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<head>
<title>libgfx: Quaternions</title>
<link rel=stylesheet href="cdoc.css" type="text/css">
<meta name="Author" content="Michael Garland">
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<body>
<h2>Quaternions</h2>
<p>This package provides the basic mathematical tools necessary for
manipulating quaternions. To begin using it, you must first include the
header file:
<pre>
#include <gfx/quat.h>
</pre>
<p>For more information on the definition of quaternions and their
associated mathematics, you might try the informative Web pages provided
by
<a href="http://mathworld.wolfram.com/Quaternion.html">MathWorld</a>,
<a href="http://www.magic-software.com/Documentation/quat.pdf">David
Eberly</a>, or
<a
href="http://graphics.cs.ucdavis.edu/GraphicsNotes/Quaternions.pdf">UC
Davis</a>.
<h3>class Quat</h3>
<p>The interface presented by the <tt>Quat</tt> class treats quaternions
as consisting of a real scalar part and a complex 3-vector part.
<h4>Constructor Methods</h4>
<p>The <tt>Quat</tt> class defines the following set of constructors:
<pre>
Quat(); <i>// Initializes to identity quaternion</i>
Quat(double x, double y, double z, double w); <i>// Specify vector & scalar part.</i>
Quat(const Vec3& a, double b); <i>// Specify vector & scalar part.</i>
Quat(const Quat& q); <i>// Copy values from q</i>
</pre>
<pre>
Quat::ident(); <i>// Return the identity quaternion</i>
</pre>
<h4>Arithmetic Methods</h4>
<p>The quaternion class supports all the usual arithmetic methods, both
as in-place assignment operators:
<pre>
Quat& operator=(const Quat& q);
Quat& operator+=(const Quat& q);
Quat& operator-=(const Quat& q);
Quat& operator=(double d);
Quat& operator*=(double d);
Quat& operator/=(double d);
</pre>
and as normal binary operations:
<pre>
Quat operator+(const Quat& q, const Quat& r);
Quat operator*(const Quat& q, const Quat& r);
Quat operator*(const Quat& q, double s);
Quat operator*(double s, const Quat& q);
Quat operator/(const Quat& q, double s);
</pre>
<h4>Quaternion Operations</h4>
<p>Using the fundamental arithmetic operations defined above, this
package also provides the following operations on quaternions:
<pre>
double norm(const Quat& q); <i>// Return the length of q</i>
Quat conjugate(const Quat& q); <i>// Return conjugate of q</i>
Quat inverse(const Quat& q); <i>// Return multiplicative inverse of q</i>
void unitize(Quat& q); <i>// Convert to unit quaternion</i>
Quat exp(const Quat& q); <i>// Exponential of a <b>unit</b> quaternion </i>
Quat log(const Quat& q); <i>// Natural logarithm of a <b>unit</b> quaternion </i>
</pre>
<p>Quaternions can be constructed from an axis/angle rotation
specification using the function:
<pre>
Quat axis_to_quat(const Vec3& a, double phi);
</pre>
At is also generally useful to be able to convert a quaternion into a
rotation matrix:
<pre>
Mat4 quat_to_matrix(const Quat& q);
Mat4 unit_quat_to_matrix(const Quat& q);
</pre>
<p>
<pre>
Quat slerp(const Quat& from, const Quat& to, double t);
</pre>
<p>Quaternions can also be read from and written to C++ iostreams using the
standard <tt><<</tt> and <tt>>></tt> operators.
</body>
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