upstream-man-pages/man2/xhtml/glFrustum.xml

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   3 <?xml-stylesheet type="text/xsl" href="mathml.xsl"?><html xmlns="http://www.w3.org/1999/xhtml" xmlns:pref="http://www.w3.org/2002/Math/preference" pref:renderer="mathplayer-dl"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>glFrustum</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2" /></head><body><div class="refentry" lang="en" xml:lang="en"><a id="glFrustum"></a><div class="titlepage"></div><div class="refnamediv"><h2>Name</h2><p>glFrustum — multiply the current matrix by a perspective matrix</p></div><div class="refsynopsisdiv"><h2>C Specification</h2><div class="funcsynopsis"><table border="0" summary="Function synopsis" cellspacing="0" cellpadding="0"><tr><td><code class="funcdef">void <b class="fsfunc">glFrustum</b>(</code></td><td>GLdouble  </td><td><var class="pdparam">left</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">right</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">bottom</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">top</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">nearVal</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">farVal</var><code>)</code>;</td></tr></table></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="parameters"></a><h2>Parameters</h2><div class="variablelist"><dl><dt><span class="term"><em class="parameter"><code>left</code></em>, </span><span class="term"><em class="parameter"><code>right</code></em></span></dt><dd><p>
   4                     Specify the coordinates for the left and right vertical clipping planes.
   5                 </p></dd><dt><span class="term"><em class="parameter"><code>bottom</code></em>, </span><span class="term"><em class="parameter"><code>top</code></em></span></dt><dd><p>
   6                     Specify the coordinates for the bottom and top horizontal clipping planes.
   7                 </p></dd><dt><span class="term"><em class="parameter"><code>nearVal</code></em>, </span><span class="term"><em class="parameter"><code>farVal</code></em></span></dt><dd><p>
   8                     Specify the distances to the near and far depth clipping planes.
   9                     Both distances must be positive.
  10                 </p></dd></dl></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="description"></a><h2>Description</h2><p>
  11             <code class="function">glFrustum</code> describes a perspective matrix that produces a perspective projection.
  12             The current matrix (see <a class="citerefentry" href="glMatrixMode.xml"><span class="citerefentry"><span class="refentrytitle">glMatrixMode</span></span></a>) is multiplied by this matrix
  13             and the result replaces the current matrix, as if
  14             <a class="citerefentry" href="glMultMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glMultMatrix</span></span></a> were called with the following matrix
  15             as its argument:
  16         </p><p>
  17         </p><p>
  18             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  19
  20                 <mml:mfenced open="[" close="]">
  21                     <mml:mtable>
  22                         <mml:mtr>
  23                             <mml:mtd>
  24                                 <mml:mfenced open="" close="">
  25                                     <mml:mfrac>
  26                                         <mml:mfenced open="" close="">
  27                                             <mml:mrow>
  28                                                 <mml:mn>2</mml:mn>
  29                                                 <mml:mo>⁢</mml:mo>
  30                                                 <mml:mi mathvariant="italic">nearVal</mml:mi>
  31                                             </mml:mrow>
  32                                         </mml:mfenced>
  33                                         <mml:mfenced open="" close="">
  34                                             <mml:mrow>
  35                                                 <mml:mi mathvariant="italic">right</mml:mi>
  36                                                 <mml:mo>-</mml:mo>
  37                                                 <mml:mi mathvariant="italic">left</mml:mi>
  38                                             </mml:mrow>
  39                                         </mml:mfenced>
  40                                     </mml:mfrac>
  41                                 </mml:mfenced>
  42                             </mml:mtd>
  43                             <mml:mtd>
  44                                 <mml:mn>0</mml:mn>
  45                             </mml:mtd>
  46                             <mml:mtd>
  47                                 <mml:mi mathvariant="italic">A</mml:mi>
  48                             </mml:mtd>
  49                             <mml:mtd>
  50                                 <mml:mn>0</mml:mn>
  51                             </mml:mtd>
  52                         </mml:mtr>
  53                         <mml:mtr>
  54                             <mml:mtd>
  55                                 <mml:mn>0</mml:mn>
  56                             </mml:mtd>
  57                             <mml:mtd>
  58                                 <mml:mfenced open="" close="">
  59                                     <mml:mfrac>
  60                                         <mml:mfenced open="" close="">
  61                                             <mml:mrow>
  62                                                 <mml:mn>2</mml:mn>
  63                                                 <mml:mo>⁢</mml:mo>
  64                                                 <mml:mi mathvariant="italic">nearVal</mml:mi>
  65                                             </mml:mrow>
  66                                         </mml:mfenced>
  67                                         <mml:mfenced open="" close="">
  68                                             <mml:mrow>
  69                                                 <mml:mi mathvariant="italic">top</mml:mi>
  70                                                 <mml:mo>-</mml:mo>
  71                                                 <mml:mi mathvariant="italic">bottom</mml:mi>
  72                                             </mml:mrow>
  73                                         </mml:mfenced>
  74                                     </mml:mfrac>
  75                                 </mml:mfenced>
  76                             </mml:mtd>
  77                             <mml:mtd>
  78                                 <mml:mi mathvariant="italic">B</mml:mi>
  79                             </mml:mtd>
  80                             <mml:mtd>
  81                                 <mml:mn>0</mml:mn>
  82                             </mml:mtd>
  83                         </mml:mtr>
  84                         <mml:mtr>
  85                             <mml:mtd>
  86                                 <mml:mn>0</mml:mn>
  87                             </mml:mtd>
  88                             <mml:mtd>
  89                                 <mml:mn>0</mml:mn>
  90                             </mml:mtd>
  91                             <mml:mtd>
  92                                 <mml:mi mathvariant="italic">C</mml:mi>
  93                             </mml:mtd>
  94                             <mml:mtd>
  95                                 <mml:mi mathvariant="italic">D</mml:mi>
  96                             </mml:mtd>
  97                         </mml:mtr>
  98                         <mml:mtr>
  99                             <mml:mtd>
 100                                 <mml:mn>0</mml:mn>
 101                             </mml:mtd>
 102                             <mml:mtd>
 103                                 <mml:mn>0</mml:mn>
 104                             </mml:mtd>
 105                             <mml:mtd>
 106                                 <mml:mn>-1</mml:mn>
 107                             </mml:mtd>
 108                             <mml:mtd>
 109                                 <mml:mn>0</mml:mn>
 110                             </mml:mtd>
 111                         </mml:mtr>
 112                     </mml:mtable>
 113                 </mml:mfenced>
 114             </mml:math></div><p>
 115         </p><p>
 116             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 117
 118                 <mml:mrow>
 119                     <mml:mi mathvariant="italic">A</mml:mi>
 120                     <mml:mo>=</mml:mo>
 121                     <mml:mfrac>
 122                         <mml:mfenced open="" close="">
 123                             <mml:mrow>
 124                                 <mml:mi mathvariant="italic">right</mml:mi>
 125                                 <mml:mo>+</mml:mo>
 126                                 <mml:mi mathvariant="italic">left</mml:mi>
 127                             </mml:mrow>
 128                         </mml:mfenced>
 129                         <mml:mfenced open="" close="">
 130                             <mml:mrow>
 131                                 <mml:mi mathvariant="italic">right</mml:mi>
 132                                 <mml:mo>-</mml:mo>
 133                                 <mml:mi mathvariant="italic">left</mml:mi>
 134                             </mml:mrow>
 135                         </mml:mfenced>
 136                     </mml:mfrac>
 137                 </mml:mrow>
 138             </mml:math></div><p>
 139         </p><p>
 140             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 141
 142                 <mml:mrow>
 143                     <mml:mi mathvariant="italic">B</mml:mi>
 144                     <mml:mo>=</mml:mo>
 145                     <mml:mfrac>
 146                         <mml:mfenced open="" close="">
 147                             <mml:mrow>
 148                                 <mml:mi mathvariant="italic">top</mml:mi>
 149                                 <mml:mo>+</mml:mo>
 150                                 <mml:mi mathvariant="italic">bottom</mml:mi>
 151                             </mml:mrow>
 152                         </mml:mfenced>
 153                         <mml:mfenced open="" close="">
 154                             <mml:mrow>
 155                                 <mml:mi mathvariant="italic">top</mml:mi>
 156                                 <mml:mo>-</mml:mo>
 157                                 <mml:mi mathvariant="italic">bottom</mml:mi>
 158                             </mml:mrow>
 159                         </mml:mfenced>
 160                     </mml:mfrac>
 161                 </mml:mrow>
 162             </mml:math></div><p>
 163         </p><p>
 164             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 165
 166                 <mml:mrow>
 167                     <mml:mi mathvariant="italic">C</mml:mi>
 168                     <mml:mo>=</mml:mo>
 169                     <mml:mrow>
 170                         <mml:mo>-</mml:mo>
 171                         <mml:mfenced open="" close="">
 172                             <mml:mfrac>
 173                                 <mml:mfenced open="" close="">
 174                                     <mml:mrow>
 175                                         <mml:mi mathvariant="italic">farVal</mml:mi>
 176                                         <mml:mo>+</mml:mo>
 177                                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 178                                     </mml:mrow>
 179                                 </mml:mfenced>
 180                                 <mml:mfenced open="" close="">
 181                                     <mml:mrow>
 182                                         <mml:mi mathvariant="italic">farVal</mml:mi>
 183                                         <mml:mo>-</mml:mo>
 184                                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 185                                     </mml:mrow>
 186                                 </mml:mfenced>
 187                             </mml:mfrac>
 188                         </mml:mfenced>
 189                     </mml:mrow>
 190                 </mml:mrow>
 191             </mml:math></div><p>
 192         </p><p>
 193             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 194
 195                 <mml:mrow>
 196                     <mml:mi mathvariant="italic">D</mml:mi>
 197                     <mml:mo>=</mml:mo>
 198                     <mml:mrow>
 199                         <mml:mo>-</mml:mo>
 200                         <mml:mfenced open="" close="">
 201                             <mml:mfrac>
 202                                 <mml:mfenced open="" close="">
 203                                     <mml:mrow>
 204                                         <mml:mn>2</mml:mn>
 205                                         <mml:mo>⁢</mml:mo>
 206                                         <mml:mi mathvariant="italic">farVal</mml:mi>
 207                                         <mml:mo>⁢</mml:mo>
 208                                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 209                                     </mml:mrow>
 210                                 </mml:mfenced>
 211                                 <mml:mfenced open="" close="">
 212                                     <mml:mrow>
 213                                         <mml:mi mathvariant="italic">farVal</mml:mi>
 214                                         <mml:mo>-</mml:mo>
 215                                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 216                                     </mml:mrow>
 217                                 </mml:mfenced>
 218                             </mml:mfrac>
 219                         </mml:mfenced>
 220                     </mml:mrow>
 221                 </mml:mrow>
 222             </mml:math></div><p>
 223         </p><p>
 224         </p><p>
 225             Typically, the matrix mode is <code class="constant">GL_PROJECTION</code>, and
 226             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 227
 228                 <mml:mfenced open="(" close=")">
 229                     <mml:mi mathvariant="italic">left</mml:mi>
 230                     <mml:mi mathvariant="italic">bottom</mml:mi>
 231                     <mml:mrow>
 232                         <mml:mo>-</mml:mo>
 233                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 234                     </mml:mrow>
 235                 </mml:mfenced>
 236             </mml:math>
 237             and
 238             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 239
 240                 <mml:mfenced open="(" close=")">
 241                     <mml:mi mathvariant="italic">right</mml:mi>
 242                     <mml:mi mathvariant="italic">top</mml:mi>
 243                     <mml:mrow>
 244                         <mml:mo>-</mml:mo>
 245                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 246                     </mml:mrow>
 247                 </mml:mfenced>
 248             </mml:math>
 249             specify the points on the near clipping plane that are mapped
 250             to the lower left and upper right corners of the window,
 251             assuming that the eye is located at (0, 0, 0).
 252             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 253
 254                 <mml:mrow>
 255                     <mml:mo>-</mml:mo>
 256                     <mml:mi mathvariant="italic">farVal</mml:mi>
 257                 </mml:mrow>
 258             </mml:math>
 259             specifies the location of the far clipping plane.
 260             Both <em class="parameter"><code>nearVal</code></em> and <em class="parameter"><code>farVal</code></em> must be positive.
 261         </p><p>
 262             Use <a class="citerefentry" href="glPushMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPushMatrix</span></span></a> and <a class="citerefentry" href="glPopMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPopMatrix</span></span></a> to save and restore
 263             the current matrix stack.
 264         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="notes"></a><h2>Notes</h2><p>
 265             Depth buffer precision is affected by the values specified for
 266             <em class="parameter"><code>nearVal</code></em> and <em class="parameter"><code>farVal</code></em>.
 267             The greater the ratio of <em class="parameter"><code>farVal</code></em> to <em class="parameter"><code>nearVal</code></em> is,
 268             the less effective the depth buffer will be at distinguishing between
 269             surfaces that are near each other.
 270             If
 271         </p><p>
 272             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 273
 274                 <mml:mrow>
 275                     <mml:mi mathvariant="italic">r</mml:mi>
 276                     <mml:mo>=</mml:mo>
 277                     <mml:mfrac>
 278                         <mml:mi mathvariant="italic">farVal</mml:mi>
 279                         <mml:mi mathvariant="italic">nearVal</mml:mi>
 280                     </mml:mfrac>
 281                 </mml:mrow>
 282             </mml:math>
 283         </p><p>
 284             roughly
 285             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 286
 287                 <mml:mrow>
 288                     <mml:msub><mml:mi mathvariant="italic">log</mml:mi>
 289                     <mml:mn>2</mml:mn>
 290                     </mml:msub>
 291                     <mml:mo>⁡</mml:mo>
 292                     <mml:mfenced open="(" close=")">
 293                         <mml:mi mathvariant="italic">r</mml:mi>
 294                     </mml:mfenced>
 295                 </mml:mrow>
 296             </mml:math>
 297             bits of depth buffer precision are lost.
 298             Because
 299             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">r</mml:mi></mml:math>
 300             approaches infinity as <em class="parameter"><code>nearVal</code></em> approaches 0,
 301             <em class="parameter"><code>nearVal</code></em> must never be set to 0.
 302         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="errors"></a><h2>Errors</h2><p>
 303             <code class="constant">GL_INVALID_VALUE</code> is generated if <em class="parameter"><code>nearVal</code></em> or <em class="parameter"><code>farVal</code></em> is not
 304             positive, or if <em class="parameter"><code>left</code></em> = <em class="parameter"><code>right</code></em>, or <em class="parameter"><code>bottom</code></em> = <em class="parameter"><code>top</code></em>,
 305             or <em class="parameter"><code>near</code></em> = <em class="parameter"><code>far</code></em>.
 306         </p><p>
 307             <code class="constant">GL_INVALID_OPERATION</code> is generated if <code class="function">glFrustum</code>
 308             is executed between the execution of <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a>
 309             and the corresponding execution of <a class="citerefentry" href="glEnd.xml"><span class="citerefentry"><span class="refentrytitle">glEnd</span></span></a>.
 310         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="associatedgets"></a><h2>Associated Gets</h2><p>
 311             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MATRIX_MODE</code>
 312         </p><p>
 313             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MODELVIEW_MATRIX</code>
 314         </p><p>
 315             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_PROJECTION_MATRIX</code>
 316         </p><p>
 317             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_TEXTURE_MATRIX</code>
 318         </p><p>
 319             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_COLOR_MATRIX</code>
 320         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="seealso"></a><h2>See Also</h2><p>
 321             <a class="citerefentry" href="glOrtho.xml"><span class="citerefentry"><span class="refentrytitle">glOrtho</span></span></a>,
 322             <a class="citerefentry" href="glMatrixMode.xml"><span class="citerefentry"><span class="refentrytitle">glMatrixMode</span></span></a>,
 323             <a class="citerefentry" href="glMultMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glMultMatrix</span></span></a>,
 324             <a class="citerefentry" href="glPushMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPushMatrix</span></span></a>,
 325             <a class="citerefentry" href="glViewport.xml"><span class="citerefentry"><span class="refentrytitle">glViewport</span></span></a>
 326         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="Copyright"></a><h2>Copyright</h2><p>
 327             Copyright <span class="trademark"></span>© 1991-2006
 328             Silicon Graphics, Inc. This document is licensed under the SGI
 329             Free Software B License. For details, see
 330             <a class="ulink" href="http://oss.sgi.com/projects/FreeB/" target="_top">http://oss.sgi.com/projects/FreeB/</a>.
 331         </p></div></div></body></html>