Commit | Line | Data |
---|---|---|
7faf1d71 AW |
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="glMultTransposeMatrix"> | |
5 | <refmeta> | |
6 | <refmetainfo> | |
7 | <copyright> | |
8 | <year>1991-2006</year> | |
9 | <holder>Silicon Graphics, Inc.</holder> | |
10 | </copyright> | |
11 | </refmetainfo> | |
12 | <refentrytitle>glMultTransposeMatrix</refentrytitle> | |
13 | <manvolnum>3G</manvolnum> | |
14 | </refmeta> | |
15 | <refnamediv> | |
16 | <refname>glMultTransposeMatrix</refname> | |
17 | <refpurpose>multiply the current matrix with the specified row-major ordered matrix</refpurpose> | |
18 | </refnamediv> | |
19 | <refsynopsisdiv><title>C Specification</title> | |
20 | <funcsynopsis> | |
21 | <funcprototype> | |
22 | <funcdef>void <function>glMultTransposeMatrixd</function></funcdef> | |
23 | <paramdef>const GLdouble * <parameter>m</parameter></paramdef> | |
24 | </funcprototype> | |
25 | </funcsynopsis> | |
26 | <funcsynopsis> | |
27 | <funcprototype> | |
28 | <funcdef>void <function>glMultTransposeMatrixf</function></funcdef> | |
29 | <paramdef>const GLfloat * <parameter>m</parameter></paramdef> | |
30 | </funcprototype> | |
31 | </funcsynopsis> | |
32 | </refsynopsisdiv> | |
33 | <!-- eqn: ignoring delim $$ --> | |
34 | <refsect1 id="parameters"><title>Parameters</title> | |
35 | <variablelist> | |
36 | <varlistentry> | |
37 | <term><parameter>m</parameter></term> | |
38 | <listitem> | |
39 | <para> | |
40 | Points to 16 consecutive values that are used as the elements of | |
41 | a | |
42 | <inlineequation><mml:math> | |
43 | <!-- eqn: 4 times 4:--> | |
44 | <mml:mrow> | |
45 | <mml:mn>4</mml:mn> | |
46 | <mml:mo>×</mml:mo> | |
47 | <mml:mn>4</mml:mn> | |
48 | </mml:mrow> | |
49 | </mml:math></inlineequation> | |
50 | row-major matrix. | |
51 | </para> | |
52 | </listitem> | |
53 | </varlistentry> | |
54 | </variablelist> | |
55 | </refsect1> | |
56 | <refsect1 id="description"><title>Description</title> | |
57 | <para> | |
58 | <function>glMultTransposeMatrix</function> multiplies the current matrix with the one specified using <parameter>m</parameter>, and | |
59 | replaces the current matrix with the product. | |
60 | </para> | |
61 | <para> | |
62 | The current matrix is determined by the current matrix mode (see | |
63 | <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>). It is either the projection matrix, modelview matrix, | |
64 | or the texture matrix. | |
65 | </para> | |
66 | </refsect1> | |
67 | <refsect1 id="examples"><title>Examples</title> | |
68 | <para> | |
69 | If the current matrix is | |
70 | <inlineequation><mml:math><mml:mi mathvariant="italic">C</mml:mi></mml:math></inlineequation> | |
71 | and the coordinates | |
72 | to be transformed are | |
73 | <inlineequation><mml:math> | |
74 | <!-- eqn: v = (v[0], v[1], v[2], v[3]):--> | |
75 | <mml:mrow> | |
76 | <mml:mi mathvariant="italic">v</mml:mi> | |
77 | <mml:mo>=</mml:mo> | |
78 | <mml:mfenced open="(" close=")"> | |
79 | <mml:mrow> | |
80 | <mml:mi mathvariant="italic">v</mml:mi> | |
81 | <mml:mo>⁡</mml:mo> | |
82 | <mml:mfenced open="[" close="]"> | |
83 | <mml:mn>0</mml:mn> | |
84 | </mml:mfenced> | |
85 | </mml:mrow> | |
86 | <mml:mrow> | |
87 | <mml:mi mathvariant="italic">v</mml:mi> | |
88 | <mml:mo>⁡</mml:mo> | |
89 | <mml:mfenced open="[" close="]"> | |
90 | <mml:mn>1</mml:mn> | |
91 | </mml:mfenced> | |
92 | </mml:mrow> | |
93 | <mml:mrow> | |
94 | <mml:mi mathvariant="italic">v</mml:mi> | |
95 | <mml:mo>⁡</mml:mo> | |
96 | <mml:mfenced open="[" close="]"> | |
97 | <mml:mn>2</mml:mn> | |
98 | </mml:mfenced> | |
99 | </mml:mrow> | |
100 | <mml:mrow> | |
101 | <mml:mi mathvariant="italic">v</mml:mi> | |
102 | <mml:mo>⁡</mml:mo> | |
103 | <mml:mfenced open="[" close="]"> | |
104 | <mml:mn>3</mml:mn> | |
105 | </mml:mfenced> | |
106 | </mml:mrow> | |
107 | </mml:mfenced> | |
108 | </mml:mrow> | |
109 | </mml:math></inlineequation>, | |
110 | then the current transformation is | |
111 | <inlineequation><mml:math> | |
112 | <!-- eqn: C times v:--> | |
113 | <mml:mrow> | |
114 | <mml:mi mathvariant="italic">C</mml:mi> | |
115 | <mml:mo>×</mml:mo> | |
116 | <mml:mi mathvariant="italic">v</mml:mi> | |
117 | </mml:mrow> | |
118 | </mml:math></inlineequation>, | |
119 | or | |
120 | </para> | |
121 | <para> | |
122 | <informalequation><mml:math> | |
123 | <!-- eqn: left ( matrix { ccol { c[0] above c[1] above c[2] above c[3] } ccol { c[4] above c[5] above c[6] above c[7] } ccol { c[8] above c[9] above c[10] above c[11] } ccol { c[12] above c[13] above c[14] above c[15] } } right ) times left ( matrix { ccol { v[0] above v[1] above v[2] above v[3] } } right ):--> | |
124 | <mml:mrow> | |
125 | <mml:mfenced open="(" close=")"> | |
126 | <mml:mtable> | |
127 | <mml:mtr> | |
128 | <mml:mtd> | |
129 | <mml:mrow> | |
130 | <mml:mi mathvariant="italic">c</mml:mi> | |
131 | <mml:mo>⁡</mml:mo> | |
132 | <mml:mfenced open="[" close="]"> | |
133 | <mml:mn>0</mml:mn> | |
134 | </mml:mfenced> | |
135 | </mml:mrow> | |
136 | </mml:mtd> | |
137 | <mml:mtd> | |
138 | <mml:mrow> | |
139 | <mml:mi mathvariant="italic">c</mml:mi> | |
140 | <mml:mo>⁡</mml:mo> | |
141 | <mml:mfenced open="[" close="]"> | |
142 | <mml:mn>4</mml:mn> | |
143 | </mml:mfenced> | |
144 | </mml:mrow> | |
145 | </mml:mtd> | |
146 | <mml:mtd> | |
147 | <mml:mrow> | |
148 | <mml:mi mathvariant="italic">c</mml:mi> | |
149 | <mml:mo>⁡</mml:mo> | |
150 | <mml:mfenced open="[" close="]"> | |
151 | <mml:mn>8</mml:mn> | |
152 | </mml:mfenced> | |
153 | </mml:mrow> | |
154 | </mml:mtd> | |
155 | <mml:mtd> | |
156 | <mml:mrow> | |
157 | <mml:mi mathvariant="italic">c</mml:mi> | |
158 | <mml:mo>⁡</mml:mo> | |
159 | <mml:mfenced open="[" close="]"> | |
160 | <mml:mn>12</mml:mn> | |
161 | </mml:mfenced> | |
162 | </mml:mrow> | |
163 | </mml:mtd> | |
164 | </mml:mtr> | |
165 | <mml:mtr> | |
166 | <mml:mtd> | |
167 | <mml:mrow> | |
168 | <mml:mi mathvariant="italic">c</mml:mi> | |
169 | <mml:mo>⁡</mml:mo> | |
170 | <mml:mfenced open="[" close="]"> | |
171 | <mml:mn>1</mml:mn> | |
172 | </mml:mfenced> | |
173 | </mml:mrow> | |
174 | </mml:mtd> | |
175 | <mml:mtd> | |
176 | <mml:mrow> | |
177 | <mml:mi mathvariant="italic">c</mml:mi> | |
178 | <mml:mo>⁡</mml:mo> | |
179 | <mml:mfenced open="[" close="]"> | |
180 | <mml:mn>5</mml:mn> | |
181 | </mml:mfenced> | |
182 | </mml:mrow> | |
183 | </mml:mtd> | |
184 | <mml:mtd> | |
185 | <mml:mrow> | |
186 | <mml:mi mathvariant="italic">c</mml:mi> | |
187 | <mml:mo>⁡</mml:mo> | |
188 | <mml:mfenced open="[" close="]"> | |
189 | <mml:mn>9</mml:mn> | |
190 | </mml:mfenced> | |
191 | </mml:mrow> | |
192 | </mml:mtd> | |
193 | <mml:mtd> | |
194 | <mml:mrow> | |
195 | <mml:mi mathvariant="italic">c</mml:mi> | |
196 | <mml:mo>⁡</mml:mo> | |
197 | <mml:mfenced open="[" close="]"> | |
198 | <mml:mn>13</mml:mn> | |
199 | </mml:mfenced> | |
200 | </mml:mrow> | |
201 | </mml:mtd> | |
202 | </mml:mtr> | |
203 | <mml:mtr> | |
204 | <mml:mtd> | |
205 | <mml:mrow> | |
206 | <mml:mi mathvariant="italic">c</mml:mi> | |
207 | <mml:mo>⁡</mml:mo> | |
208 | <mml:mfenced open="[" close="]"> | |
209 | <mml:mn>2</mml:mn> | |
210 | </mml:mfenced> | |
211 | </mml:mrow> | |
212 | </mml:mtd> | |
213 | <mml:mtd> | |
214 | <mml:mrow> | |
215 | <mml:mi mathvariant="italic">c</mml:mi> | |
216 | <mml:mo>⁡</mml:mo> | |
217 | <mml:mfenced open="[" close="]"> | |
218 | <mml:mn>6</mml:mn> | |
219 | </mml:mfenced> | |
220 | </mml:mrow> | |
221 | </mml:mtd> | |
222 | <mml:mtd> | |
223 | <mml:mrow> | |
224 | <mml:mi mathvariant="italic">c</mml:mi> | |
225 | <mml:mo>⁡</mml:mo> | |
226 | <mml:mfenced open="[" close="]"> | |
227 | <mml:mn>10</mml:mn> | |
228 | </mml:mfenced> | |
229 | </mml:mrow> | |
230 | </mml:mtd> | |
231 | <mml:mtd> | |
232 | <mml:mrow> | |
233 | <mml:mi mathvariant="italic">c</mml:mi> | |
234 | <mml:mo>⁡</mml:mo> | |
235 | <mml:mfenced open="[" close="]"> | |
236 | <mml:mn>14</mml:mn> | |
237 | </mml:mfenced> | |
238 | </mml:mrow> | |
239 | </mml:mtd> | |
240 | </mml:mtr> | |
241 | <mml:mtr> | |
242 | <mml:mtd> | |
243 | <mml:mrow> | |
244 | <mml:mi mathvariant="italic">c</mml:mi> | |
245 | <mml:mo>⁡</mml:mo> | |
246 | <mml:mfenced open="[" close="]"> | |
247 | <mml:mn>3</mml:mn> | |
248 | </mml:mfenced> | |
249 | </mml:mrow> | |
250 | </mml:mtd> | |
251 | <mml:mtd> | |
252 | <mml:mrow> | |
253 | <mml:mi mathvariant="italic">c</mml:mi> | |
254 | <mml:mo>⁡</mml:mo> | |
255 | <mml:mfenced open="[" close="]"> | |
256 | <mml:mn>7</mml:mn> | |
257 | </mml:mfenced> | |
258 | </mml:mrow> | |
259 | </mml:mtd> | |
260 | <mml:mtd> | |
261 | <mml:mrow> | |
262 | <mml:mi mathvariant="italic">c</mml:mi> | |
263 | <mml:mo>⁡</mml:mo> | |
264 | <mml:mfenced open="[" close="]"> | |
265 | <mml:mn>11</mml:mn> | |
266 | </mml:mfenced> | |
267 | </mml:mrow> | |
268 | </mml:mtd> | |
269 | <mml:mtd> | |
270 | <mml:mrow> | |
271 | <mml:mi mathvariant="italic">c</mml:mi> | |
272 | <mml:mo>⁡</mml:mo> | |
273 | <mml:mfenced open="[" close="]"> | |
274 | <mml:mn>15</mml:mn> | |
275 | </mml:mfenced> | |
276 | </mml:mrow> | |
277 | </mml:mtd> | |
278 | </mml:mtr> | |
279 | </mml:mtable> | |
280 | </mml:mfenced> | |
281 | <mml:mo>×</mml:mo> | |
282 | <mml:mfenced open="(" close=")"> | |
283 | <mml:mtable> | |
284 | <mml:mtr> | |
285 | <mml:mtd> | |
286 | <mml:mrow> | |
287 | <mml:mi mathvariant="italic">v</mml:mi> | |
288 | <mml:mo>⁡</mml:mo> | |
289 | <mml:mfenced open="[" close="]"> | |
290 | <mml:mn>0</mml:mn> | |
291 | </mml:mfenced> | |
292 | </mml:mrow> | |
293 | </mml:mtd> | |
294 | </mml:mtr> | |
295 | <mml:mtr> | |
296 | <mml:mtd> | |
297 | <mml:mrow> | |
298 | <mml:mi mathvariant="italic">v</mml:mi> | |
299 | <mml:mo>⁡</mml:mo> | |
300 | <mml:mfenced open="[" close="]"> | |
301 | <mml:mn>1</mml:mn> | |
302 | </mml:mfenced> | |
303 | </mml:mrow> | |
304 | </mml:mtd> | |
305 | </mml:mtr> | |
306 | <mml:mtr> | |
307 | <mml:mtd> | |
308 | <mml:mrow> | |
309 | <mml:mi mathvariant="italic">v</mml:mi> | |
310 | <mml:mo>⁡</mml:mo> | |
311 | <mml:mfenced open="[" close="]"> | |
312 | <mml:mn>2</mml:mn> | |
313 | </mml:mfenced> | |
314 | </mml:mrow> | |
315 | </mml:mtd> | |
316 | </mml:mtr> | |
317 | <mml:mtr> | |
318 | <mml:mtd> | |
319 | <mml:mrow> | |
320 | <mml:mi mathvariant="italic">v</mml:mi> | |
321 | <mml:mo>⁡</mml:mo> | |
322 | <mml:mfenced open="[" close="]"> | |
323 | <mml:mn>3</mml:mn> | |
324 | </mml:mfenced> | |
325 | </mml:mrow> | |
326 | </mml:mtd> | |
327 | </mml:mtr> | |
328 | </mml:mtable> | |
329 | </mml:mfenced> | |
330 | </mml:mrow> | |
331 | </mml:math></informalequation> | |
332 | </para> | |
333 | <para> | |
334 | </para> | |
335 | <para> | |
336 | Calling <function>glMultTransposeMatrix</function> with an argument of | |
337 | <inlineequation><mml:math> | |
338 | <!-- eqn: m = left { m[0], m[1], ..., m[15] right }:--> | |
339 | <mml:mrow> | |
340 | <mml:mrow> | |
341 | <mml:mi mathvariant="italic">m</mml:mi> | |
342 | <mml:mo>⁡</mml:mo> | |
343 | <mml:mfenced open="[" close="]"> | |
344 | <mml:mn>16</mml:mn> | |
345 | </mml:mfenced> | |
346 | </mml:mrow> | |
347 | <mml:mo>=</mml:mo> | |
348 | <mml:mfenced open="{" close="}"> | |
349 | <mml:mrow> | |
350 | <mml:mi mathvariant="italic">m</mml:mi> | |
351 | <mml:mo>⁡</mml:mo> | |
352 | <mml:mfenced open="[" close="]"> | |
353 | <mml:mn>0</mml:mn> | |
354 | </mml:mfenced> | |
355 | </mml:mrow> | |
356 | <mml:mrow> | |
357 | <mml:mi mathvariant="italic">m</mml:mi> | |
358 | <mml:mo>⁡</mml:mo> | |
359 | <mml:mfenced open="[" close="]"> | |
360 | <mml:mn>1</mml:mn> | |
361 | </mml:mfenced> | |
362 | </mml:mrow> | |
363 | <mml:mi mathvariant="italic">...</mml:mi> | |
364 | <mml:mrow> | |
365 | <mml:mi mathvariant="italic">m</mml:mi> | |
366 | <mml:mo>⁡</mml:mo> | |
367 | <mml:mfenced open="[" close="]"> | |
368 | <mml:mn>15</mml:mn> | |
369 | </mml:mfenced> | |
370 | </mml:mrow> | |
371 | </mml:mfenced> | |
372 | </mml:mrow> | |
373 | </mml:math></inlineequation> | |
374 | replaces the current transformation with | |
375 | <inlineequation><mml:math> | |
376 | <!-- eqn: (C times M) times v:--> | |
377 | <mml:mrow> | |
378 | <mml:mfenced open="(" close=")"> | |
379 | <mml:mrow> | |
380 | <mml:mi mathvariant="italic">C</mml:mi> | |
381 | <mml:mo>×</mml:mo> | |
382 | <mml:mi mathvariant="italic">M</mml:mi> | |
383 | </mml:mrow> | |
384 | </mml:mfenced> | |
385 | <mml:mo>×</mml:mo> | |
386 | <mml:mi mathvariant="italic">v</mml:mi> | |
387 | </mml:mrow> | |
388 | </mml:math></inlineequation>, | |
389 | or | |
390 | </para> | |
391 | <para> | |
392 | <informalequation><mml:math> | |
393 | <!-- eqn: left ( matrix { ccol { c[0] above c[1] above c[2] above c[3] } ccol { c[4] above c[5] above c[6] above c[7] } ccol { c[8] above c[9] above c[10] above c[11] } ccol { c[12] above c[13] above c[14] above c[15] } } right ) times left ( matrix { ccol { m[0] above m[4] above m[8] above m[12] } ccol { m[1] above m[5] above m[9] above m[13] } ccol { m[2] above m[6] above m[10] above m[14] } ccol { m[3] above m[7] above m[11] above m[15] } } right ) times left ( matrix { ccol { v[0] above v[1] above v[2] above v[3] } } right ):--> | |
394 | <mml:mrow> | |
395 | <mml:mfenced open="(" close=")"> | |
396 | <mml:mtable> | |
397 | <mml:mtr> | |
398 | <mml:mtd> | |
399 | <mml:mrow> | |
400 | <mml:mi mathvariant="italic">c</mml:mi> | |
401 | <mml:mo>⁡</mml:mo> | |
402 | <mml:mfenced open="[" close="]"> | |
403 | <mml:mn>0</mml:mn> | |
404 | </mml:mfenced> | |
405 | </mml:mrow> | |
406 | </mml:mtd> | |
407 | <mml:mtd> | |
408 | <mml:mrow> | |
409 | <mml:mi mathvariant="italic">c</mml:mi> | |
410 | <mml:mo>⁡</mml:mo> | |
411 | <mml:mfenced open="[" close="]"> | |
412 | <mml:mn>4</mml:mn> | |
413 | </mml:mfenced> | |
414 | </mml:mrow> | |
415 | </mml:mtd> | |
416 | <mml:mtd> | |
417 | <mml:mrow> | |
418 | <mml:mi mathvariant="italic">c</mml:mi> | |
419 | <mml:mo>⁡</mml:mo> | |
420 | <mml:mfenced open="[" close="]"> | |
421 | <mml:mn>8</mml:mn> | |
422 | </mml:mfenced> | |
423 | </mml:mrow> | |
424 | </mml:mtd> | |
425 | <mml:mtd> | |
426 | <mml:mrow> | |
427 | <mml:mi mathvariant="italic">c</mml:mi> | |
428 | <mml:mo>⁡</mml:mo> | |
429 | <mml:mfenced open="[" close="]"> | |
430 | <mml:mn>12</mml:mn> | |
431 | </mml:mfenced> | |
432 | </mml:mrow> | |
433 | </mml:mtd> | |
434 | </mml:mtr> | |
435 | <mml:mtr> | |
436 | <mml:mtd> | |
437 | <mml:mrow> | |
438 | <mml:mi mathvariant="italic">c</mml:mi> | |
439 | <mml:mo>⁡</mml:mo> | |
440 | <mml:mfenced open="[" close="]"> | |
441 | <mml:mn>1</mml:mn> | |
442 | </mml:mfenced> | |
443 | </mml:mrow> | |
444 | </mml:mtd> | |
445 | <mml:mtd> | |
446 | <mml:mrow> | |
447 | <mml:mi mathvariant="italic">c</mml:mi> | |
448 | <mml:mo>⁡</mml:mo> | |
449 | <mml:mfenced open="[" close="]"> | |
450 | <mml:mn>5</mml:mn> | |
451 | </mml:mfenced> | |
452 | </mml:mrow> | |
453 | </mml:mtd> | |
454 | <mml:mtd> | |
455 | <mml:mrow> | |
456 | <mml:mi mathvariant="italic">c</mml:mi> | |
457 | <mml:mo>⁡</mml:mo> | |
458 | <mml:mfenced open="[" close="]"> | |
459 | <mml:mn>9</mml:mn> | |
460 | </mml:mfenced> | |
461 | </mml:mrow> | |
462 | </mml:mtd> | |
463 | <mml:mtd> | |
464 | <mml:mrow> | |
465 | <mml:mi mathvariant="italic">c</mml:mi> | |
466 | <mml:mo>⁡</mml:mo> | |
467 | <mml:mfenced open="[" close="]"> | |
468 | <mml:mn>13</mml:mn> | |
469 | </mml:mfenced> | |
470 | </mml:mrow> | |
471 | </mml:mtd> | |
472 | </mml:mtr> | |
473 | <mml:mtr> | |
474 | <mml:mtd> | |
475 | <mml:mrow> | |
476 | <mml:mi mathvariant="italic">c</mml:mi> | |
477 | <mml:mo>⁡</mml:mo> | |
478 | <mml:mfenced open="[" close="]"> | |
479 | <mml:mn>2</mml:mn> | |
480 | </mml:mfenced> | |
481 | </mml:mrow> | |
482 | </mml:mtd> | |
483 | <mml:mtd> | |
484 | <mml:mrow> | |
485 | <mml:mi mathvariant="italic">c</mml:mi> | |
486 | <mml:mo>⁡</mml:mo> | |
487 | <mml:mfenced open="[" close="]"> | |
488 | <mml:mn>6</mml:mn> | |
489 | </mml:mfenced> | |
490 | </mml:mrow> | |
491 | </mml:mtd> | |
492 | <mml:mtd> | |
493 | <mml:mrow> | |
494 | <mml:mi mathvariant="italic">c</mml:mi> | |
495 | <mml:mo>⁡</mml:mo> | |
496 | <mml:mfenced open="[" close="]"> | |
497 | <mml:mn>10</mml:mn> | |
498 | </mml:mfenced> | |
499 | </mml:mrow> | |
500 | </mml:mtd> | |
501 | <mml:mtd> | |
502 | <mml:mrow> | |
503 | <mml:mi mathvariant="italic">c</mml:mi> | |
504 | <mml:mo>⁡</mml:mo> | |
505 | <mml:mfenced open="[" close="]"> | |
506 | <mml:mn>14</mml:mn> | |
507 | </mml:mfenced> | |
508 | </mml:mrow> | |
509 | </mml:mtd> | |
510 | </mml:mtr> | |
511 | <mml:mtr> | |
512 | <mml:mtd> | |
513 | <mml:mrow> | |
514 | <mml:mi mathvariant="italic">c</mml:mi> | |
515 | <mml:mo>⁡</mml:mo> | |
516 | <mml:mfenced open="[" close="]"> | |
517 | <mml:mn>3</mml:mn> | |
518 | </mml:mfenced> | |
519 | </mml:mrow> | |
520 | </mml:mtd> | |
521 | <mml:mtd> | |
522 | <mml:mrow> | |
523 | <mml:mi mathvariant="italic">c</mml:mi> | |
524 | <mml:mo>⁡</mml:mo> | |
525 | <mml:mfenced open="[" close="]"> | |
526 | <mml:mn>7</mml:mn> | |
527 | </mml:mfenced> | |
528 | </mml:mrow> | |
529 | </mml:mtd> | |
530 | <mml:mtd> | |
531 | <mml:mrow> | |
532 | <mml:mi mathvariant="italic">c</mml:mi> | |
533 | <mml:mo>⁡</mml:mo> | |
534 | <mml:mfenced open="[" close="]"> | |
535 | <mml:mn>11</mml:mn> | |
536 | </mml:mfenced> | |
537 | </mml:mrow> | |
538 | </mml:mtd> | |
539 | <mml:mtd> | |
540 | <mml:mrow> | |
541 | <mml:mi mathvariant="italic">c</mml:mi> | |
542 | <mml:mo>⁡</mml:mo> | |
543 | <mml:mfenced open="[" close="]"> | |
544 | <mml:mn>15</mml:mn> | |
545 | </mml:mfenced> | |
546 | </mml:mrow> | |
547 | </mml:mtd> | |
548 | </mml:mtr> | |
549 | </mml:mtable> | |
550 | </mml:mfenced> | |
551 | <mml:mo>×</mml:mo> | |
552 | <mml:mfenced open="(" close=")"> | |
553 | <mml:mtable> | |
554 | <mml:mtr> | |
555 | <mml:mtd> | |
556 | <mml:mrow> | |
557 | <mml:mi mathvariant="italic">m</mml:mi> | |
558 | <mml:mo>⁡</mml:mo> | |
559 | <mml:mfenced open="[" close="]"> | |
560 | <mml:mn>0</mml:mn> | |
561 | </mml:mfenced> | |
562 | </mml:mrow> | |
563 | </mml:mtd> | |
564 | <mml:mtd> | |
565 | <mml:mrow> | |
566 | <mml:mi mathvariant="italic">m</mml:mi> | |
567 | <mml:mo>⁡</mml:mo> | |
568 | <mml:mfenced open="[" close="]"> | |
569 | <mml:mn>1</mml:mn> | |
570 | </mml:mfenced> | |
571 | </mml:mrow> | |
572 | </mml:mtd> | |
573 | <mml:mtd> | |
574 | <mml:mrow> | |
575 | <mml:mi mathvariant="italic">m</mml:mi> | |
576 | <mml:mo>⁡</mml:mo> | |
577 | <mml:mfenced open="[" close="]"> | |
578 | <mml:mn>2</mml:mn> | |
579 | </mml:mfenced> | |
580 | </mml:mrow> | |
581 | </mml:mtd> | |
582 | <mml:mtd> | |
583 | <mml:mrow> | |
584 | <mml:mi mathvariant="italic">m</mml:mi> | |
585 | <mml:mo>⁡</mml:mo> | |
586 | <mml:mfenced open="[" close="]"> | |
587 | <mml:mn>3</mml:mn> | |
588 | </mml:mfenced> | |
589 | </mml:mrow> | |
590 | </mml:mtd> | |
591 | </mml:mtr> | |
592 | <mml:mtr> | |
593 | <mml:mtd> | |
594 | <mml:mrow> | |
595 | <mml:mi mathvariant="italic">m</mml:mi> | |
596 | <mml:mo>⁡</mml:mo> | |
597 | <mml:mfenced open="[" close="]"> | |
598 | <mml:mn>4</mml:mn> | |
599 | </mml:mfenced> | |
600 | </mml:mrow> | |
601 | </mml:mtd> | |
602 | <mml:mtd> | |
603 | <mml:mrow> | |
604 | <mml:mi mathvariant="italic">m</mml:mi> | |
605 | <mml:mo>⁡</mml:mo> | |
606 | <mml:mfenced open="[" close="]"> | |
607 | <mml:mn>5</mml:mn> | |
608 | </mml:mfenced> | |
609 | </mml:mrow> | |
610 | </mml:mtd> | |
611 | <mml:mtd> | |
612 | <mml:mrow> | |
613 | <mml:mi mathvariant="italic">m</mml:mi> | |
614 | <mml:mo>⁡</mml:mo> | |
615 | <mml:mfenced open="[" close="]"> | |
616 | <mml:mn>6</mml:mn> | |
617 | </mml:mfenced> | |
618 | </mml:mrow> | |
619 | </mml:mtd> | |
620 | <mml:mtd> | |
621 | <mml:mrow> | |
622 | <mml:mi mathvariant="italic">m</mml:mi> | |
623 | <mml:mo>⁡</mml:mo> | |
624 | <mml:mfenced open="[" close="]"> | |
625 | <mml:mn>7</mml:mn> | |
626 | </mml:mfenced> | |
627 | </mml:mrow> | |
628 | </mml:mtd> | |
629 | </mml:mtr> | |
630 | <mml:mtr> | |
631 | <mml:mtd> | |
632 | <mml:mrow> | |
633 | <mml:mi mathvariant="italic">m</mml:mi> | |
634 | <mml:mo>⁡</mml:mo> | |
635 | <mml:mfenced open="[" close="]"> | |
636 | <mml:mn>8</mml:mn> | |
637 | </mml:mfenced> | |
638 | </mml:mrow> | |
639 | </mml:mtd> | |
640 | <mml:mtd> | |
641 | <mml:mrow> | |
642 | <mml:mi mathvariant="italic">m</mml:mi> | |
643 | <mml:mo>⁡</mml:mo> | |
644 | <mml:mfenced open="[" close="]"> | |
645 | <mml:mn>9</mml:mn> | |
646 | </mml:mfenced> | |
647 | </mml:mrow> | |
648 | </mml:mtd> | |
649 | <mml:mtd> | |
650 | <mml:mrow> | |
651 | <mml:mi mathvariant="italic">m</mml:mi> | |
652 | <mml:mo>⁡</mml:mo> | |
653 | <mml:mfenced open="[" close="]"> | |
654 | <mml:mn>10</mml:mn> | |
655 | </mml:mfenced> | |
656 | </mml:mrow> | |
657 | </mml:mtd> | |
658 | <mml:mtd> | |
659 | <mml:mrow> | |
660 | <mml:mi mathvariant="italic">m</mml:mi> | |
661 | <mml:mo>⁡</mml:mo> | |
662 | <mml:mfenced open="[" close="]"> | |
663 | <mml:mn>11</mml:mn> | |
664 | </mml:mfenced> | |
665 | </mml:mrow> | |
666 | </mml:mtd> | |
667 | </mml:mtr> | |
668 | <mml:mtr> | |
669 | <mml:mtd> | |
670 | <mml:mrow> | |
671 | <mml:mi mathvariant="italic">m</mml:mi> | |
672 | <mml:mo>⁡</mml:mo> | |
673 | <mml:mfenced open="[" close="]"> | |
674 | <mml:mn>12</mml:mn> | |
675 | </mml:mfenced> | |
676 | </mml:mrow> | |
677 | </mml:mtd> | |
678 | <mml:mtd> | |
679 | <mml:mrow> | |
680 | <mml:mi mathvariant="italic">m</mml:mi> | |
681 | <mml:mo>⁡</mml:mo> | |
682 | <mml:mfenced open="[" close="]"> | |
683 | <mml:mn>13</mml:mn> | |
684 | </mml:mfenced> | |
685 | </mml:mrow> | |
686 | </mml:mtd> | |
687 | <mml:mtd> | |
688 | <mml:mrow> | |
689 | <mml:mi mathvariant="italic">m</mml:mi> | |
690 | <mml:mo>⁡</mml:mo> | |
691 | <mml:mfenced open="[" close="]"> | |
692 | <mml:mn>14</mml:mn> | |
693 | </mml:mfenced> | |
694 | </mml:mrow> | |
695 | </mml:mtd> | |
696 | <mml:mtd> | |
697 | <mml:mrow> | |
698 | <mml:mi mathvariant="italic">m</mml:mi> | |
699 | <mml:mo>⁡</mml:mo> | |
700 | <mml:mfenced open="[" close="]"> | |
701 | <mml:mn>15</mml:mn> | |
702 | </mml:mfenced> | |
703 | </mml:mrow> | |
704 | </mml:mtd> | |
705 | </mml:mtr> | |
706 | </mml:mtable> | |
707 | </mml:mfenced> | |
708 | <mml:mo>×</mml:mo> | |
709 | <mml:mfenced open="(" close=")"> | |
710 | <mml:mtable> | |
711 | <mml:mtr> | |
712 | <mml:mtd> | |
713 | <mml:mrow> | |
714 | <mml:mi mathvariant="italic">v</mml:mi> | |
715 | <mml:mo>⁡</mml:mo> | |
716 | <mml:mfenced open="[" close="]"> | |
717 | <mml:mn>0</mml:mn> | |
718 | </mml:mfenced> | |
719 | </mml:mrow> | |
720 | </mml:mtd> | |
721 | </mml:mtr> | |
722 | <mml:mtr> | |
723 | <mml:mtd> | |
724 | <mml:mrow> | |
725 | <mml:mi mathvariant="italic">v</mml:mi> | |
726 | <mml:mo>⁡</mml:mo> | |
727 | <mml:mfenced open="[" close="]"> | |
728 | <mml:mn>1</mml:mn> | |
729 | </mml:mfenced> | |
730 | </mml:mrow> | |
731 | </mml:mtd> | |
732 | </mml:mtr> | |
733 | <mml:mtr> | |
734 | <mml:mtd> | |
735 | <mml:mrow> | |
736 | <mml:mi mathvariant="italic">v</mml:mi> | |
737 | <mml:mo>⁡</mml:mo> | |
738 | <mml:mfenced open="[" close="]"> | |
739 | <mml:mn>2</mml:mn> | |
740 | </mml:mfenced> | |
741 | </mml:mrow> | |
742 | </mml:mtd> | |
743 | </mml:mtr> | |
744 | <mml:mtr> | |
745 | <mml:mtd> | |
746 | <mml:mrow> | |
747 | <mml:mi mathvariant="italic">v</mml:mi> | |
748 | <mml:mo>⁡</mml:mo> | |
749 | <mml:mfenced open="[" close="]"> | |
750 | <mml:mn>3</mml:mn> | |
751 | </mml:mfenced> | |
752 | </mml:mrow> | |
753 | </mml:mtd> | |
754 | </mml:mtr> | |
755 | </mml:mtable> | |
756 | </mml:mfenced> | |
757 | </mml:mrow> | |
758 | </mml:math></informalequation> | |
759 | </para> | |
760 | <para> | |
761 | </para> | |
762 | <para> | |
763 | Where | |
764 | <inlineequation><mml:math><mml:mi mathvariant="italic">v</mml:mi></mml:math></inlineequation> | |
765 | is represented as a | |
766 | <inlineequation><mml:math> | |
767 | <!-- eqn: 4 times 1:--> | |
768 | <mml:mrow> | |
769 | <mml:mn>4</mml:mn> | |
770 | <mml:mo>×</mml:mo> | |
771 | <mml:mn>1</mml:mn> | |
772 | </mml:mrow> | |
773 | </mml:math></inlineequation> | |
774 | matrix. | |
775 | </para> | |
776 | <para> | |
777 | Calling <function>glMultTransposeMatrix</function> with matrix | |
778 | <inlineequation><mml:math><mml:mi mathvariant="italic">M</mml:mi></mml:math></inlineequation> | |
779 | is identical in operation to | |
780 | <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> with | |
781 | <inlineequation><mml:math> | |
782 | <!-- eqn: M sup T:--> | |
783 | <mml:msup><mml:mi mathvariant="italic">M</mml:mi> | |
784 | <mml:mi mathvariant="italic">T</mml:mi> | |
785 | </mml:msup> | |
786 | </mml:math></inlineequation>, | |
787 | where | |
788 | <inlineequation><mml:math><mml:mi mathvariant="italic">T</mml:mi></mml:math></inlineequation> | |
789 | represents the transpose. | |
790 | </para> | |
791 | </refsect1> | |
792 | <refsect1 id="notes"><title>Notes</title> | |
793 | <para> | |
794 | <function>glMultTransposeMatrix</function> is available only if the GL version is 1.3 or greater. | |
795 | </para> | |
796 | <para> | |
797 | While the elements of the matrix may be specified with | |
798 | single or double precision, the GL may store or operate on these | |
799 | values in less-than-single precision. | |
800 | </para> | |
801 | <para> | |
802 | The order of the multiplication is important. For example, if the current | |
803 | transformation is a rotation, and <function>glMultTransposeMatrix</function> is called with a translation matrix, | |
804 | the translation is done directly on the coordinates to be transformed, | |
805 | while the rotation is done on the results of that translation. | |
806 | </para> | |
807 | </refsect1> | |
808 | <refsect1 id="errors"><title>Errors</title> | |
809 | <para> | |
810 | <constant>GL_INVALID_OPERATION</constant> is generated if <function>glMultTransposeMatrix</function> | |
811 | is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry> | |
812 | and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>. | |
813 | </para> | |
814 | </refsect1> | |
815 | <refsect1 id="associatedgets"><title>Associated Gets</title> | |
816 | <para> | |
817 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MATRIX_MODE</constant> | |
818 | </para> | |
819 | <para> | |
820 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_COLOR_MATRIX</constant> | |
821 | </para> | |
822 | <para> | |
823 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MODELVIEW_MATRIX</constant> | |
824 | </para> | |
825 | <para> | |
826 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_PROJECTION_MATRIX</constant> | |
827 | </para> | |
828 | <para> | |
829 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_TEXTURE_MATRIX</constant> | |
830 | </para> | |
831 | </refsect1> | |
832 | <refsect1 id="seealso"><title>See Also</title> | |
833 | <para> | |
834 | <citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>, | |
835 | <citerefentry><refentrytitle>glLoadMatrix</refentrytitle></citerefentry>, | |
836 | <citerefentry><refentrytitle>glLoadTransposeMatrix</refentrytitle></citerefentry>, | |
837 | <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>, | |
838 | <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry> | |
839 | </para> | |
840 | </refsect1> | |
841 | <refsect1 id="Copyright"><title>Copyright</title> | |
842 | <para> | |
843 | Copyright <trademark class="copyright"></trademark> 1991-2006 | |
844 | Silicon Graphics, Inc. This document is licensed under the SGI | |
845 | Free Software B License. For details, see | |
846 | <ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>. | |
847 | </para> | |
848 | </refsect1> | |
849 | </refentry> |