upstream-man-pages/man2/xhtml/gluLookAt.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>gluLookAt</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2" /></head><body><div class="refentry" lang="en" xml:lang="en"><a id="gluLookAt"></a><div class="titlepage"></div><div class="refnamediv"><h2>Name</h2><p>gluLookAt — define a viewing transformation</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">gluLookAt</b>(</code></td><td>GLdouble  </td><td><var class="pdparam">eyeX</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">eyeY</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">eyeZ</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">centerX</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">centerY</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">centerZ</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">upX</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">upY</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">upZ</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>eyeX</code></em>, </span><span class="term"><em class="parameter"><code>eyeY</code></em>, </span><span class="term"><em class="parameter"><code>eyeZ</code></em></span></dt><dd><p>
   4                     Specifies the position of the eye point.
   5                 </p></dd><dt><span class="term"><em class="parameter"><code>centerX</code></em>, </span><span class="term"><em class="parameter"><code>centerY</code></em>, </span><span class="term"><em class="parameter"><code>centerZ</code></em></span></dt><dd><p>
   6                     Specifies the position of the reference point.
   7                 </p></dd><dt><span class="term"><em class="parameter"><code>upX</code></em>, </span><span class="term"><em class="parameter"><code>upY</code></em>, </span><span class="term"><em class="parameter"><code>upZ</code></em></span></dt><dd><p>
   8                     Specifies the direction of the <span class="emphasis"><em>up</em></span> vector.
   9                 </p></dd></dl></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="description"></a><h2>Description</h2><p>
  10             <code class="function">gluLookAt</code> creates a viewing matrix derived from an eye point, a reference
  11             point indicating the center of the scene, and an <span class="emphasis"><em>UP</em></span> vector.
  12         </p><p>
  13             The matrix
  14             maps the reference point to the negative <span class="emphasis"><em>z</em></span> axis and the
  15             eye point to the origin.
  16             When a typical projection matrix is used,
  17             the center of the scene therefore maps to the center of the viewport.
  18             Similarly, the direction described by the <span class="emphasis"><em>UP</em></span>
  19             vector projected onto the viewing plane is mapped to the positive <span class="emphasis"><em>y</em></span>
  20             axis so that it points upward in the viewport.
  21             The <span class="emphasis"><em>UP</em></span> vector must not be parallel to the line of sight from the
  22             eye point to the reference point.
  23         </p><p>
  24             Let
  25         </p><p>
  26             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  27
  28                 <mml:mrow>
  29                     <mml:mi mathvariant="italic">F</mml:mi>
  30                     <mml:mo>=</mml:mo>
  31                     <mml:mfenced open="(" close=")">
  32                         <mml:mtable>
  33                             <mml:mtr>
  34                                 <mml:mtd>
  35                                     <mml:mrow>
  36                                         <mml:mi mathvariant="italic">centerX</mml:mi>
  37                                         <mml:mo>-</mml:mo>
  38                                         <mml:mi mathvariant="italic">eyeX</mml:mi>
  39                                     </mml:mrow>
  40                                 </mml:mtd>
  41                             </mml:mtr>
  42                             <mml:mtr>
  43                                 <mml:mtd>
  44                                     <mml:mrow>
  45                                         <mml:mi mathvariant="italic">centerY</mml:mi>
  46                                         <mml:mo>-</mml:mo>
  47                                         <mml:mi mathvariant="italic">eyeY</mml:mi>
  48                                     </mml:mrow>
  49                                 </mml:mtd>
  50                             </mml:mtr>
  51                             <mml:mtr>
  52                                 <mml:mtd>
  53                                     <mml:mrow>
  54                                         <mml:mi mathvariant="italic">centerZ</mml:mi>
  55                                         <mml:mo>-</mml:mo>
  56                                         <mml:mi mathvariant="italic">eyeZ</mml:mi>
  57                                     </mml:mrow>
  58                                 </mml:mtd>
  59                             </mml:mtr>
  60                         </mml:mtable>
  61                     </mml:mfenced>
  62                 </mml:mrow>
  63             </mml:math></div><p>
  64         </p><p>
  65         </p><p>
  66             Let <span class="emphasis"><em>UP</em></span> be the vector
  67             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  68
  69                 <mml:mfenced open="(" close=")">
  70                     <mml:mi mathvariant="italic">upX</mml:mi>
  71                     <mml:mi mathvariant="italic">upY</mml:mi>
  72                     <mml:mi mathvariant="italic">upZ</mml:mi>
  73                 </mml:mfenced>
  74             </mml:math>.
  75         </p><p>
  76             Then normalize as follows:
  77             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  78
  79                 <mml:mrow>
  80                     <mml:mi mathvariant="italic">f</mml:mi>
  81                     <mml:mo>=</mml:mo>
  82                     <mml:mfrac>
  83                         <mml:mi mathvariant="italic">F</mml:mi>
  84                         <mml:mfenced open="" close="">
  85                             <mml:mfenced open="&#x2225;" close="&#x2225;">
  86                                 <mml:mi mathvariant="italic">F</mml:mi>
  87                             </mml:mfenced>
  88                         </mml:mfenced>
  89                     </mml:mfrac>
  90                 </mml:mrow>
  91             </mml:math></div><p>
  92         </p><p>
  93             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  94
  95                 <mml:mrow>
  96                     <mml:msup><mml:mi mathvariant="italic">UP</mml:mi>
  97                     <mml:mo>″</mml:mo>
  98                     </mml:msup>
  99                     <mml:mo>=</mml:mo>
 100                     <mml:mfrac>
 101                         <mml:mi mathvariant="italic">UP</mml:mi>
 102                         <mml:mfenced open="" close="">
 103                             <mml:mfenced open="&#x2225;" close="&#x2225;">
 104                                 <mml:mi mathvariant="italic">UP</mml:mi>
 105                             </mml:mfenced>
 106                         </mml:mfenced>
 107                     </mml:mfrac>
 108                 </mml:mrow>
 109             </mml:math></div><p>
 110         </p><p>
 111         </p><p>
 112             Finally, let
 113             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 114
 115                 <mml:mrow>
 116                     <mml:mi mathvariant="italic">s</mml:mi>
 117                     <mml:mo>=</mml:mo>
 118                     <mml:mrow>
 119                         <mml:mi mathvariant="italic">f</mml:mi>
 120                         <mml:mo>×</mml:mo>
 121                         <mml:msup><mml:mi mathvariant="italic">UP</mml:mi>
 122                         <mml:mo>″</mml:mo>
 123                         </mml:msup>
 124                     </mml:mrow>
 125                 </mml:mrow>
 126             </mml:math>,
 127             and
 128             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 129
 130                 <mml:mrow>
 131                     <mml:mi mathvariant="italic">u</mml:mi>
 132                     <mml:mo>=</mml:mo>
 133                     <mml:mrow>
 134                         <mml:mi mathvariant="italic">s</mml:mi>
 135                         <mml:mo>×</mml:mo>
 136                         <mml:mi mathvariant="italic">f</mml:mi>
 137                     </mml:mrow>
 138                 </mml:mrow>
 139             </mml:math>.
 140         </p><p>
 141         </p><p>
 142             M is then constructed as follows:
 143             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 144
 145                 <mml:mrow>
 146                     <mml:mi mathvariant="italic">M</mml:mi>
 147                     <mml:mo>=</mml:mo>
 148                     <mml:mfenced open="(" close=")">
 149                         <mml:mtable>
 150                             <mml:mtr>
 151                                 <mml:mtd>
 152                                     <mml:mrow>
 153                                         <mml:mi mathvariant="italic">s</mml:mi>
 154                                         <mml:mo>⁡</mml:mo>
 155                                         <mml:mfenced open="[" close="]">
 156                                             <mml:mn>0</mml:mn>
 157                                         </mml:mfenced>
 158                                     </mml:mrow>
 159                                 </mml:mtd>
 160                                 <mml:mtd>
 161                                     <mml:mrow>
 162                                         <mml:mi mathvariant="italic">s</mml:mi>
 163                                         <mml:mo>⁡</mml:mo>
 164                                         <mml:mfenced open="[" close="]">
 165                                             <mml:mn>1</mml:mn>
 166                                         </mml:mfenced>
 167                                     </mml:mrow>
 168                                 </mml:mtd>
 169                                 <mml:mtd>
 170                                     <mml:mrow>
 171                                         <mml:mi mathvariant="italic">s</mml:mi>
 172                                         <mml:mo>⁡</mml:mo>
 173                                         <mml:mfenced open="[" close="]">
 174                                             <mml:mn>2</mml:mn>
 175                                         </mml:mfenced>
 176                                     </mml:mrow>
 177                                 </mml:mtd>
 178                                 <mml:mtd>
 179                                     <mml:mn>0</mml:mn>
 180                                 </mml:mtd>
 181                             </mml:mtr>
 182                             <mml:mtr>
 183                                 <mml:mtd>
 184                                     <mml:mrow>
 185                                         <mml:mi mathvariant="italic">u</mml:mi>
 186                                         <mml:mo>⁡</mml:mo>
 187                                         <mml:mfenced open="[" close="]">
 188                                             <mml:mn>0</mml:mn>
 189                                         </mml:mfenced>
 190                                     </mml:mrow>
 191                                 </mml:mtd>
 192                                 <mml:mtd>
 193                                     <mml:mrow>
 194                                         <mml:mi mathvariant="italic">u</mml:mi>
 195                                         <mml:mo>⁡</mml:mo>
 196                                         <mml:mfenced open="[" close="]">
 197                                             <mml:mn>1</mml:mn>
 198                                         </mml:mfenced>
 199                                     </mml:mrow>
 200                                 </mml:mtd>
 201                                 <mml:mtd>
 202                                     <mml:mrow>
 203                                         <mml:mi mathvariant="italic">u</mml:mi>
 204                                         <mml:mo>⁡</mml:mo>
 205                                         <mml:mfenced open="[" close="]">
 206                                             <mml:mn>2</mml:mn>
 207                                         </mml:mfenced>
 208                                     </mml:mrow>
 209                                 </mml:mtd>
 210                                 <mml:mtd>
 211                                     <mml:mn>0</mml:mn>
 212                                 </mml:mtd>
 213                             </mml:mtr>
 214                             <mml:mtr>
 215                                 <mml:mtd>
 216                                     <mml:mrow>
 217                                         <mml:mo>-</mml:mo>
 218                                         <mml:mrow>
 219                                             <mml:mi mathvariant="italic">f</mml:mi>
 220                                             <mml:mo>⁡</mml:mo>
 221                                             <mml:mfenced open="[" close="]">
 222                                                 <mml:mn>0</mml:mn>
 223                                             </mml:mfenced>
 224                                         </mml:mrow>
 225                                     </mml:mrow>
 226                                 </mml:mtd>
 227                                 <mml:mtd>
 228                                     <mml:mrow>
 229                                         <mml:mo>-</mml:mo>
 230                                         <mml:mrow>
 231                                             <mml:mi mathvariant="italic">f</mml:mi>
 232                                             <mml:mo>⁡</mml:mo>
 233                                             <mml:mfenced open="[" close="]">
 234                                                 <mml:mn>1</mml:mn>
 235                                             </mml:mfenced>
 236                                         </mml:mrow>
 237                                     </mml:mrow>
 238                                 </mml:mtd>
 239                                 <mml:mtd>
 240                                     <mml:mrow>
 241                                         <mml:mo>-</mml:mo>
 242                                         <mml:mrow>
 243                                             <mml:mi mathvariant="italic">f</mml:mi>
 244                                             <mml:mo>⁡</mml:mo>
 245                                             <mml:mfenced open="[" close="]">
 246                                                 <mml:mn>2</mml:mn>
 247                                             </mml:mfenced>
 248                                         </mml:mrow>
 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:mn>0</mml:mn>
 258                                 </mml:mtd>
 259                                 <mml:mtd>
 260                                     <mml:mn>0</mml:mn>
 261                                 </mml:mtd>
 262                                 <mml:mtd>
 263                                     <mml:mn>0</mml:mn>
 264                                 </mml:mtd>
 265                                 <mml:mtd>
 266                                     <mml:mn>1</mml:mn>
 267                                 </mml:mtd>
 268                             </mml:mtr>
 269                         </mml:mtable>
 270                     </mml:mfenced>
 271                 </mml:mrow>
 272             </mml:math></div><p>
 273         </p><p>
 274             and <code class="function">gluLookAt</code> is equivalent to
 275             </p><pre class="programlisting">
 276 glMultMatrixf(M);
 277 glTranslated(-eyex, -eyey, -eyez);
 278             </pre><p>
 279         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="seealso"></a><h2>See Also</h2><p>
 280             <a class="citerefentry" href="gluPerspective.xml"><span class="citerefentry"><span class="refentrytitle">gluPerspective</span></span></a>,
 281             <a class="citerefentry" href="glFrustum.xml"><span class="citerefentry"><span class="refentrytitle">glFrustum</span></span></a>
 282         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="Copyright"></a><h2>Copyright</h2><p>
 283             Copyright <span class="trademark"></span>© 1991-2006
 284             Silicon Graphics, Inc. This document is licensed under the SGI
 285             Free Software B License. For details, see
 286             <a class="ulink" href="http://oss.sgi.com/projects/FreeB/" target="_top">http://oss.sgi.com/projects/FreeB/</a>.
 287         </p></div></div></body></html>