upstream-man-pages/man2/glEvalMesh.xml

   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="glEvalMesh">
   5     <refmeta>
   6         <refmetainfo>
   7             <copyright>
   8                 <year>1991-2006</year>
   9                 <holder>Silicon Graphics, Inc.</holder>
  10             </copyright>
  11         </refmetainfo>
  12         <refentrytitle>glEvalMesh</refentrytitle>
  13         <manvolnum>3G</manvolnum>
  14     </refmeta>
  15     <refnamediv>
  16         <refname>glEvalMesh</refname>
  17         <refpurpose>compute a one- or two-dimensional grid of points or lines</refpurpose>
  18     </refnamediv>
  19     <refsynopsisdiv><title>C Specification</title>
  20         <funcsynopsis>
  21             <funcprototype>
  22                 <funcdef>void <function>glEvalMesh1</function></funcdef>
  23                 <paramdef>GLenum <parameter>mode</parameter></paramdef>
  24                 <paramdef>GLint <parameter>i1</parameter></paramdef>
  25                 <paramdef>GLint <parameter>i2</parameter></paramdef>
  26             </funcprototype>
  27         </funcsynopsis>
  28     </refsynopsisdiv>
  29     <!-- eqn: ignoring delim $$ -->
  30     <refsect1 id="parameters"><title>Parameters</title>
  31         <variablelist>
  32         <varlistentry>
  33             <term><parameter>mode</parameter></term>
  34             <listitem>
  35                 <para>
  36                     In <function>glEvalMesh1</function>, specifies whether to compute a one-dimensional mesh of points or lines.
  37                     Symbolic constants
  38                     <constant>GL_POINT</constant> and
  39                     <constant>GL_LINE</constant> are accepted.
  40                 </para>
  41             </listitem>
  42         </varlistentry>
  43         <varlistentry>
  44             <term><parameter>i1</parameter></term>
  45             <term><parameter>i2</parameter></term>
  46             <listitem>
  47                 <para>
  48                     Specify the first and last integer values for grid domain variable
  49                     <inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
  50                 </para>
  51             </listitem>
  52         </varlistentry>
  53         </variablelist>
  54     </refsect1>
  55     <refsynopsisdiv><title>C Specification</title>
  56         <funcsynopsis>
  57             <funcprototype>
  58                 <funcdef>void <function>glEvalMesh2</function></funcdef>
  59                 <paramdef>GLenum <parameter>mode</parameter></paramdef>
  60                 <paramdef>GLint <parameter>i1</parameter></paramdef>
  61                 <paramdef>GLint <parameter>i2</parameter></paramdef>
  62                 <paramdef>GLint <parameter>j1</parameter></paramdef>
  63                 <paramdef>GLint <parameter>j2</parameter></paramdef>
  64             </funcprototype>
  65         </funcsynopsis>
  66     </refsynopsisdiv>
  67     <refsect1 id="parameters2"><title>Parameters</title>
  68         <variablelist>
  69         <varlistentry>
  70             <term><parameter>mode</parameter></term>
  71             <listitem>
  72                 <para>
  73                     In <function>glEvalMesh2</function>, specifies whether to compute a two-dimensional mesh of points, lines,
  74                     or polygons.
  75                     Symbolic constants
  76                     <constant>GL_POINT</constant>,
  77                     <constant>GL_LINE</constant>, and
  78                     <constant>GL_FILL</constant> are accepted.
  79                 </para>
  80             </listitem>
  81         </varlistentry>
  82         <varlistentry>
  83             <term><parameter>i1</parameter></term>
  84             <term><parameter>i2</parameter></term>
  85             <listitem>
  86                 <para>
  87                     Specify the first and last integer values for grid domain variable
  88                     <inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
  89                 </para>
  90             </listitem>
  91         </varlistentry>
  92         <varlistentry>
  93             <term><parameter>j1</parameter></term>
  94             <term><parameter>j2</parameter></term>
  95             <listitem>
  96                 <para>
  97                     Specify the first and last integer values for grid domain variable
  98                     <inlineequation><mml:math><mml:mi mathvariant="italic">j</mml:mi></mml:math></inlineequation>.
  99                 </para>
 100             </listitem>
 101         </varlistentry>
 102         </variablelist>
 103     </refsect1>
 104     <refsect1 id="description"><title>Description</title>
 105         <para>
 106             <citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry> and <function>glEvalMesh</function> are used in tandem to efficiently
 107             generate and evaluate a series of evenly-spaced map domain values.
 108             <function>glEvalMesh</function> steps through the integer domain of a one- or two-dimensional grid,
 109             whose range is the domain of the evaluation maps specified by
 110             <citerefentry><refentrytitle>glMap1</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glMap2</refentrytitle></citerefentry>.
 111             <parameter>mode</parameter> determines whether the resulting vertices are connected as
 112             points,
 113             lines,
 114             or filled polygons.
 115         </para>
 116         <para>
 117             In the one-dimensional case,
 118             <function>glEvalMesh1</function>,
 119             the mesh is generated as if the following code fragment were executed:
 120         </para>
 121         <para>
 122             <programlisting>
 123 glBegin( <parameter>type</parameter> );
 124 for ( i = <parameter>i1</parameter>; i &lt;= <parameter>i2</parameter>; i += 1 )
 125    glEvalCoord1( <mml:math>
 126                       <!-- eqn: i \cdot DELTA u + u sub 1 :-->
 127                       <mml:mrow>
 128                           <mml:mrow>
 129                               <mml:mn>i</mml:mn>
 130                               <mml:mo>&CenterDot;</mml:mo>
 131                               <mml:mo>&Delta;</mml:mo>
 132                               <mml:mi mathvariant="italic">u</mml:mi>
 133                           </mml:mrow>
 134                           <mml:mo>+</mml:mo>
 135                           <mml:msub>
 136                               <mml:mi mathvariant="italic">u</mml:mi>
 137                               <mml:mn>1</mml:mn>
 138                           </mml:msub>
 139                       </mml:mrow>
 140                   </mml:math> );
 141 glEnd();
 142             </programlisting>
 143             where
 144         </para>
 145         <para>
 146             <informalequation><mml:math>
 147                 <!-- eqn: DELTA u  =  (u sub 2  -  u sub 1 )  /  n:-->
 148                 <mml:mrow>
 149                     <mml:mrow>
 150                         <mml:mo>&Delta;</mml:mo>
 151                         <mml:mi mathvariant="italic">u</mml:mi>
 152                     </mml:mrow>
 153                     <mml:mo>=</mml:mo>
 154                     <mml:mfrac>
 155                         <mml:mfenced open="(" close=")">
 156                             <mml:mrow>
 157                                 <mml:msub>
 158                                     <mml:mi mathvariant="italic">u</mml:mi>
 159                                     <mml:mn>2</mml:mn>
 160                                 </mml:msub>
 161                                 <mml:mo>-</mml:mo>
 162                                 <mml:msub>
 163                                     <mml:mi mathvariant="italic">u</mml:mi>
 164                                     <mml:mn>1</mml:mn>
 165                                 </mml:msub>
 166                             </mml:mrow>
 167                         </mml:mfenced>
 168                         <mml:mi mathvariant="italic">n</mml:mi>
 169                     </mml:mfrac>
 170                 </mml:mrow>
 171             </mml:math></informalequation>
 172         </para>
 173         <para>
 174             and
 175             <inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
 176             <inlineequation><mml:math>
 177                 <!-- eqn: u sub 1:-->
 178                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 179                 <mml:mn>1</mml:mn>
 180                 </mml:msub>
 181             </mml:math></inlineequation>,
 182             and
 183             <inlineequation><mml:math>
 184                 <!-- eqn: u sub 2:-->
 185                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 186                 <mml:mn>2</mml:mn>
 187                 </mml:msub>
 188             </mml:math></inlineequation>
 189             are the arguments to the most recent
 190             <citerefentry><refentrytitle>glMapGrid1</refentrytitle></citerefentry> command.
 191             <emphasis>type</emphasis> is <constant>GL_POINTS</constant> if <parameter>mode</parameter> is <constant>GL_POINT</constant>,
 192             or <constant>GL_LINES</constant> if <parameter>mode</parameter> is <constant>GL_LINE</constant>.
 193         </para>
 194         <para>
 195             The one absolute numeric requirement is that if
 196             <inlineequation><mml:math>
 197                 <!-- eqn: i  =  n:-->
 198                 <mml:mrow>
 199                     <mml:mi mathvariant="italic">i</mml:mi>
 200                     <mml:mo>=</mml:mo>
 201                     <mml:mi mathvariant="italic">n</mml:mi>
 202                 </mml:mrow>
 203             </mml:math></inlineequation>,
 204             then the
 205             value computed from
 206             <inlineequation><mml:math>
 207                 <!-- eqn: i cdot DELTA u  +  u sub 1:-->
 208                 <mml:mrow>
 209                     <mml:mrow>
 210                         <mml:mi mathvariant="italic">i</mml:mi>
 211                         <mml:mo>&CenterDot;</mml:mo>
 212                         <mml:mrow>
 213                             <mml:mo>&Delta;</mml:mo>
 214                             <mml:mi mathvariant="italic">u</mml:mi>
 215                         </mml:mrow>
 216                     </mml:mrow>
 217                     <mml:mo>+</mml:mo>
 218                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 219                     <mml:mn>1</mml:mn>
 220                     </mml:msub>
 221                 </mml:mrow>
 222             </mml:math></inlineequation>
 223             is exactly
 224             <inlineequation><mml:math>
 225                 <!-- eqn: u sub 2:-->
 226                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 227                 <mml:mn>2</mml:mn>
 228                 </mml:msub>
 229             </mml:math></inlineequation>.
 230         </para>
 231         <para>
 232             In the two-dimensional case, <function>glEvalMesh2</function>, let
 233             .cp
 234             <informalequation><mml:math>
 235                 <!-- eqn: DELTA u  =    ( u sub 2  -  u sub 1 )  /  n:-->
 236                 <mml:mrow>
 237                     <mml:mrow>
 238                         <mml:mo>&Delta;</mml:mo>
 239                         <mml:mi mathvariant="italic">u</mml:mi>
 240                     </mml:mrow>
 241                     <mml:mo>=</mml:mo>
 242                     <mml:mfrac>
 243                         <mml:mfenced open="(" close=")">
 244                             <mml:mrow>
 245                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 246                                 <mml:mn>2</mml:mn>
 247                                 </mml:msub>
 248                                 <mml:mo>-</mml:mo>
 249                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 250                                 <mml:mn>1</mml:mn>
 251                                 </mml:msub>
 252                             </mml:mrow>
 253                         </mml:mfenced>
 254                         <mml:mi mathvariant="italic">n</mml:mi>
 255                     </mml:mfrac>
 256                 </mml:mrow>
 257             </mml:math></informalequation>
 258         </para>
 259         <para>
 260             <informalequation><mml:math>
 261                 <!-- eqn: DELTA v  =    ( v sub 2  -  v sub 1 )  /  m:-->
 262                 <mml:mrow>
 263                     <mml:mrow>
 264                         <mml:mo>&Delta;</mml:mo>
 265                         <mml:mi mathvariant="italic">v</mml:mi>
 266                     </mml:mrow>
 267                     <mml:mo>=</mml:mo>
 268                     <mml:mfrac>
 269                         <mml:mfenced open="(" close=")">
 270                             <mml:mrow>
 271                                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 272                                 <mml:mn>2</mml:mn>
 273                                 </mml:msub>
 274                                 <mml:mo>-</mml:mo>
 275                                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 276                                 <mml:mn>1</mml:mn>
 277                                 </mml:msub>
 278                             </mml:mrow>
 279                         </mml:mfenced>
 280                         <mml:mi mathvariant="italic">m</mml:mi>
 281                     </mml:mfrac>
 282                 </mml:mrow>
 283             </mml:math></informalequation>
 284         </para>
 285         <para>
 286             where
 287             <inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
 288             <inlineequation><mml:math>
 289                 <!-- eqn: u sub 1:-->
 290                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 291                 <mml:mn>1</mml:mn>
 292                 </mml:msub>
 293             </mml:math></inlineequation>,
 294             <inlineequation><mml:math>
 295                 <!-- eqn: u sub 2:-->
 296                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 297                 <mml:mn>2</mml:mn>
 298                 </mml:msub>
 299             </mml:math></inlineequation>,
 300             <inlineequation><mml:math><mml:mi mathvariant="italic">m</mml:mi></mml:math></inlineequation>,
 301             <inlineequation><mml:math>
 302                 <!-- eqn: v sub 1:-->
 303                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 304                 <mml:mn>1</mml:mn>
 305                 </mml:msub>
 306             </mml:math></inlineequation>,
 307             and
 308             <inlineequation><mml:math>
 309                 <!-- eqn: v sub 2:-->
 310                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 311                 <mml:mn>2</mml:mn>
 312                 </mml:msub>
 313             </mml:math></inlineequation>
 314             are the
 315             arguments to the most recent <citerefentry><refentrytitle>glMapGrid2</refentrytitle></citerefentry> command.  Then, if
 316             <parameter>mode</parameter> is <constant>GL_FILL</constant>, the <function>glEvalMesh2</function> command is equivalent
 317             to:
 318         </para>
 319         <para>
 320             <programlisting>
 321 for ( j = <parameter>j1</parameter>; j &lt; <parameter>j2</parameter>; j += 1 ) {
 322    glBegin( GL_QUAD_STRIP );
 323    for ( i = <parameter>i1</parameter>; i &lt;= <parameter>i2</parameter>; i += 1 ) {
 324       glEvalCoord2( <mml:math>
 325                         <!-- i \cdot DELTA u + u sub 1 :-->
 326                         <mml:mrow>
 327                             <mml:mrow>
 328                                 <mml:mn>i</mml:mn>
 329                                 <mml:mo>&CenterDot;</mml:mo>
 330                                 <mml:mo>&Delta;</mml:mo>
 331                                 <mml:mi mathvariant="italic">u</mml:mi>
 332                             </mml:mrow>
 333                             <mml:mo>+</mml:mo>
 334                             <mml:msub>
 335                                 <mml:mi mathvariant="italic">u</mml:mi>
 336                                 <mml:mn>1</mml:mn>
 337                             </mml:msub>
 338                             <mml:mo>,</mml:mo>
 339                             <!-- j \cdot DELTA v + v sub 1 :-->
 340                             <mml:mrow>
 341                                 <mml:mn>j</mml:mn>
 342                                 <mml:mo>&CenterDot;</mml:mo>
 343                                 <mml:mo>&Delta;</mml:mo>
 344                                 <mml:mi mathvariant="italic">v</mml:mi>
 345
 346                             </mml:mrow>
 347                             <mml:mo>+</mml:mo>
 348                             <mml:msub>
 349                                 <mml:mi mathvariant="italic">v</mml:mi>
 350                                 <mml:mn>1</mml:mn>
 351                             </mml:msub>
 352                         </mml:mrow>
 353                     </mml:math> );
 354       glEvalCoord2( <mml:math>
 355                         <!-- i \cdot DELTA u + u sub 1, :-->
 356                         <mml:mrow>
 357                             <mml:mrow>
 358                                 <mml:mn>i</mml:mn>
 359                                 <mml:mo>&CenterDot;</mml:mo>
 360                                 <mml:mo>&Delta;</mml:mo>
 361                                 <mml:mi mathvariant="italic">u</mml:mi>
 362                             </mml:mrow>
 363                             <mml:mo>+</mml:mo>
 364                             <mml:msub>
 365                                 <mml:mi mathvariant="italic">u</mml:mi>
 366                                 <mml:mn>1</mml:mn>
 367                             </mml:msub>
 368                             <mml:mo>,</mml:mo>
 369                             <!-- (j + 1) \cdot DELTA v + v sub 1 :-->
 370                             <mml:mrow>
 371                                 <mml:mrow>
 372                                     <mml:mfenced open="(" close=")">
 373                                         <mml:mrow>
 374                                             <mml:mn>j</mml:mn>
 375                                             <mml:mo>+</mml:mo>
 376                                             <mml:mn>1</mml:mn>
 377                                         </mml:mrow>
 378                                     </mml:mfenced>
 379                                 </mml:mrow>
 380                                 <mml:mo>&CenterDot;</mml:mo>
 381                                 <mml:mo>&Delta;</mml:mo>
 382                                 <mml:mi mathvariant="italic">v</mml:mi>
 383                             </mml:mrow>
 384                             <mml:mo>+</mml:mo>
 385                             <mml:msub>
 386                                 <mml:mi mathvariant="italic">v</mml:mi>
 387                                 <mml:mn>1</mml:mn>
 388                             </mml:msub>
 389                         </mml:mrow>
 390                     </mml:math> );
 391    }
 392    glEnd();
 393 }
 394             </programlisting>
 395         </para>
 396         <para>
 397             If <parameter>mode</parameter> is <constant>GL_LINE</constant>, then a call to <function>glEvalMesh2</function> is equivalent to:
 398         </para>
 399         <para>
 400             <programlisting>
 401 for ( j = <parameter>j1</parameter>; j &lt;= <parameter>j2</parameter>; j += 1 ) {
 402    glBegin( GL_LINE_STRIP );
 403    for ( i = <parameter>i1</parameter>; i &lt;= <parameter>i2</parameter>; i += 1 )
 404       glEvalCoord2( <mml:math>
 405                         <!-- i \cdot DELTA u + u sub 1 :-->
 406                         <mml:mrow>
 407                             <mml:mrow>
 408                                 <mml:mn>i</mml:mn>
 409                                 <mml:mo>&CenterDot;</mml:mo>
 410                                 <mml:mo>&Delta;</mml:mo>
 411                                 <mml:mi mathvariant="italic">u</mml:mi>
 412                             </mml:mrow>
 413                             <mml:mo>+</mml:mo>
 414                             <mml:msub>
 415                                 <mml:mi mathvariant="italic">u</mml:mi>
 416                                 <mml:mn>1</mml:mn>
 417                             </mml:msub>
 418                             <mml:mo>,</mml:mo>
 419                             <!-- i \cdot DELTA v + v sub 1 :-->
 420                             <mml:mrow>
 421                                 <mml:mn>j</mml:mn>
 422                                 <mml:mo>&CenterDot;</mml:mo>
 423                                 <mml:mo>&Delta;</mml:mo>
 424                                 <mml:mi mathvariant="italic">v</mml:mi>
 425                             </mml:mrow>
 426                             <mml:mo>+</mml:mo>
 427                             <mml:msub>
 428                                 <mml:mi mathvariant="italic">v</mml:mi>
 429                                 <mml:mn>1</mml:mn>
 430                             </mml:msub>
 431                         </mml:mrow>
 432                     </mml:math> );
 433    glEnd();
 434 }
 435
 436 for ( i = <parameter>i1</parameter>;  i &lt;= <parameter>i2</parameter>; i += 1 ) {
 437    glBegin( GL_LINE_STRIP );
 438    for ( j = <parameter>j1</parameter>; j &lt;= <parameter>j1</parameter>; j += 1 )
 439       glEvalCoord2( <mml:math>
 440                         <!-- i \cdot DELTA u + u sub 1 :-->
 441                         <mml:mrow>
 442                             <mml:mrow>
 443                                 <mml:mn>i</mml:mn>
 444                                 <mml:mo>&CenterDot;</mml:mo>
 445                                 <mml:mo>&Delta;</mml:mo>
 446                                 <mml:mi mathvariant="italic">u</mml:mi>
 447                             </mml:mrow>
 448                             <mml:mo>+</mml:mo>
 449                             <mml:msub>
 450                                 <mml:mi mathvariant="italic">u</mml:mi>
 451                                 <mml:mn>1</mml:mn>
 452                             </mml:msub>
 453                             <mml:mo>,</mml:mo>
 454                             <!-- i \cdot DELTA v + v sub 1 :-->
 455                             <mml:mrow>
 456                                 <mml:mn>j</mml:mn>
 457                                 <mml:mo>&CenterDot;</mml:mo>
 458                                 <mml:mo>&Delta;</mml:mo>
 459                                 <mml:mi mathvariant="italic">v</mml:mi>
 460                             </mml:mrow>
 461                             <mml:mo>+</mml:mo>
 462                             <mml:msub>
 463                                 <mml:mi mathvariant="italic">v</mml:mi>
 464                                 <mml:mn>1</mml:mn>
 465                             </mml:msub>
 466                         </mml:mrow>
 467                     </mml:math> );
 468    glEnd();
 469 }
 470             </programlisting>
 471         </para>
 472         <para>
 473             And finally, if <parameter>mode</parameter> is <constant>GL_POINT</constant>, then a call to
 474             <function>glEvalMesh2</function> is equivalent to:
 475         </para>
 476         <para>
 477             <programlisting>
 478 glBegin( GL_POINTS );
 479 for ( j = <parameter>j1</parameter>; j &lt;= <parameter>j2</parameter>; j += 1 )
 480    for ( i = <parameter>i1</parameter>; i &lt;= <parameter>i2</parameter>; i += 1 )
 481       glEvalCoord2( <mml:math>
 482                         <!-- i \cdot DELTA u + u sub 1 :-->
 483                         <mml:mrow>
 484                             <mml:mrow>
 485                                 <mml:mn>i</mml:mn>
 486                                 <mml:mo>&CenterDot;</mml:mo>
 487                                 <mml:mo>&Delta;</mml:mo>
 488                                 <mml:mi mathvariant="italic">u</mml:mi>
 489                             </mml:mrow>
 490                             <mml:mo>+</mml:mo>
 491                             <mml:msub>
 492                                 <mml:mi mathvariant="italic">u</mml:mi>
 493                                 <mml:mn>1</mml:mn>
 494                             </mml:msub>
 495                             <mml:mo>,</mml:mo>
 496                             <!-- i \cdot DELTA v + v sub 1 :-->
 497                             <mml:mrow>
 498                                 <mml:mn>j</mml:mn>
 499                                 <mml:mo>&CenterDot;</mml:mo>
 500                                 <mml:mo>&Delta;</mml:mo>
 501                                 <mml:mi mathvariant="italic">v</mml:mi>
 502                             </mml:mrow>
 503                             <mml:mo>+</mml:mo>
 504                             <mml:msub>
 505                                 <mml:mi mathvariant="italic">v</mml:mi>
 506                                 <mml:mn>1</mml:mn>
 507                             </mml:msub>
 508                         </mml:mrow>
 509                     </mml:math> );
 510 glEnd();
 511             </programlisting>
 512         </para>
 513         <para>
 514             In all three cases, the only absolute numeric requirements are that if
 515             <inlineequation><mml:math>
 516                 <!-- eqn: i = n:-->
 517                 <mml:mrow>
 518                     <mml:mi mathvariant="italic">i</mml:mi>
 519                     <mml:mo>=</mml:mo>
 520                     <mml:mi mathvariant="italic">n</mml:mi>
 521                 </mml:mrow>
 522             </mml:math></inlineequation>,
 523             then the value computed from
 524             <inlineequation><mml:math>
 525                 <!-- eqn: i cdot DELTA u  +  u sub 1:-->
 526                 <mml:mrow>
 527                     <mml:mrow>
 528                         <mml:mi mathvariant="italic">i</mml:mi>
 529                         <mml:mo>&CenterDot;</mml:mo>
 530                         <mml:mrow>
 531                             <mml:mo>&Delta;</mml:mo>
 532                             <mml:mi mathvariant="italic">u</mml:mi>
 533                         </mml:mrow>
 534                     </mml:mrow>
 535                     <mml:mo>+</mml:mo>
 536                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 537                     <mml:mn>1</mml:mn>
 538                     </mml:msub>
 539                 </mml:mrow>
 540             </mml:math></inlineequation>
 541             is exactly
 542             <inlineequation><mml:math>
 543                 <!-- eqn: u sub 2:-->
 544                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 545                 <mml:mn>2</mml:mn>
 546                 </mml:msub>
 547             </mml:math></inlineequation>,
 548             and if
 549             <inlineequation><mml:math>
 550                 <!-- eqn: j = m:-->
 551                 <mml:mrow>
 552                     <mml:mi mathvariant="italic">j</mml:mi>
 553                     <mml:mo>=</mml:mo>
 554                     <mml:mi mathvariant="italic">m</mml:mi>
 555                 </mml:mrow>
 556             </mml:math></inlineequation>,
 557             then the value computed from
 558             <inlineequation><mml:math>
 559                 <!-- eqn: j  cdot  DELTA v  +  v sub 1:-->
 560                 <mml:mrow>
 561                     <mml:mrow>
 562                         <mml:mi mathvariant="italic">j</mml:mi>
 563                         <mml:mo>&CenterDot;</mml:mo>
 564                         <mml:mrow>
 565                             <mml:mo>&Delta;</mml:mo>
 566                             <mml:mi mathvariant="italic">v</mml:mi>
 567                         </mml:mrow>
 568                     </mml:mrow>
 569                     <mml:mo>+</mml:mo>
 570                     <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 571                     <mml:mn>1</mml:mn>
 572                     </mml:msub>
 573                 </mml:mrow>
 574             </mml:math></inlineequation>
 575             is exactly
 576             <inlineequation><mml:math>
 577                 <!-- eqn: v sub 2:-->
 578                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 579                 <mml:mn>2</mml:mn>
 580                 </mml:msub>
 581             </mml:math></inlineequation>.
 582         </para>
 583     </refsect1>
 584     <refsect1 id="errors"><title>Errors</title>
 585         <para>
 586             <constant>GL_INVALID_ENUM</constant> is generated if <parameter>mode</parameter> is not an accepted value.
 587         </para>
 588         <para>
 589             <constant>GL_INVALID_OPERATION</constant> is generated if <function>glEvalMesh</function>
 590             is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry>
 591             and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>.
 592         </para>
 593     </refsect1>
 594     <refsect1 id="associatedgets"><title>Associated Gets</title>
 595         <para>
 596             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_DOMAIN</constant>
 597         </para>
 598         <para>
 599             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_DOMAIN</constant>
 600         </para>
 601         <para>
 602             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_SEGMENTS</constant>
 603         </para>
 604         <para>
 605             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_SEGMENTS</constant>
 606         </para>
 607     </refsect1>
 608     <refsect1 id="seealso"><title>See Also</title>
 609         <para>
 610             <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry>,
 611             <citerefentry><refentrytitle>glEvalCoord</refentrytitle></citerefentry>,
 612             <citerefentry><refentrytitle>glEvalPoint</refentrytitle></citerefentry>,
 613             <citerefentry><refentrytitle>glMap1</refentrytitle></citerefentry>,
 614             <citerefentry><refentrytitle>glMap2</refentrytitle></citerefentry>,
 615             <citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry>
 616         </para>
 617     </refsect1>
 618     <refsect1 id="Copyright"><title>Copyright</title>
 619         <para>
 620             Copyright <trademark class="copyright"></trademark> 1991-2006
 621             Silicon Graphics, Inc. This document is licensed under the SGI
 622             Free Software B License. For details, see
 623             <ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>.
 624         </para>
 625     </refsect1>
 626 </refentry>