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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="glFrustum"> | |
5 | <refmeta> | |
6 | <refmetainfo> | |
7 | <copyright> | |
8 | <year>1991-2006</year> | |
9 | <holder>Silicon Graphics, Inc.</holder> | |
10 | </copyright> | |
11 | </refmetainfo> | |
12 | <refentrytitle>glFrustum</refentrytitle> | |
13 | <manvolnum>3G</manvolnum> | |
14 | </refmeta> | |
15 | <refnamediv> | |
16 | <refname>glFrustum</refname> | |
17 | <refpurpose>multiply the current matrix by a perspective matrix</refpurpose> | |
18 | </refnamediv> | |
19 | <refsynopsisdiv><title>C Specification</title> | |
20 | <funcsynopsis> | |
21 | <funcprototype> | |
22 | <funcdef>void <function>glFrustum</function></funcdef> | |
23 | <paramdef>GLdouble <parameter>left</parameter></paramdef> | |
24 | <paramdef>GLdouble <parameter>right</parameter></paramdef> | |
25 | <paramdef>GLdouble <parameter>bottom</parameter></paramdef> | |
26 | <paramdef>GLdouble <parameter>top</parameter></paramdef> | |
27 | <paramdef>GLdouble <parameter>nearVal</parameter></paramdef> | |
28 | <paramdef>GLdouble <parameter>farVal</parameter></paramdef> | |
29 | </funcprototype> | |
30 | </funcsynopsis> | |
31 | </refsynopsisdiv> | |
32 | <!-- eqn: ignoring delim $$ --> | |
33 | <refsect1 id="parameters"><title>Parameters</title> | |
34 | <variablelist> | |
35 | <varlistentry> | |
36 | <term><parameter>left</parameter></term> | |
37 | <term><parameter>right</parameter></term> | |
38 | <listitem> | |
39 | <para> | |
40 | Specify the coordinates for the left and right vertical clipping planes. | |
41 | </para> | |
42 | </listitem> | |
43 | </varlistentry> | |
44 | <varlistentry> | |
45 | <term><parameter>bottom</parameter></term> | |
46 | <term><parameter>top</parameter></term> | |
47 | <listitem> | |
48 | <para> | |
49 | Specify the coordinates for the bottom and top horizontal clipping planes. | |
50 | </para> | |
51 | </listitem> | |
52 | </varlistentry> | |
53 | <varlistentry> | |
54 | <term><parameter>nearVal</parameter></term> | |
55 | <term><parameter>farVal</parameter></term> | |
56 | <listitem> | |
57 | <para> | |
58 | Specify the distances to the near and far depth clipping planes. | |
59 | Both distances must be positive. | |
60 | </para> | |
61 | </listitem> | |
62 | </varlistentry> | |
63 | </variablelist> | |
64 | </refsect1> | |
65 | <refsect1 id="description"><title>Description</title> | |
66 | <para> | |
67 | <function>glFrustum</function> describes a perspective matrix that produces a perspective projection. | |
68 | The current matrix (see <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>) is multiplied by this matrix | |
69 | and the result replaces the current matrix, as if | |
70 | <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the following matrix | |
71 | as its argument: | |
72 | </para> | |
73 | <para> | |
74 | </para> | |
75 | <para> | |
76 | <informalequation><mml:math> | |
77 | <!-- eqn: left [ matrix { ccol { {{2 nearVal} over {right - left}} above 0 above 0 above 0 } ccol { 0 above {{2 nearVal} over {top - bottom}} above 0 above 0 } ccol { A above B above C above -1 } ccol { 0 above 0 above D above 0} } right ]:--> | |
78 | <mml:mfenced open="[" close="]"> | |
79 | <mml:mtable> | |
80 | <mml:mtr> | |
81 | <mml:mtd> | |
82 | <mml:mfenced open="" close=""> | |
83 | <mml:mfrac> | |
84 | <mml:mfenced open="" close=""> | |
85 | <mml:mrow> | |
86 | <mml:mn>2</mml:mn> | |
87 | <mml:mo>⁢</mml:mo> | |
88 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
89 | </mml:mrow> | |
90 | </mml:mfenced> | |
91 | <mml:mfenced open="" close=""> | |
92 | <mml:mrow> | |
93 | <mml:mi mathvariant="italic">right</mml:mi> | |
94 | <mml:mo>-</mml:mo> | |
95 | <mml:mi mathvariant="italic">left</mml:mi> | |
96 | </mml:mrow> | |
97 | </mml:mfenced> | |
98 | </mml:mfrac> | |
99 | </mml:mfenced> | |
100 | </mml:mtd> | |
101 | <mml:mtd> | |
102 | <mml:mn>0</mml:mn> | |
103 | </mml:mtd> | |
104 | <mml:mtd> | |
105 | <mml:mi mathvariant="italic">A</mml:mi> | |
106 | </mml:mtd> | |
107 | <mml:mtd> | |
108 | <mml:mn>0</mml:mn> | |
109 | </mml:mtd> | |
110 | </mml:mtr> | |
111 | <mml:mtr> | |
112 | <mml:mtd> | |
113 | <mml:mn>0</mml:mn> | |
114 | </mml:mtd> | |
115 | <mml:mtd> | |
116 | <mml:mfenced open="" close=""> | |
117 | <mml:mfrac> | |
118 | <mml:mfenced open="" close=""> | |
119 | <mml:mrow> | |
120 | <mml:mn>2</mml:mn> | |
121 | <mml:mo>⁢</mml:mo> | |
122 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
123 | </mml:mrow> | |
124 | </mml:mfenced> | |
125 | <mml:mfenced open="" close=""> | |
126 | <mml:mrow> | |
127 | <mml:mi mathvariant="italic">top</mml:mi> | |
128 | <mml:mo>-</mml:mo> | |
129 | <mml:mi mathvariant="italic">bottom</mml:mi> | |
130 | </mml:mrow> | |
131 | </mml:mfenced> | |
132 | </mml:mfrac> | |
133 | </mml:mfenced> | |
134 | </mml:mtd> | |
135 | <mml:mtd> | |
136 | <mml:mi mathvariant="italic">B</mml:mi> | |
137 | </mml:mtd> | |
138 | <mml:mtd> | |
139 | <mml:mn>0</mml:mn> | |
140 | </mml:mtd> | |
141 | </mml:mtr> | |
142 | <mml:mtr> | |
143 | <mml:mtd> | |
144 | <mml:mn>0</mml:mn> | |
145 | </mml:mtd> | |
146 | <mml:mtd> | |
147 | <mml:mn>0</mml:mn> | |
148 | </mml:mtd> | |
149 | <mml:mtd> | |
150 | <mml:mi mathvariant="italic">C</mml:mi> | |
151 | </mml:mtd> | |
152 | <mml:mtd> | |
153 | <mml:mi mathvariant="italic">D</mml:mi> | |
154 | </mml:mtd> | |
155 | </mml:mtr> | |
156 | <mml:mtr> | |
157 | <mml:mtd> | |
158 | <mml:mn>0</mml:mn> | |
159 | </mml:mtd> | |
160 | <mml:mtd> | |
161 | <mml:mn>0</mml:mn> | |
162 | </mml:mtd> | |
163 | <mml:mtd> | |
164 | <mml:mn>-1</mml:mn> | |
165 | </mml:mtd> | |
166 | <mml:mtd> | |
167 | <mml:mn>0</mml:mn> | |
168 | </mml:mtd> | |
169 | </mml:mtr> | |
170 | </mml:mtable> | |
171 | </mml:mfenced> | |
172 | </mml:math></informalequation> | |
173 | </para> | |
174 | <para> | |
175 | <informalequation><mml:math> | |
176 | <!-- eqn: A = {right + left} over {right - left}:--> | |
177 | <mml:mrow> | |
178 | <mml:mi mathvariant="italic">A</mml:mi> | |
179 | <mml:mo>=</mml:mo> | |
180 | <mml:mfrac> | |
181 | <mml:mfenced open="" close=""> | |
182 | <mml:mrow> | |
183 | <mml:mi mathvariant="italic">right</mml:mi> | |
184 | <mml:mo>+</mml:mo> | |
185 | <mml:mi mathvariant="italic">left</mml:mi> | |
186 | </mml:mrow> | |
187 | </mml:mfenced> | |
188 | <mml:mfenced open="" close=""> | |
189 | <mml:mrow> | |
190 | <mml:mi mathvariant="italic">right</mml:mi> | |
191 | <mml:mo>-</mml:mo> | |
192 | <mml:mi mathvariant="italic">left</mml:mi> | |
193 | </mml:mrow> | |
194 | </mml:mfenced> | |
195 | </mml:mfrac> | |
196 | </mml:mrow> | |
197 | </mml:math></informalequation> | |
198 | </para> | |
199 | <para> | |
200 | <informalequation><mml:math> | |
201 | <!-- eqn: B = {top + bottom} over {top - bottom}:--> | |
202 | <mml:mrow> | |
203 | <mml:mi mathvariant="italic">B</mml:mi> | |
204 | <mml:mo>=</mml:mo> | |
205 | <mml:mfrac> | |
206 | <mml:mfenced open="" close=""> | |
207 | <mml:mrow> | |
208 | <mml:mi mathvariant="italic">top</mml:mi> | |
209 | <mml:mo>+</mml:mo> | |
210 | <mml:mi mathvariant="italic">bottom</mml:mi> | |
211 | </mml:mrow> | |
212 | </mml:mfenced> | |
213 | <mml:mfenced open="" close=""> | |
214 | <mml:mrow> | |
215 | <mml:mi mathvariant="italic">top</mml:mi> | |
216 | <mml:mo>-</mml:mo> | |
217 | <mml:mi mathvariant="italic">bottom</mml:mi> | |
218 | </mml:mrow> | |
219 | </mml:mfenced> | |
220 | </mml:mfrac> | |
221 | </mml:mrow> | |
222 | </mml:math></informalequation> | |
223 | </para> | |
224 | <para> | |
225 | <informalequation><mml:math> | |
226 | <!-- eqn: C = -{{farVal + nearVal} over {farVal - nearVal}}:--> | |
227 | <mml:mrow> | |
228 | <mml:mi mathvariant="italic">C</mml:mi> | |
229 | <mml:mo>=</mml:mo> | |
230 | <mml:mrow> | |
231 | <mml:mo>-</mml:mo> | |
232 | <mml:mfenced open="" close=""> | |
233 | <mml:mfrac> | |
234 | <mml:mfenced open="" close=""> | |
235 | <mml:mrow> | |
236 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
237 | <mml:mo>+</mml:mo> | |
238 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
239 | </mml:mrow> | |
240 | </mml:mfenced> | |
241 | <mml:mfenced open="" close=""> | |
242 | <mml:mrow> | |
243 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
244 | <mml:mo>-</mml:mo> | |
245 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
246 | </mml:mrow> | |
247 | </mml:mfenced> | |
248 | </mml:mfrac> | |
249 | </mml:mfenced> | |
250 | </mml:mrow> | |
251 | </mml:mrow> | |
252 | </mml:math></informalequation> | |
253 | </para> | |
254 | <para> | |
255 | <informalequation><mml:math> | |
256 | <!-- eqn: D = -{{2 farVal nearVal} over {farVal - nearVal}}:--> | |
257 | <mml:mrow> | |
258 | <mml:mi mathvariant="italic">D</mml:mi> | |
259 | <mml:mo>=</mml:mo> | |
260 | <mml:mrow> | |
261 | <mml:mo>-</mml:mo> | |
262 | <mml:mfenced open="" close=""> | |
263 | <mml:mfrac> | |
264 | <mml:mfenced open="" close=""> | |
265 | <mml:mrow> | |
266 | <mml:mn>2</mml:mn> | |
267 | <mml:mo>⁢</mml:mo> | |
268 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
269 | <mml:mo>⁢</mml:mo> | |
270 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
271 | </mml:mrow> | |
272 | </mml:mfenced> | |
273 | <mml:mfenced open="" close=""> | |
274 | <mml:mrow> | |
275 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
276 | <mml:mo>-</mml:mo> | |
277 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
278 | </mml:mrow> | |
279 | </mml:mfenced> | |
280 | </mml:mfrac> | |
281 | </mml:mfenced> | |
282 | </mml:mrow> | |
283 | </mml:mrow> | |
284 | </mml:math></informalequation> | |
285 | </para> | |
286 | <para> | |
287 | </para> | |
288 | <para> | |
289 | Typically, the matrix mode is <constant>GL_PROJECTION</constant>, and | |
290 | <inlineequation><mml:math> | |
291 | <!-- eqn: (left, bottom, -nearVal):--> | |
292 | <mml:mfenced open="(" close=")"> | |
293 | <mml:mi mathvariant="italic">left</mml:mi> | |
294 | <mml:mi mathvariant="italic">bottom</mml:mi> | |
295 | <mml:mrow> | |
296 | <mml:mo>-</mml:mo> | |
297 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
298 | </mml:mrow> | |
299 | </mml:mfenced> | |
300 | </mml:math></inlineequation> | |
301 | and | |
302 | <inlineequation><mml:math> | |
303 | <!-- eqn: (right, top, -nearVal):--> | |
304 | <mml:mfenced open="(" close=")"> | |
305 | <mml:mi mathvariant="italic">right</mml:mi> | |
306 | <mml:mi mathvariant="italic">top</mml:mi> | |
307 | <mml:mrow> | |
308 | <mml:mo>-</mml:mo> | |
309 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
310 | </mml:mrow> | |
311 | </mml:mfenced> | |
312 | </mml:math></inlineequation> | |
313 | specify the points on the near clipping plane that are mapped | |
314 | to the lower left and upper right corners of the window, | |
315 | assuming that the eye is located at (0, 0, 0). | |
316 | <inlineequation><mml:math> | |
317 | <!-- eqn: -farVal:--> | |
318 | <mml:mrow> | |
319 | <mml:mo>-</mml:mo> | |
320 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
321 | </mml:mrow> | |
322 | </mml:math></inlineequation> | |
323 | specifies the location of the far clipping plane. | |
324 | Both <parameter>nearVal</parameter> and <parameter>farVal</parameter> must be positive. | |
325 | </para> | |
326 | <para> | |
327 | Use <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glPopMatrix</refentrytitle></citerefentry> to save and restore | |
328 | the current matrix stack. | |
329 | </para> | |
330 | </refsect1> | |
331 | <refsect1 id="notes"><title>Notes</title> | |
332 | <para> | |
333 | Depth buffer precision is affected by the values specified for | |
334 | <parameter>nearVal</parameter> and <parameter>farVal</parameter>. | |
335 | The greater the ratio of <parameter>farVal</parameter> to <parameter>nearVal</parameter> is, | |
336 | the less effective the depth buffer will be at distinguishing between | |
337 | surfaces that are near each other. | |
338 | If | |
339 | </para> | |
340 | <para> | |
341 | <inlineequation><mml:math> | |
342 | <!-- eqn: r = farVal over nearVal:--> | |
343 | <mml:mrow> | |
344 | <mml:mi mathvariant="italic">r</mml:mi> | |
345 | <mml:mo>=</mml:mo> | |
346 | <mml:mfrac> | |
347 | <mml:mi mathvariant="italic">farVal</mml:mi> | |
348 | <mml:mi mathvariant="italic">nearVal</mml:mi> | |
349 | </mml:mfrac> | |
350 | </mml:mrow> | |
351 | </mml:math></inlineequation> | |
352 | </para> | |
353 | <para> | |
354 | roughly | |
355 | <inlineequation><mml:math> | |
356 | <!-- eqn: log sub 2 (r):--> | |
357 | <mml:mrow> | |
358 | <mml:msub><mml:mi mathvariant="italic">log</mml:mi> | |
359 | <mml:mn>2</mml:mn> | |
360 | </mml:msub> | |
361 | <mml:mo>⁡</mml:mo> | |
362 | <mml:mfenced open="(" close=")"> | |
363 | <mml:mi mathvariant="italic">r</mml:mi> | |
364 | </mml:mfenced> | |
365 | </mml:mrow> | |
366 | </mml:math></inlineequation> | |
367 | bits of depth buffer precision are lost. | |
368 | Because | |
369 | <inlineequation><mml:math><mml:mi mathvariant="italic">r</mml:mi></mml:math></inlineequation> | |
370 | approaches infinity as <parameter>nearVal</parameter> approaches 0, | |
371 | <parameter>nearVal</parameter> must never be set to 0. | |
372 | </para> | |
373 | </refsect1> | |
374 | <refsect1 id="errors"><title>Errors</title> | |
375 | <para> | |
376 | <constant>GL_INVALID_VALUE</constant> is generated if <parameter>nearVal</parameter> or <parameter>farVal</parameter> is not | |
377 | positive, or if <parameter>left</parameter> = <parameter>right</parameter>, or <parameter>bottom</parameter> = <parameter>top</parameter>, | |
378 | or <parameter>near</parameter> = <parameter>far</parameter>. | |
379 | </para> | |
380 | <para> | |
381 | <constant>GL_INVALID_OPERATION</constant> is generated if <function>glFrustum</function> | |
382 | is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry> | |
383 | and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>. | |
384 | </para> | |
385 | </refsect1> | |
386 | <refsect1 id="associatedgets"><title>Associated Gets</title> | |
387 | <para> | |
388 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MATRIX_MODE</constant> | |
389 | </para> | |
390 | <para> | |
391 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MODELVIEW_MATRIX</constant> | |
392 | </para> | |
393 | <para> | |
394 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_PROJECTION_MATRIX</constant> | |
395 | </para> | |
396 | <para> | |
397 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_TEXTURE_MATRIX</constant> | |
398 | </para> | |
399 | <para> | |
400 | <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_COLOR_MATRIX</constant> | |
401 | </para> | |
402 | </refsect1> | |
403 | <refsect1 id="seealso"><title>See Also</title> | |
404 | <para> | |
405 | <citerefentry><refentrytitle>glOrtho</refentrytitle></citerefentry>, | |
406 | <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>, | |
407 | <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry>, | |
408 | <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry>, | |
409 | <citerefentry><refentrytitle>glViewport</refentrytitle></citerefentry> | |
410 | </para> | |
411 | </refsect1> | |
412 | <refsect1 id="Copyright"><title>Copyright</title> | |
413 | <para> | |
414 | Copyright <trademark class="copyright"></trademark> 1991-2006 | |
415 | Silicon Graphics, Inc. This document is licensed under the SGI | |
416 | Free Software B License. For details, see | |
417 | <ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>. | |
418 | </para> | |
419 | </refsect1> | |
420 | </refentry> |