1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
<html>
<head>
<title>Castle Game Engine: CastleQuaternions: Object TQuaternion</title>
<meta name="generator" content="PasDoc 0.13.0">
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<link rel="StyleSheet" type="text/css" href="pasdoc.css">
</head>
<body>
<table class="container"><tr><td class="navigation">
<h2>Castle Game Engine</h2><p><a href="introduction.html" class="navigation">Introduction</a></p><p><a href="AllUnits.html" class="navigation">Units</a></p><p><a href="ClassHierarchy.html" class="navigation">Class Hierarchy</a></p><p><a href="AllClasses.html" class="navigation">Classes, Interfaces, Objects and Records</a></p><p><a href="AllTypes.html" class="navigation">Types</a></p><p><a href="AllVariables.html" class="navigation">Variables</a></p><p><a href="AllConstants.html" class="navigation">Constants</a></p><p><a href="AllFunctions.html" class="navigation">Functions and Procedures</a></p><p><a href="AllIdentifiers.html" class="navigation">Identifiers</a></p></td><td class="content">
<a name="TQuaternion"></a><h1 class="cio">Object TQuaternion</h1>
<table class="sections wide_list">
<tr>
<td><a class="section" href="#PasDoc-Description">Description</a></td><td><a class="section" href="#PasDoc-Hierarchy">Hierarchy</a></td><td><a class="section" href="#PasDoc-Fields">Fields</a></td><td><a class="section" href="#PasDoc-Methods">Methods</a></td><td>Properties</td></tr></table>
<a name="PasDoc-Description"></a><h2 class="unit">Unit</h2>
<p class="unitlink">
<a href="CastleQuaternions.html">CastleQuaternions</a></p>
<h2 class="declaration">Declaration</h2>
<p class="declaration">
<code>type TQuaternion = object(TObject)</code></p>
<h2 class="description">Description</h2>
<a name="PasDoc-Hierarchy"></a><h2 class="hierarchy">Hierarchy</h2>
<ul class="hierarchy"><li class="ancestor">TObject</li>
<li class="thisitem">TQuaternion</li></ul><h2 class="overview">Overview</h2>
<a name="PasDoc-Fields"></a><h3 class="summary">Fields</h3>
<table class="summary wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code><b><a href="CastleQuaternions.TQuaternion.html#Data">Data</a></b>: packed</code></td>
</tr>
</table>
<a name="PasDoc-Methods"></a><h3 class="summary">Methods</h3>
<table class="summary wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>procedure <b><a href="CastleQuaternions.TQuaternion.html#ToAxisAngle">ToAxisAngle</a></b>(out Axis: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; out AngleRad: Single);</code></td>
</tr>
<tr class="list2">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>function <b><a href="CastleQuaternions.TQuaternion.html#ToAxisAngle">ToAxisAngle</a></b>: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>;</code></td>
</tr>
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>function <b><a href="CastleQuaternions.TQuaternion.html#ToRotationMatrix">ToRotationMatrix</a></b>: <a href="CastleVectors.html#TMatrix4Single">TMatrix4Single</a>;</code></td>
</tr>
<tr class="list2">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>function <b><a href="CastleQuaternions.TQuaternion.html#Rotate">Rotate</a></b>(const Point: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>): <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; overload;</code></td>
</tr>
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>function <b><a href="CastleQuaternions.TQuaternion.html#Rotate">Rotate</a></b>(const Point: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>): <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; overload;</code></td>
</tr>
<tr class="list2">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>function <b><a href="CastleQuaternions.TQuaternion.html#Conjugate">Conjugate</a></b>: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
</tr>
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>procedure <b><a href="CastleQuaternions.TQuaternion.html#ConjugateMe">ConjugateMe</a></b>;</code></td>
</tr>
<tr class="list2">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>procedure <b><a href="CastleQuaternions.TQuaternion.html#Normalize">Normalize</a></b>;</code></td>
</tr>
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><code>procedure <b><a href="CastleQuaternions.TQuaternion.html#LazyNormalize">LazyNormalize</a></b>;</code></td>
</tr>
</table>
<h2 class="description">Description</h2>
<h3 class="detail">Fields</h3>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="Data"></a><code><b>Data</b>: packed</code></td>
</tr>
<tr><td colspan="2">
</td></tr>
</table>
<h3 class="detail">Methods</h3>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="ToAxisAngle"></a><code>procedure <b>ToAxisAngle</b>(out Axis: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; out AngleRad: Single);</code></td>
</tr>
<tr><td colspan="2">
<p>
Calculate axis (will be normalized) and angle (will be in radians) of rotation encoded in unit quaternion Q. This is the reverse of <a class="normal" href="CastleQuaternions.html#QuatFromAxisAngle">QuatFromAxisAngle</a>.</p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="ToAxisAngle"></a><code>function <b>ToAxisAngle</b>: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>;</code></td>
</tr>
<tr><td colspan="2">
<p>
Convert quaternion to a rotation axis and angle encoded in 4D vector. Axis is normalized if quaternion was also normalized (which is true if working with rotation quaternions). Angle is in radians.</p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="ToRotationMatrix"></a><code>function <b>ToRotationMatrix</b>: <a href="CastleVectors.html#TMatrix4Single">TMatrix4Single</a>;</code></td>
</tr>
<tr><td colspan="2">
<p>
Calculate matrix doing rotation described by unit quaternion.</p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="Rotate"></a><code>function <b>Rotate</b>(const Point: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>): <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; overload;</code></td>
</tr>
<tr><td colspan="2">
<p>
Rotate by unit quaternion.
<p>You can pass here <a class="normal" href="CastleVectors.html#TVector4Single">TVector4Single</a>, which is then understood to be a 3D position in homogeneous coordinates. </p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="Rotate"></a><code>function <b>Rotate</b>(const Point: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>): <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; overload;</code></td>
</tr>
<tr><td colspan="2">
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="Conjugate"></a><code>function <b>Conjugate</b>: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
</tr>
<tr><td colspan="2">
<p>
Quaternion conjugation. This is just a fancy name for negating Q.Vector. </p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="ConjugateMe"></a><code>procedure <b>ConjugateMe</b>;</code></td>
</tr>
<tr><td colspan="2">
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="Normalize"></a><code>procedure <b>Normalize</b>;</code></td>
</tr>
<tr><td colspan="2">
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="visibility"><a href="legend.html"><img src="public.gif" alt="Public" title="Public"></a></td>
<td class="itemcode"><a name="LazyNormalize"></a><code>procedure <b>LazyNormalize</b>;</code></td>
</tr>
<tr><td colspan="2">
<p>
Perform normalization, only if the quaternion is detected to be "significantly unnormalized". It checks if the quaternion needs normalization using fast <a class="normal" href="CastleVectors.html#VectorLenSqr">VectorLenSqr</a>, that is quaternion length is not needed for the check (sqrt not needed). Only if it's significantly different that 1.0, sqrt is done and quaternion is normalized.
<p>This may be useful if you fear of eventual errors because of floating-point error cumulations, e.g. when you repeatedly multiply one quaternion by another, and yet another, and yet another etc. Calling this will trigger normalization from time to time (although will tolerate very small, epsilon-like, differences that are normal). Thus it prevents the quaternion from getting "too unnormalized".
<p>Generally, this is not needed, as quaternions are nicely numerically stable (which means that quaternion "very slightly unnormalized" will only generate "very slightly wrong" results, so it's not that bad). And no, I didn't actually observe the need for this in my programs. But you can see it actually called when you use TMatrixExaminer and deliberately cause spinning by very very large value (e.g. run view3dscene and press and hold right key, this will cause model spinning very fast, which causes quat multiplication every frame). So possibly this would trigger incorrect quaternions at some point.
<p>Anyway, this remains mostly a paranoid correctness measure.</p>
</td></tr>
</table>
<!-- Piwik -->
<script type="text/javascript">
var _paq = _paq || [];
_paq.push(["trackPageView"]);
_paq.push(["enableLinkTracking"]);
(function() {
var u=(("https:" == document.location.protocol) ? "https" : "http") + "://michalis.ii.uni.wroc.pl/piwik-castle-engine/";
_paq.push(["setTrackerUrl", u+"piwik.php"]);
_paq.push(["setSiteId", "1"]);
var d=document, g=d.createElement("script"), s=d.getElementsByTagName("script")[0]; g.type="text/javascript";
g.defer=true; g.async=true; g.src=u+"piwik.js"; s.parentNode.insertBefore(g,s);
})();
</script>
<!-- End Piwik Code -->
<noscript>
<!-- Piwik Image Tracker -->
<img src="http://michalis.ii.uni.wroc.pl/piwik-castle-engine/piwik.php?idsite=1&rec=1" style="border:0" alt="" />
<!-- End Piwik -->
</noscript>
<hr noshade size="1"><span class="appinfo"><em>Generated by <a href="http://pasdoc.sourceforge.net/">PasDoc 0.13.0</a> on 2015-06-15 04:43:11</em>
</span>
</td></tr></table></body></html>
|
