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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"
"http://www.w3.org/TR/REC-html40/loose.dtd">
<!-- $Id: vec4.html 86 2000-06-13 18:59:13Z garland $ -->
<html>
<head>
<title>libgfx: Vector Math</title>
<link rel=stylesheet href="cdoc.css" type="text/css">
<meta name="Author" content="Michael Garland">
</head>
<body>
<h2>Vector Math</h2>
<h3>class Vec4</h3>
<p> This class implements a 4-dimensional real-valued vector.
Individual elements are represent with <code>double</code> precision
floating point numbers. To use the <tt>Vec4</tt> class you must
include the header
<pre>
#include <gfx/vec4.h>
</pre>
<h4>Constructor Methods</h4>
<p>The <tt>Vec4</tt> class defines the following set of constructors:
<pre>
Vec4(); <i>// Initializes vector to (0 0 0 0).</i>
Vec4(double x, double y, double z, double w); <i>// Initializes vector to (x y z w).</i>
Vec3(double s); <i>// Initializes vector to (s s s s)</i>
Vec4(const Vec4& v); <i>// </i>
Vec4(const float v[4]); <i>// These copy values from v</i>
Vec4(const double v[4]); <i>// </i>
Vec4(const Vec3& v, double w); <i>// Initializes vector to (v[0] v[1] v[2] w)</i>
</pre>
<h4>Specialized Functions</h4>
<p>In addition to the standard functions provided by all vector classes,
the <tt>Vec4</tt> class defines certain specialized functions which
operate only on 4-D vectors.
<p>The <em>cross product</em> of three 4-vectors <tt>u, v, w</tt> is a
fourth vector which is perpendicular to all of <tt>u, v, w</tt>.
It can be computed with the function call
<pre>
t = cross(u, v, w);
</pre>
<p>Since 4-D vectors are frequently
used to represent 3-D homogeneous
coordinates, a projection function is provided.
<pre>
Vec3 proj(const Vec4& v);
</pre>
This routine takes a homogeneous vector <i>(x y z w)</i> and returns the
corresponding 3-vector <i>(x/w y/w z/w)</i>. If <i>w</i> is 0 then
the vector <i>(x y z)</i> is returned.
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