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

   1 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "xhtml1-transitional.dtd">
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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>glEvalMesh</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2" /></head><body><div class="refentry" lang="en" xml:lang="en"><a id="glEvalMesh"></a><div class="titlepage"></div><div class="refnamediv"><h2>Name</h2><p>glEvalMesh — compute a one- or two-dimensional grid of points or lines</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">glEvalMesh1</b>(</code></td><td>GLenum  </td><td><var class="pdparam">mode</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">i1</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">i2</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>mode</code></em></span></dt><dd><p>
   4                     In <code class="function">glEvalMesh1</code>, specifies whether to compute a one-dimensional mesh of points or lines.
   5                     Symbolic constants
   6                     <code class="constant">GL_POINT</code> and
   7                     <code class="constant">GL_LINE</code> are accepted.
   8                 </p></dd><dt><span class="term"><em class="parameter"><code>i1</code></em>, </span><span class="term"><em class="parameter"><code>i2</code></em></span></dt><dd><p>
   9                     Specify the first and last integer values for grid domain variable
  10                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">i</mml:mi></mml:math>.
  11                 </p></dd></dl></div></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">glEvalMesh2</b>(</code></td><td>GLenum  </td><td><var class="pdparam">mode</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">i1</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">i2</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">j1</var>, </td></tr><tr><td> </td><td>GLint  </td><td><var class="pdparam">j2</var><code>)</code>;</td></tr></table></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="parameters2"></a><h2>Parameters</h2><div class="variablelist"><dl><dt><span class="term"><em class="parameter"><code>mode</code></em></span></dt><dd><p>
  12                     In <code class="function">glEvalMesh2</code>, specifies whether to compute a two-dimensional mesh of points, lines,
  13                     or polygons.
  14                     Symbolic constants
  15                     <code class="constant">GL_POINT</code>,
  16                     <code class="constant">GL_LINE</code>, and
  17                     <code class="constant">GL_FILL</code> are accepted.
  18                 </p></dd><dt><span class="term"><em class="parameter"><code>i1</code></em>, </span><span class="term"><em class="parameter"><code>i2</code></em></span></dt><dd><p>
  19                     Specify the first and last integer values for grid domain variable
  20                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">i</mml:mi></mml:math>.
  21                 </p></dd><dt><span class="term"><em class="parameter"><code>j1</code></em>, </span><span class="term"><em class="parameter"><code>j2</code></em></span></dt><dd><p>
  22                     Specify the first and last integer values for grid domain variable
  23                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">j</mml:mi></mml:math>.
  24                 </p></dd></dl></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="description"></a><h2>Description</h2><p>
  25             <a class="citerefentry" href="glMapGrid.xml"><span class="citerefentry"><span class="refentrytitle">glMapGrid</span></span></a> and <code class="function">glEvalMesh</code> are used in tandem to efficiently
  26             generate and evaluate a series of evenly-spaced map domain values.
  27             <code class="function">glEvalMesh</code> steps through the integer domain of a one- or two-dimensional grid,
  28             whose range is the domain of the evaluation maps specified by
  29             <a class="citerefentry" href="glMap1.xml"><span class="citerefentry"><span class="refentrytitle">glMap1</span></span></a> and <a class="citerefentry" href="glMap2.xml"><span class="citerefentry"><span class="refentrytitle">glMap2</span></span></a>.
  30             <em class="parameter"><code>mode</code></em> determines whether the resulting vertices are connected as
  31             points,
  32             lines,
  33             or filled polygons.
  34         </p><p>
  35             In the one-dimensional case,
  36             <code class="function">glEvalMesh1</code>,
  37             the mesh is generated as if the following code fragment were executed:
  38         </p><p>
  39             </p><pre class="programlisting">
  40 glBegin( <em class="parameter"><code>type</code></em> );
  41 for ( i = <em class="parameter"><code>i1</code></em>; i &lt;= <em class="parameter"><code>i2</code></em>; i += 1 )
  42    glEvalCoord1( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  43
  44                       <mml:mrow>
  45                           <mml:mrow>
  46                               <mml:mn>i</mml:mn>
  47                               <mml:mo>·</mml:mo>
  48                               <mml:mo>Δ</mml:mo>
  49                               <mml:mi mathvariant="italic">u</mml:mi>
  50                           </mml:mrow>
  51                           <mml:mo>+</mml:mo>
  52                           <mml:msub>
  53                               <mml:mi mathvariant="italic">u</mml:mi>
  54                               <mml:mn>1</mml:mn>
  55                           </mml:msub>
  56                       </mml:mrow>
  57                   </mml:math> );
  58 glEnd();
  59             </pre><p>
  60             where
  61         </p><p>
  62             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  63
  64                 <mml:mrow>
  65                     <mml:mrow>
  66                         <mml:mo>Δ</mml:mo>
  67                         <mml:mi mathvariant="italic">u</mml:mi>
  68                     </mml:mrow>
  69                     <mml:mo>=</mml:mo>
  70                     <mml:mfrac>
  71                         <mml:mfenced open="(" close=")">
  72                             <mml:mrow>
  73                                 <mml:msub>
  74                                     <mml:mi mathvariant="italic">u</mml:mi>
  75                                     <mml:mn>2</mml:mn>
  76                                 </mml:msub>
  77                                 <mml:mo>-</mml:mo>
  78                                 <mml:msub>
  79                                     <mml:mi mathvariant="italic">u</mml:mi>
  80                                     <mml:mn>1</mml:mn>
  81                                 </mml:msub>
  82                             </mml:mrow>
  83                         </mml:mfenced>
  84                         <mml:mi mathvariant="italic">n</mml:mi>
  85                     </mml:mfrac>
  86                 </mml:mrow>
  87             </mml:math></div><p>
  88         </p><p>
  89             and
  90             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">n</mml:mi></mml:math>,
  91             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  92
  93                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
  94                 <mml:mn>1</mml:mn>
  95                 </mml:msub>
  96             </mml:math>,
  97             and
  98             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
  99
 100                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 101                 <mml:mn>2</mml:mn>
 102                 </mml:msub>
 103             </mml:math>
 104             are the arguments to the most recent
 105             <a class="citerefentry" href="glMapGrid1.xml"><span class="citerefentry"><span class="refentrytitle">glMapGrid1</span></span></a> command.
 106             <span class="emphasis"><em>type</em></span> is <code class="constant">GL_POINTS</code> if <em class="parameter"><code>mode</code></em> is <code class="constant">GL_POINT</code>,
 107             or <code class="constant">GL_LINES</code> if <em class="parameter"><code>mode</code></em> is <code class="constant">GL_LINE</code>.
 108         </p><p>
 109             The one absolute numeric requirement is that if
 110             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 111
 112                 <mml:mrow>
 113                     <mml:mi mathvariant="italic">i</mml:mi>
 114                     <mml:mo>=</mml:mo>
 115                     <mml:mi mathvariant="italic">n</mml:mi>
 116                 </mml:mrow>
 117             </mml:math>,
 118             then the
 119             value computed from
 120             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 121
 122                 <mml:mrow>
 123                     <mml:mrow>
 124                         <mml:mi mathvariant="italic">i</mml:mi>
 125                         <mml:mo>·</mml:mo>
 126                         <mml:mrow>
 127                             <mml:mo>Δ</mml:mo>
 128                             <mml:mi mathvariant="italic">u</mml:mi>
 129                         </mml:mrow>
 130                     </mml:mrow>
 131                     <mml:mo>+</mml:mo>
 132                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 133                     <mml:mn>1</mml:mn>
 134                     </mml:msub>
 135                 </mml:mrow>
 136             </mml:math>
 137             is exactly
 138             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 139
 140                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 141                 <mml:mn>2</mml:mn>
 142                 </mml:msub>
 143             </mml:math>.
 144         </p><p>
 145             In the two-dimensional case, <code class="function">glEvalMesh2</code>, let
 146             .cp
 147             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 148
 149                 <mml:mrow>
 150                     <mml:mrow>
 151                         <mml:mo>Δ</mml:mo>
 152                         <mml:mi mathvariant="italic">u</mml:mi>
 153                     </mml:mrow>
 154                     <mml:mo>=</mml:mo>
 155                     <mml:mfrac>
 156                         <mml:mfenced open="(" close=")">
 157                             <mml:mrow>
 158                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 159                                 <mml:mn>2</mml:mn>
 160                                 </mml:msub>
 161                                 <mml:mo>-</mml:mo>
 162                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 163                                 <mml:mn>1</mml:mn>
 164                                 </mml:msub>
 165                             </mml:mrow>
 166                         </mml:mfenced>
 167                         <mml:mi mathvariant="italic">n</mml:mi>
 168                     </mml:mfrac>
 169                 </mml:mrow>
 170             </mml:math></div><p>
 171         </p><p>
 172             </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 173
 174                 <mml:mrow>
 175                     <mml:mrow>
 176                         <mml:mo>Δ</mml:mo>
 177                         <mml:mi mathvariant="italic">v</mml:mi>
 178                     </mml:mrow>
 179                     <mml:mo>=</mml:mo>
 180                     <mml:mfrac>
 181                         <mml:mfenced open="(" close=")">
 182                             <mml:mrow>
 183                                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 184                                 <mml:mn>2</mml:mn>
 185                                 </mml:msub>
 186                                 <mml:mo>-</mml:mo>
 187                                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 188                                 <mml:mn>1</mml:mn>
 189                                 </mml:msub>
 190                             </mml:mrow>
 191                         </mml:mfenced>
 192                         <mml:mi mathvariant="italic">m</mml:mi>
 193                     </mml:mfrac>
 194                 </mml:mrow>
 195             </mml:math></div><p>
 196         </p><p>
 197             where
 198             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">n</mml:mi></mml:math>,
 199             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 200
 201                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 202                 <mml:mn>1</mml:mn>
 203                 </mml:msub>
 204             </mml:math>,
 205             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 206
 207                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 208                 <mml:mn>2</mml:mn>
 209                 </mml:msub>
 210             </mml:math>,
 211             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">m</mml:mi></mml:math>,
 212             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 213
 214                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 215                 <mml:mn>1</mml:mn>
 216                 </mml:msub>
 217             </mml:math>,
 218             and
 219             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 220
 221                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 222                 <mml:mn>2</mml:mn>
 223                 </mml:msub>
 224             </mml:math>
 225             are the
 226             arguments to the most recent <a class="citerefentry" href="glMapGrid2.xml"><span class="citerefentry"><span class="refentrytitle">glMapGrid2</span></span></a> command.  Then, if
 227             <em class="parameter"><code>mode</code></em> is <code class="constant">GL_FILL</code>, the <code class="function">glEvalMesh2</code> command is equivalent
 228             to:
 229         </p><p>
 230             </p><pre class="programlisting">
 231 for ( j = <em class="parameter"><code>j1</code></em>; j &lt; <em class="parameter"><code>j2</code></em>; j += 1 ) {
 232    glBegin( GL_QUAD_STRIP );
 233    for ( i = <em class="parameter"><code>i1</code></em>; i &lt;= <em class="parameter"><code>i2</code></em>; i += 1 ) {
 234       glEvalCoord2( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 235
 236                         <mml:mrow>
 237                             <mml:mrow>
 238                                 <mml:mn>i</mml:mn>
 239                                 <mml:mo>·</mml:mo>
 240                                 <mml:mo>Δ</mml:mo>
 241                                 <mml:mi mathvariant="italic">u</mml:mi>
 242                             </mml:mrow>
 243                             <mml:mo>+</mml:mo>
 244                             <mml:msub>
 245                                 <mml:mi mathvariant="italic">u</mml:mi>
 246                                 <mml:mn>1</mml:mn>
 247                             </mml:msub>
 248                             <mml:mo>,</mml:mo>
 249
 250                             <mml:mrow>
 251                                 <mml:mn>j</mml:mn>
 252                                 <mml:mo>·</mml:mo>
 253                                 <mml:mo>Δ</mml:mo>
 254                                 <mml:mi mathvariant="italic">v</mml:mi>
 255
 256                             </mml:mrow>
 257                             <mml:mo>+</mml:mo>
 258                             <mml:msub>
 259                                 <mml:mi mathvariant="italic">v</mml:mi>
 260                                 <mml:mn>1</mml:mn>
 261                             </mml:msub>
 262                         </mml:mrow>
 263                     </mml:math> );
 264       glEvalCoord2( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 265
 266                         <mml:mrow>
 267                             <mml:mrow>
 268                                 <mml:mn>i</mml:mn>
 269                                 <mml:mo>·</mml:mo>
 270                                 <mml:mo>Δ</mml:mo>
 271                                 <mml:mi mathvariant="italic">u</mml:mi>
 272                             </mml:mrow>
 273                             <mml:mo>+</mml:mo>
 274                             <mml:msub>
 275                                 <mml:mi mathvariant="italic">u</mml:mi>
 276                                 <mml:mn>1</mml:mn>
 277                             </mml:msub>
 278                             <mml:mo>,</mml:mo>
 279
 280                             <mml:mrow>
 281                                 <mml:mrow>
 282                                     <mml:mfenced open="(" close=")">
 283                                         <mml:mrow>
 284                                             <mml:mn>j</mml:mn>
 285                                             <mml:mo>+</mml:mo>
 286                                             <mml:mn>1</mml:mn>
 287                                         </mml:mrow>
 288                                     </mml:mfenced>
 289                                 </mml:mrow>
 290                                 <mml:mo>·</mml:mo>
 291                                 <mml:mo>Δ</mml:mo>
 292                                 <mml:mi mathvariant="italic">v</mml:mi>
 293                             </mml:mrow>
 294                             <mml:mo>+</mml:mo>
 295                             <mml:msub>
 296                                 <mml:mi mathvariant="italic">v</mml:mi>
 297                                 <mml:mn>1</mml:mn>
 298                             </mml:msub>
 299                         </mml:mrow>
 300                     </mml:math> );
 301    }
 302    glEnd();
 303 }
 304             </pre><p>
 305         </p><p>
 306             If <em class="parameter"><code>mode</code></em> is <code class="constant">GL_LINE</code>, then a call to <code class="function">glEvalMesh2</code> is equivalent to:
 307         </p><p>
 308             </p><pre class="programlisting">
 309 for ( j = <em class="parameter"><code>j1</code></em>; j &lt;= <em class="parameter"><code>j2</code></em>; j += 1 ) {
 310    glBegin( GL_LINE_STRIP );
 311    for ( i = <em class="parameter"><code>i1</code></em>; i &lt;= <em class="parameter"><code>i2</code></em>; i += 1 )
 312       glEvalCoord2( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 313
 314                         <mml:mrow>
 315                             <mml:mrow>
 316                                 <mml:mn>i</mml:mn>
 317                                 <mml:mo>·</mml:mo>
 318                                 <mml:mo>Δ</mml:mo>
 319                                 <mml:mi mathvariant="italic">u</mml:mi>
 320                             </mml:mrow>
 321                             <mml:mo>+</mml:mo>
 322                             <mml:msub>
 323                                 <mml:mi mathvariant="italic">u</mml:mi>
 324                                 <mml:mn>1</mml:mn>
 325                             </mml:msub>
 326                             <mml:mo>,</mml:mo>
 327
 328                             <mml:mrow>
 329                                 <mml:mn>j</mml:mn>
 330                                 <mml:mo>·</mml:mo>
 331                                 <mml:mo>Δ</mml:mo>
 332                                 <mml:mi mathvariant="italic">v</mml:mi>
 333                             </mml:mrow>
 334                             <mml:mo>+</mml:mo>
 335                             <mml:msub>
 336                                 <mml:mi mathvariant="italic">v</mml:mi>
 337                                 <mml:mn>1</mml:mn>
 338                             </mml:msub>
 339                         </mml:mrow>
 340                     </mml:math> );
 341    glEnd();
 342 }
 343
 344 for ( i = <em class="parameter"><code>i1</code></em>;  i &lt;= <em class="parameter"><code>i2</code></em>; i += 1 ) {
 345    glBegin( GL_LINE_STRIP );
 346    for ( j = <em class="parameter"><code>j1</code></em>; j &lt;= <em class="parameter"><code>j1</code></em>; j += 1 )
 347       glEvalCoord2( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 348
 349                         <mml:mrow>
 350                             <mml:mrow>
 351                                 <mml:mn>i</mml:mn>
 352                                 <mml:mo>·</mml:mo>
 353                                 <mml:mo>Δ</mml:mo>
 354                                 <mml:mi mathvariant="italic">u</mml:mi>
 355                             </mml:mrow>
 356                             <mml:mo>+</mml:mo>
 357                             <mml:msub>
 358                                 <mml:mi mathvariant="italic">u</mml:mi>
 359                                 <mml:mn>1</mml:mn>
 360                             </mml:msub>
 361                             <mml:mo>,</mml:mo>
 362
 363                             <mml:mrow>
 364                                 <mml:mn>j</mml:mn>
 365                                 <mml:mo>·</mml:mo>
 366                                 <mml:mo>Δ</mml:mo>
 367                                 <mml:mi mathvariant="italic">v</mml:mi>
 368                             </mml:mrow>
 369                             <mml:mo>+</mml:mo>
 370                             <mml:msub>
 371                                 <mml:mi mathvariant="italic">v</mml:mi>
 372                                 <mml:mn>1</mml:mn>
 373                             </mml:msub>
 374                         </mml:mrow>
 375                     </mml:math> );
 376    glEnd();
 377 }
 378             </pre><p>
 379         </p><p>
 380             And finally, if <em class="parameter"><code>mode</code></em> is <code class="constant">GL_POINT</code>, then a call to
 381             <code class="function">glEvalMesh2</code> is equivalent to:
 382         </p><p>
 383             </p><pre class="programlisting">
 384 glBegin( GL_POINTS );
 385 for ( j = <em class="parameter"><code>j1</code></em>; j &lt;= <em class="parameter"><code>j2</code></em>; j += 1 )
 386    for ( i = <em class="parameter"><code>i1</code></em>; i &lt;= <em class="parameter"><code>i2</code></em>; i += 1 )
 387       glEvalCoord2( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 388
 389                         <mml:mrow>
 390                             <mml:mrow>
 391                                 <mml:mn>i</mml:mn>
 392                                 <mml:mo>·</mml:mo>
 393                                 <mml:mo>Δ</mml:mo>
 394                                 <mml:mi mathvariant="italic">u</mml:mi>
 395                             </mml:mrow>
 396                             <mml:mo>+</mml:mo>
 397                             <mml:msub>
 398                                 <mml:mi mathvariant="italic">u</mml:mi>
 399                                 <mml:mn>1</mml:mn>
 400                             </mml:msub>
 401                             <mml:mo>,</mml:mo>
 402
 403                             <mml:mrow>
 404                                 <mml:mn>j</mml:mn>
 405                                 <mml:mo>·</mml:mo>
 406                                 <mml:mo>Δ</mml:mo>
 407                                 <mml:mi mathvariant="italic">v</mml:mi>
 408                             </mml:mrow>
 409                             <mml:mo>+</mml:mo>
 410                             <mml:msub>
 411                                 <mml:mi mathvariant="italic">v</mml:mi>
 412                                 <mml:mn>1</mml:mn>
 413                             </mml:msub>
 414                         </mml:mrow>
 415                     </mml:math> );
 416 glEnd();
 417             </pre><p>
 418         </p><p>
 419             In all three cases, the only absolute numeric requirements are that if
 420             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 421
 422                 <mml:mrow>
 423                     <mml:mi mathvariant="italic">i</mml:mi>
 424                     <mml:mo>=</mml:mo>
 425                     <mml:mi mathvariant="italic">n</mml:mi>
 426                 </mml:mrow>
 427             </mml:math>,
 428             then the value computed from
 429             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 430
 431                 <mml:mrow>
 432                     <mml:mrow>
 433                         <mml:mi mathvariant="italic">i</mml:mi>
 434                         <mml:mo>·</mml:mo>
 435                         <mml:mrow>
 436                             <mml:mo>Δ</mml:mo>
 437                             <mml:mi mathvariant="italic">u</mml:mi>
 438                         </mml:mrow>
 439                     </mml:mrow>
 440                     <mml:mo>+</mml:mo>
 441                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 442                     <mml:mn>1</mml:mn>
 443                     </mml:msub>
 444                 </mml:mrow>
 445             </mml:math>
 446             is exactly
 447             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 448
 449                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 450                 <mml:mn>2</mml:mn>
 451                 </mml:msub>
 452             </mml:math>,
 453             and if
 454             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 455
 456                 <mml:mrow>
 457                     <mml:mi mathvariant="italic">j</mml:mi>
 458                     <mml:mo>=</mml:mo>
 459                     <mml:mi mathvariant="italic">m</mml:mi>
 460                 </mml:mrow>
 461             </mml:math>,
 462             then the value computed from
 463             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 464
 465                 <mml:mrow>
 466                     <mml:mrow>
 467                         <mml:mi mathvariant="italic">j</mml:mi>
 468                         <mml:mo>·</mml:mo>
 469                         <mml:mrow>
 470                             <mml:mo>Δ</mml:mo>
 471                             <mml:mi mathvariant="italic">v</mml:mi>
 472                         </mml:mrow>
 473                     </mml:mrow>
 474                     <mml:mo>+</mml:mo>
 475                     <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 476                     <mml:mn>1</mml:mn>
 477                     </mml:msub>
 478                 </mml:mrow>
 479             </mml:math>
 480             is exactly
 481             <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
 482
 483                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 484                 <mml:mn>2</mml:mn>
 485                 </mml:msub>
 486             </mml:math>.
 487         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="errors"></a><h2>Errors</h2><p>
 488             <code class="constant">GL_INVALID_ENUM</code> is generated if <em class="parameter"><code>mode</code></em> is not an accepted value.
 489         </p><p>
 490             <code class="constant">GL_INVALID_OPERATION</code> is generated if <code class="function">glEvalMesh</code>
 491             is executed between the execution of <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a>
 492             and the corresponding execution of <a class="citerefentry" href="glEnd.xml"><span class="citerefentry"><span class="refentrytitle">glEnd</span></span></a>.
 493         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="associatedgets"></a><h2>Associated Gets</h2><p>
 494             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MAP1_GRID_DOMAIN</code>
 495         </p><p>
 496             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MAP2_GRID_DOMAIN</code>
 497         </p><p>
 498             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MAP1_GRID_SEGMENTS</code>
 499         </p><p>
 500             <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MAP2_GRID_SEGMENTS</code>
 501         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="seealso"></a><h2>See Also</h2><p>
 502             <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a>,
 503             <a class="citerefentry" href="glEvalCoord.xml"><span class="citerefentry"><span class="refentrytitle">glEvalCoord</span></span></a>,
 504             <a class="citerefentry" href="glEvalPoint.xml"><span class="citerefentry"><span class="refentrytitle">glEvalPoint</span></span></a>,
 505             <a class="citerefentry" href="glMap1.xml"><span class="citerefentry"><span class="refentrytitle">glMap1</span></span></a>,
 506             <a class="citerefentry" href="glMap2.xml"><span class="citerefentry"><span class="refentrytitle">glMap2</span></span></a>,
 507             <a class="citerefentry" href="glMapGrid.xml"><span class="citerefentry"><span class="refentrytitle">glMapGrid</span></span></a>
 508         </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="Copyright"></a><h2>Copyright</h2><p>
 509             Copyright <span class="trademark"></span>© 1991-2006
 510             Silicon Graphics, Inc. This document is licensed under the SGI
 511             Free Software B License. For details, see
 512             <a class="ulink" href="http://oss.sgi.com/projects/FreeB/" target="_top">http://oss.sgi.com/projects/FreeB/</a>.
 513         </p></div></div></body></html>