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diff --git a/manuals/sly/Quaternions.html b/manuals/sly/Quaternions.html new file mode 100644 index 0000000..bde3992 --- /dev/null +++ b/manuals/sly/Quaternions.html @@ -0,0 +1,185 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<html> +<!-- Copyright (C) 2013, 2014 David Thompson davet@gnu.org + +Permission is granted to copy, distribute and/or modify this document +under the terms of the GNU Free Documentation License, Version 1.3 +or any later version published by the Free Software Foundation; +with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. +A copy of the license is included in the section entitled "GNU +Free Documentation License". + +A copy of the license is also available from the Free Software +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 6.0, http://www.gnu.org/software/texinfo/ --> +<head> +<title>Sly: Quaternions</title> + +<meta name="description" content="Sly: Quaternions"> +<meta name="keywords" content="Sly: Quaternions"> +<meta name="resource-type" content="document"> +<meta name="distribution" content="global"> +<meta name="Generator" content="makeinfo"> +<meta 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="Miscellaneous.html#Miscellaneous" rel="next" title="Miscellaneous"> +<link href="Tweening.html#Tweening" rel="prev" title="Tweening"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.indentedblock {margin-right: 0em} +blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smalllisp {margin-left: 3.2em} +kbd {font-style: oblique} +pre.display {font-family: inherit} +pre.format {font-family: inherit} +pre.menu-comment {font-family: serif} +pre.menu-preformatted {font-family: serif} +pre.smalldisplay {font-family: inherit; font-size: smaller} +pre.smallexample {font-size: smaller} +pre.smallformat {font-family: inherit; font-size: smaller} +pre.smalllisp {font-size: smaller} +span.nocodebreak {white-space: nowrap} +span.nolinebreak {white-space: nowrap} +span.roman {font-family: serif; font-weight: normal} +span.sansserif {font-family: sans-serif; font-weight: normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en"> +<a name="Quaternions"></a> +<div class="header"> +<p> +Next: <a href="Miscellaneous.html#Miscellaneous" accesskey="n" rel="next">Miscellaneous</a>, Previous: <a href="Tweens.html#Tweens" accesskey="p" rel="prev">Tweens</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="Quaternions-1"></a> +<h4 class="subsection">4.2.5 Quaternions</h4> + +<div class="example"> +<pre class="example">(use-modules (sly math quaternion)) +</pre></div> + +<p>Quaternions are used to express rotations about an arbitrary axis in a +way that avoids “gimbal lock” and allows for useful interpolation, +unlike matrices or Euler angles. +</p> +<p>Quaternions can be used in rotation transformations +(see <a href="Transforms.html#Transforms">Transforms</a>), as well as converted to and from <a href="Vectors.html#Vectors">Vectors</a>. +</p> +<dl> +<dt><a name="index-_003cquaternion_003e"></a>Record Type: <strong><quaternion></strong></dt> +<dd><p>Data type with 4 fields: <code>w</code>, <code>x</code>, <code>y</code>, <code>z</code>, in +that order. This type descriptor has been exposed for destructuring +via Guile’s <code>(ice-9 match)</code> module. +</p></dd></dl> + +<dl> +<dt><a name="index-make_002dquaternion"></a>Scheme Procedure: <strong>make-quaternion</strong> <em><var>v</var> <var>theta</var></em></dt> +<dt><a name="index-make_002dquaternion-1"></a>Scheme Procedure: <strong>make-quaternion</strong> <em><var>w</var> <var>x</var> <var>y</var> <var>z</var></em></dt> +<dd><p>Create a new quaternion from an axis angle (a 3D vector <var>v</var> plus +an angle <var>theta</var>) or from individual coordinates <var>w</var>, <var>x</var>, +<var>y</var>, and <var>z</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion"></a>Scheme Procedure: <strong>quaternion</strong> <em><var>v</var> <var>theta</var></em></dt> +<dt><a name="index-quaternion-1"></a>Scheme Procedure: <strong>quaternion</strong> <em><var>w</var> <var>x</var> <var>y</var> <var>z</var></em></dt> +<dd><p>Alternate spelling of <code>make-quaternion</code>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_003f"></a>Scheme Syntax: <strong>quaternion?</strong> <em><var>obj</var></em></dt> +<dd><p>Return <code>#t</code> if <var>obj</var> is a quaternion. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dw"></a>Scheme Syntax: <strong>quaternion-w</strong> <em><var>q</var></em></dt> +<dd><p>Return the w coordinate of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dx"></a>Scheme Syntax: <strong>quaternion-x</strong> <em><var>q</var></em></dt> +<dd><p>Return the x coordinate of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dy"></a>Scheme Syntax: <strong>quaternion-y</strong> <em><var>q</var></em></dt> +<dd><p>Return the y coordinate of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dz"></a>Scheme Syntax: <strong>quaternion-z</strong> <em><var>q</var></em></dt> +<dd><p>Return the z coordinate of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-identity_002dquaternion"></a>Scheme Variable: <strong>identity-quaternion</strong></dt> +<dd><p>The multiplicative identity quaternion. +</p></dd></dl> + +<dl> +<dt><a name="index-null_002dquaternion"></a>Scheme Variable: <strong>null-quaternion</strong></dt> +<dd><p>A quaternion with all fields set to zero. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002a"></a>Scheme Procedure: <strong>quaternion*</strong> <em>. <var>quaternions</var></em></dt> +<dd><p>Return the product of all <var>quaternions</var>. Return +<code>identity-quaternion</code> if called without arguments. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dslerp"></a>Scheme Procedure: <strong>quaternion-slerp</strong> <em><var>q1</var> <var>q2</var> <var>delta</var></em></dt> +<dd><p>Perform a spherical linear interpolation of the quaternions <var>q1</var> +and <var>q2</var> and blending factor <var>delta</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dmagnitude"></a>Scheme Procedure: <strong>quaternion-magnitude</strong> <em><var>q</var></em></dt> +<dd><p>Return the magnitude of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002dnormalize"></a>Scheme Procedure: <strong>quaternion-normalize</strong> <em><var>q</var></em></dt> +<dd><p>Return the normalized form of the quaternion <var>q</var>. +</p></dd></dl> + +<dl> +<dt><a name="index-vector_002d_003equaternion"></a>Scheme Procedure: <strong>vector->quaternion</strong> <em><var>v</var></em></dt> +<dd><p>Convert the 4D vector <var>v</var> to a quaternion. +</p></dd></dl> + +<dl> +<dt><a name="index-quaternion_002d_003evector"></a>Scheme Procedure: <strong>quaternion->vector</strong> <em><var>q</var></em></dt> +<dd><p>Convert the quaternion <var>q</var> to a 4D vector. +</p></dd></dl> + +<hr> +<div class="header"> +<p> +Next: <a href="Miscellaneous.html#Miscellaneous" accesskey="n" rel="next">Miscellaneous</a>, Previous: <a href="Tweens.html#Tweens" accesskey="p" rel="prev">Tweens</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> + + + +</body> +</html> |