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1 | <?xml version="1.0" encoding="UTF-8"?> |
2 | <!DOCTYPE book PUBLIC "-//OASIS//DTD DocBook MathML Module V1.1b1//EN" | |
3 | "http://www.oasis-open.org/docbook/xml/mathml/1.1CR1/dbmathml.dtd"> | |
4 | <refentry id="gluLookAt"> | |
5 | <refmeta> | |
6 | <refmetainfo> | |
7 | <copyright> | |
8 | <year>1991-2006</year> | |
9 | <holder>Silicon Graphics, Inc.</holder> | |
10 | </copyright> | |
11 | </refmetainfo> | |
12 | <refentrytitle>gluLookAt</refentrytitle> | |
13 | <manvolnum>3G</manvolnum> | |
14 | </refmeta> | |
15 | <refnamediv> | |
16 | <refname>gluLookAt</refname> | |
17 | <refpurpose>define a viewing transformation</refpurpose> | |
18 | </refnamediv> | |
19 | <refsynopsisdiv><title>C Specification</title> | |
20 | <funcsynopsis> | |
21 | <funcprototype> | |
22 | <funcdef>void <function>gluLookAt</function></funcdef> | |
23 | <paramdef>GLdouble <parameter>eyeX</parameter></paramdef> | |
24 | <paramdef>GLdouble <parameter>eyeY</parameter></paramdef> | |
25 | <paramdef>GLdouble <parameter>eyeZ</parameter></paramdef> | |
26 | <paramdef>GLdouble <parameter>centerX</parameter></paramdef> | |
27 | <paramdef>GLdouble <parameter>centerY</parameter></paramdef> | |
28 | <paramdef>GLdouble <parameter>centerZ</parameter></paramdef> | |
29 | <paramdef>GLdouble <parameter>upX</parameter></paramdef> | |
30 | <paramdef>GLdouble <parameter>upY</parameter></paramdef> | |
31 | <paramdef>GLdouble <parameter>upZ</parameter></paramdef> | |
32 | </funcprototype> | |
33 | </funcsynopsis> | |
34 | </refsynopsisdiv> | |
35 | <!-- eqn: ignoring delim $$ --> | |
36 | <refsect1 id="parameters"><title>Parameters</title> | |
37 | <variablelist> | |
38 | <varlistentry> | |
39 | <term><parameter>eyeX</parameter></term> | |
40 | <term><parameter>eyeY</parameter></term> | |
41 | <term><parameter>eyeZ</parameter></term> | |
42 | <listitem> | |
43 | <para> | |
44 | Specifies the position of the eye point. | |
45 | </para> | |
46 | </listitem> | |
47 | </varlistentry> | |
48 | <varlistentry> | |
49 | <term><parameter>centerX</parameter></term> | |
50 | <term><parameter>centerY</parameter></term> | |
51 | <term><parameter>centerZ</parameter></term> | |
52 | <listitem> | |
53 | <para> | |
54 | Specifies the position of the reference point. | |
55 | </para> | |
56 | </listitem> | |
57 | </varlistentry> | |
58 | <varlistentry> | |
59 | <term><parameter>upX</parameter></term> | |
60 | <term><parameter>upY</parameter></term> | |
61 | <term><parameter>upZ</parameter></term> | |
62 | <listitem> | |
63 | <para> | |
64 | Specifies the direction of the <emphasis>up</emphasis> vector. | |
65 | </para> | |
66 | </listitem> | |
67 | </varlistentry> | |
68 | </variablelist> | |
69 | </refsect1> | |
70 | <refsect1 id="description"><title>Description</title> | |
71 | <para> | |
72 | <function>gluLookAt</function> creates a viewing matrix derived from an eye point, a reference | |
73 | point indicating the center of the scene, and an <emphasis>UP</emphasis> vector. | |
74 | </para> | |
75 | <para> | |
76 | The matrix | |
77 | maps the reference point to the negative <emphasis>z</emphasis> axis and the | |
78 | eye point to the origin. | |
79 | When a typical projection matrix is used, | |
80 | the center of the scene therefore maps to the center of the viewport. | |
81 | Similarly, the direction described by the <emphasis>UP</emphasis> | |
82 | vector projected onto the viewing plane is mapped to the positive <emphasis>y</emphasis> | |
83 | axis so that it points upward in the viewport. | |
84 | The <emphasis>UP</emphasis> vector must not be parallel to the line of sight from the | |
85 | eye point to the reference point. | |
86 | </para> | |
87 | <para> | |
88 | Let | |
89 | </para> | |
90 | <para> | |
91 | <informalequation><mml:math> | |
92 | <!-- eqn: F = left ( matrix { ccol { centerX - eyeX above centerY - eyeY above centerZ - eyeZ } } right ):--> | |
93 | <mml:mrow> | |
94 | <mml:mi mathvariant="italic">F</mml:mi> | |
95 | <mml:mo>=</mml:mo> | |
96 | <mml:mfenced open="(" close=")"> | |
97 | <mml:mtable> | |
98 | <mml:mtr> | |
99 | <mml:mtd> | |
100 | <mml:mrow> | |
101 | <mml:mi mathvariant="italic">centerX</mml:mi> | |
102 | <mml:mo>-</mml:mo> | |
103 | <mml:mi mathvariant="italic">eyeX</mml:mi> | |
104 | </mml:mrow> | |
105 | </mml:mtd> | |
106 | </mml:mtr> | |
107 | <mml:mtr> | |
108 | <mml:mtd> | |
109 | <mml:mrow> | |
110 | <mml:mi mathvariant="italic">centerY</mml:mi> | |
111 | <mml:mo>-</mml:mo> | |
112 | <mml:mi mathvariant="italic">eyeY</mml:mi> | |
113 | </mml:mrow> | |
114 | </mml:mtd> | |
115 | </mml:mtr> | |
116 | <mml:mtr> | |
117 | <mml:mtd> | |
118 | <mml:mrow> | |
119 | <mml:mi mathvariant="italic">centerZ</mml:mi> | |
120 | <mml:mo>-</mml:mo> | |
121 | <mml:mi mathvariant="italic">eyeZ</mml:mi> | |
122 | </mml:mrow> | |
123 | </mml:mtd> | |
124 | </mml:mtr> | |
125 | </mml:mtable> | |
126 | </mml:mfenced> | |
127 | </mml:mrow> | |
128 | </mml:math></informalequation> | |
129 | </para> | |
130 | <para> | |
131 | </para> | |
132 | <para> | |
133 | Let <emphasis>UP</emphasis> be the vector | |
134 | <inlineequation><mml:math> | |
135 | <!-- eqn: (upX, upY, upZ):--> | |
136 | <mml:mfenced open="(" close=")"> | |
137 | <mml:mi mathvariant="italic">upX</mml:mi> | |
138 | <mml:mi mathvariant="italic">upY</mml:mi> | |
139 | <mml:mi mathvariant="italic">upZ</mml:mi> | |
140 | </mml:mfenced> | |
141 | </mml:math></inlineequation>. | |
142 | </para> | |
143 | <para> | |
144 | Then normalize as follows: | |
145 | <informalequation><mml:math> | |
146 | <!-- eqn: f = F over {|| F ||}:--> | |
147 | <mml:mrow> | |
148 | <mml:mi mathvariant="italic">f</mml:mi> | |
149 | <mml:mo>=</mml:mo> | |
150 | <mml:mfrac> | |
151 | <mml:mi mathvariant="italic">F</mml:mi> | |
152 | <mml:mfenced open="" close=""> | |
153 | <mml:mfenced open="∥" close="∥"> | |
154 | <mml:mi mathvariant="italic">F</mml:mi> | |
155 | </mml:mfenced> | |
156 | </mml:mfenced> | |
157 | </mml:mfrac> | |
158 | </mml:mrow> | |
159 | </mml:math></informalequation> | |
160 | </para> | |
161 | <para> | |
162 | <informalequation><mml:math> | |
163 | <!-- eqn: UP sup prime = UP over {|| UP ||}:--> | |
164 | <mml:mrow> | |
165 | <mml:msup><mml:mi mathvariant="italic">UP</mml:mi> | |
166 | <mml:mo>″</mml:mo> | |
167 | </mml:msup> | |
168 | <mml:mo>=</mml:mo> | |
169 | <mml:mfrac> | |
170 | <mml:mi mathvariant="italic">UP</mml:mi> | |
171 | <mml:mfenced open="" close=""> | |
172 | <mml:mfenced open="∥" close="∥"> | |
173 | <mml:mi mathvariant="italic">UP</mml:mi> | |
174 | </mml:mfenced> | |
175 | </mml:mfenced> | |
176 | </mml:mfrac> | |
177 | </mml:mrow> | |
178 | </mml:math></informalequation> | |
179 | </para> | |
180 | <para> | |
181 | </para> | |
182 | <para> | |
183 | Finally, let | |
184 | <inlineequation><mml:math> | |
185 | <!-- eqn: s = f times UP sup prime:--> | |
186 | <mml:mrow> | |
187 | <mml:mi mathvariant="italic">s</mml:mi> | |
188 | <mml:mo>=</mml:mo> | |
189 | <mml:mrow> | |
190 | <mml:mi mathvariant="italic">f</mml:mi> | |
191 | <mml:mo>×</mml:mo> | |
192 | <mml:msup><mml:mi mathvariant="italic">UP</mml:mi> | |
193 | <mml:mo>″</mml:mo> | |
194 | </mml:msup> | |
195 | </mml:mrow> | |
196 | </mml:mrow> | |
197 | </mml:math></inlineequation>, | |
198 | and | |
199 | <inlineequation><mml:math> | |
200 | <!-- eqn: u = s times f:--> | |
201 | <mml:mrow> | |
202 | <mml:mi mathvariant="italic">u</mml:mi> | |
203 | <mml:mo>=</mml:mo> | |
204 | <mml:mrow> | |
205 | <mml:mi mathvariant="italic">s</mml:mi> | |
206 | <mml:mo>×</mml:mo> | |
207 | <mml:mi mathvariant="italic">f</mml:mi> | |
208 | </mml:mrow> | |
209 | </mml:mrow> | |
210 | </mml:math></inlineequation>. | |
211 | </para> | |
212 | <para> | |
213 | </para> | |
214 | <para> | |
215 | M is then constructed as follows: | |
216 | <informalequation><mml:math> | |
217 | <!-- eqn: M = left ( matrix { ccol { s[0] above u[0] above -f[0] above 0 } ccol { s[1] above u[1] above -f[1] above 0 } ccol { s[2] above u[2] above -f[2] above 0 } ccol { 0 above 0 above 0 above 1 } } right ):--> | |
218 | <mml:mrow> | |
219 | <mml:mi mathvariant="italic">M</mml:mi> | |
220 | <mml:mo>=</mml:mo> | |
221 | <mml:mfenced open="(" close=")"> | |
222 | <mml:mtable> | |
223 | <mml:mtr> | |
224 | <mml:mtd> | |
225 | <mml:mrow> | |
226 | <mml:mi mathvariant="italic">s</mml:mi> | |
227 | <mml:mo>⁡</mml:mo> | |
228 | <mml:mfenced open="[" close="]"> | |
229 | <mml:mn>0</mml:mn> | |
230 | </mml:mfenced> | |
231 | </mml:mrow> | |
232 | </mml:mtd> | |
233 | <mml:mtd> | |
234 | <mml:mrow> | |
235 | <mml:mi mathvariant="italic">s</mml:mi> | |
236 | <mml:mo>⁡</mml:mo> | |
237 | <mml:mfenced open="[" close="]"> | |
238 | <mml:mn>1</mml:mn> | |
239 | </mml:mfenced> | |
240 | </mml:mrow> | |
241 | </mml:mtd> | |
242 | <mml:mtd> | |
243 | <mml:mrow> | |
244 | <mml:mi mathvariant="italic">s</mml:mi> | |
245 | <mml:mo>⁡</mml:mo> | |
246 | <mml:mfenced open="[" close="]"> | |
247 | <mml:mn>2</mml:mn> | |
248 | </mml:mfenced> | |
249 | </mml:mrow> | |
250 | </mml:mtd> | |
251 | <mml:mtd> | |
252 | <mml:mn>0</mml:mn> | |
253 | </mml:mtd> | |
254 | </mml:mtr> | |
255 | <mml:mtr> | |
256 | <mml:mtd> | |
257 | <mml:mrow> | |
258 | <mml:mi mathvariant="italic">u</mml:mi> | |
259 | <mml:mo>⁡</mml:mo> | |
260 | <mml:mfenced open="[" close="]"> | |
261 | <mml:mn>0</mml:mn> | |
262 | </mml:mfenced> | |
263 | </mml:mrow> | |
264 | </mml:mtd> | |
265 | <mml:mtd> | |
266 | <mml:mrow> | |
267 | <mml:mi mathvariant="italic">u</mml:mi> | |
268 | <mml:mo>⁡</mml:mo> | |
269 | <mml:mfenced open="[" close="]"> | |
270 | <mml:mn>1</mml:mn> | |
271 | </mml:mfenced> | |
272 | </mml:mrow> | |
273 | </mml:mtd> | |
274 | <mml:mtd> | |
275 | <mml:mrow> | |
276 | <mml:mi mathvariant="italic">u</mml:mi> | |
277 | <mml:mo>⁡</mml:mo> | |
278 | <mml:mfenced open="[" close="]"> | |
279 | <mml:mn>2</mml:mn> | |
280 | </mml:mfenced> | |
281 | </mml:mrow> | |
282 | </mml:mtd> | |
283 | <mml:mtd> | |
284 | <mml:mn>0</mml:mn> | |
285 | </mml:mtd> | |
286 | </mml:mtr> | |
287 | <mml:mtr> | |
288 | <mml:mtd> | |
289 | <mml:mrow> | |
290 | <mml:mo>-</mml:mo> | |
291 | <mml:mrow> | |
292 | <mml:mi mathvariant="italic">f</mml:mi> | |
293 | <mml:mo>⁡</mml:mo> | |
294 | <mml:mfenced open="[" close="]"> | |
295 | <mml:mn>0</mml:mn> | |
296 | </mml:mfenced> | |
297 | </mml:mrow> | |
298 | </mml:mrow> | |
299 | </mml:mtd> | |
300 | <mml:mtd> | |
301 | <mml:mrow> | |
302 | <mml:mo>-</mml:mo> | |
303 | <mml:mrow> | |
304 | <mml:mi mathvariant="italic">f</mml:mi> | |
305 | <mml:mo>⁡</mml:mo> | |
306 | <mml:mfenced open="[" close="]"> | |
307 | <mml:mn>1</mml:mn> | |
308 | </mml:mfenced> | |
309 | </mml:mrow> | |
310 | </mml:mrow> | |
311 | </mml:mtd> | |
312 | <mml:mtd> | |
313 | <mml:mrow> | |
314 | <mml:mo>-</mml:mo> | |
315 | <mml:mrow> | |
316 | <mml:mi mathvariant="italic">f</mml:mi> | |
317 | <mml:mo>⁡</mml:mo> | |
318 | <mml:mfenced open="[" close="]"> | |
319 | <mml:mn>2</mml:mn> | |
320 | </mml:mfenced> | |
321 | </mml:mrow> | |
322 | </mml:mrow> | |
323 | </mml:mtd> | |
324 | <mml:mtd> | |
325 | <mml:mn>0</mml:mn> | |
326 | </mml:mtd> | |
327 | </mml:mtr> | |
328 | <mml:mtr> | |
329 | <mml:mtd> | |
330 | <mml:mn>0</mml:mn> | |
331 | </mml:mtd> | |
332 | <mml:mtd> | |
333 | <mml:mn>0</mml:mn> | |
334 | </mml:mtd> | |
335 | <mml:mtd> | |
336 | <mml:mn>0</mml:mn> | |
337 | </mml:mtd> | |
338 | <mml:mtd> | |
339 | <mml:mn>1</mml:mn> | |
340 | </mml:mtd> | |
341 | </mml:mtr> | |
342 | </mml:mtable> | |
343 | </mml:mfenced> | |
344 | </mml:mrow> | |
345 | </mml:math></informalequation> | |
346 | </para> | |
347 | <para> | |
348 | and <function>gluLookAt</function> is equivalent to | |
349 | <programlisting> | |
350 | glMultMatrixf(M); | |
351 | glTranslated(-eyex, -eyey, -eyez); | |
352 | </programlisting> | |
353 | </para> | |
354 | </refsect1> | |
355 | <refsect1 id="seealso"><title>See Also</title> | |
356 | <para> | |
357 | <citerefentry><refentrytitle>gluPerspective</refentrytitle></citerefentry>, | |
358 | <citerefentry><refentrytitle>glFrustum</refentrytitle></citerefentry> | |
359 | </para> | |
360 | </refsect1> | |
361 | <refsect1 id="Copyright"><title>Copyright</title> | |
362 | <para> | |
363 | Copyright <trademark class="copyright"></trademark> 1991-2006 | |
364 | Silicon Graphics, Inc. This document is licensed under the SGI | |
365 | Free Software B License. For details, see | |
366 | <ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>. | |
367 | </para> | |
368 | </refsect1> | |
369 | </refentry> |