax: <strong>vector2</strong> <em><var>x</var> <var>y</var></em></dt>
<dd><p>Create a new 2D vector with coordinates (<var>x</var>, <var>y</var>).
</p></dd></dl>
<dl>
<dt><a name="index-vector3"></a>Scheme Syntax: <strong>vector3</strong> <em><var>x</var> <var>y</var> <var>z</var></em></dt>
<dd><p>Create a new 3D vector with coordinates (<var>x</var>, <var>y</var>, <var>z</var>).
</p></dd></dl>
<dl>
<dt><a name="index-vector4"></a>Scheme Syntax: <strong>vector4</strong> <em><var>x</var> <var>y</var> <var>z</var> <var>w</var></em></dt>
<dd><p>Create a new 4D vector with coordinates (<var>x</var>, <var>y</var>, <var>z</var>,
<var>w</var>).
</p></dd></dl>
<dl>
<dt><a name="index-vector2_003f"></a>Scheme Syntax: <strong>vector2?</strong> <em><var>v</var></em></dt>
<dd><p>Return <code>#t</code> if <code>v</code> is a 2D vector.
</p></dd></dl>
<dl>
<dt><a name="index-vector3_003f"></a>Scheme Syntax: <strong>vector3?</strong> <em><var>v</var></em></dt>
<dd><p>Return <code>#t</code> if <code>v</code> is a 3D vector.
</p></dd></dl>
<dl>
<dt><a name="index-vector4_003f"></a>Scheme Syntax: <strong>vector4?</strong> <em><var>v</var></em></dt>
<dd><p>Return <code>#t</code> if <code>v</code> is a 4D vector.
</p></dd></dl>
<dl>
<dt><a name="index-vx"></a>Scheme Procedure: <strong>vx</strong> <em><var>v</var></em></dt>
<dd><p>Return the x coordinate of the 2D, 3D, or 4D vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vy"></a>Scheme Procedure: <strong>vy</strong> <em><var>v</var></em></dt>
<dd><p>Return the y coordinate of the 2D, 3D, or 4D vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vz"></a>Scheme Procedure: <strong>vz</strong> <em><var>v</var></em></dt>
<dd><p>Return the z coordinate of the 3D or 4D vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vw"></a>Scheme Procedure: <strong>vw</strong> <em><var>v</var></em></dt>
<dd><p>Return the w coordinate of the 4D vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vmap"></a>Scheme Procedure: <strong>vmap</strong> <em><var>proc</var> <var>v</var></em></dt>
<dd><p>Return a new vector that is the result of applying <var>proc</var> to each
element of the 2D, 3D, or 4D vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-v_002b"></a>Scheme Procedure: <strong>v+</strong> <em>. <var>vectors</var></em></dt>
<dd><p>Return the sum of all <var>vectors</var>. <var>vectors</var> may contain scalar
values, but it may not contain vectors of mixed dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-v_002d"></a>Scheme Procedure: <strong>v-</strong> <em>. <var>vectors</var></em></dt>
<dd><p>Return the difference of all <var>vectors</var>. <var>vectors</var> may contain scalar
values, but it may not contain vectors of mixed dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-v_002a"></a>Scheme Procedure: <strong>v*</strong> <em>. <var>vectors</var></em></dt>
<dd><p>Return the product of all <var>vectors</var>. <var>vectors</var> may contain
scalar values, but it may not contain vectors of mixed dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-vdot"></a>Scheme Procedure: <strong>vdot</strong> <em><var>v1</var> <var>v2</var></em></dt>
<dd><p>Return the dot product of <var>v1</var> and <var>v2</var>. Both vectors must be
of the same dimensionality.
</p></dd></dl>
<dl>
<dt><a name="index-vcross"></a>Scheme Procedure: <strong>vcross</strong> <em><var>v1</var> <var>v2</var></em></dt>
<dd><p>Return the cross product of the 3D vectors <var>v1</var> and <var>v2</var>.
</p></dd></dl>
<dl>
<dt><a name="index-magnitude"></a>Scheme Procedure: <strong>magnitude</strong> <em><var>v</var></em></dt>
<dd><p>Return the magnitude of the vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-normalize"></a>Scheme Procedure: <strong>normalize</strong> <em><var>v</var></em></dt>
<dd><p>Return the normalized form of the vector <var>v</var>.
</p></dd></dl>
<dl>
<dt><a name="index-vlerp"></a>Scheme Procedure: <strong>vlerp</strong> <em><var>v1</var> <var>v2</var> <var>alpha</var></em></dt>
<dd><p>Return the linear interpolation of <var>v1</var> and <var>v2</var> by the scalar
<var>alpha</var>. <var>alpha</var> is expected to be in the range [0, 1].
</p></dd></dl>
<hr>
<div class="header">
<p>
Next: <a href="Rectangles.html#Rectangles" accesskey="n" rel="next">Rectangles</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>
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