| 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> |