upstream-man-pages/man2/glEvalPoint.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="glEvalPoint">
   5     <refmeta>
   6         <refmetainfo>
   7             <copyright>
   8                 <year>1991-2006</year>
   9                 <holder>Silicon Graphics, Inc.</holder>
  10             </copyright>
  11         </refmetainfo>
  12         <refentrytitle>glEvalPoint</refentrytitle>
  13         <manvolnum>3G</manvolnum>
  14     </refmeta>
  15     <refnamediv>
  16         <refname>glEvalPoint</refname>
  17         <refpurpose>generate and evaluate a single point in a mesh</refpurpose>
  18     </refnamediv>
  19     <refsynopsisdiv><title>C Specification</title>
  20         <funcsynopsis>
  21             <funcprototype>
  22                 <funcdef>void <function>glEvalPoint1</function></funcdef>
  23                 <paramdef>GLint <parameter>i</parameter></paramdef>
  24             </funcprototype>
  25         </funcsynopsis>
  26         <funcsynopsis>
  27             <funcprototype>
  28                 <funcdef>void <function>glEvalPoint2</function></funcdef>
  29                 <paramdef>GLint <parameter>i</parameter></paramdef>
  30                 <paramdef>GLint <parameter>j</parameter></paramdef>
  31             </funcprototype>
  32         </funcsynopsis>
  33     </refsynopsisdiv>
  34     <!-- eqn: ignoring delim $$ -->
  35     <refsect1 id="parameters"><title>Parameters</title>
  36         <variablelist>
  37         <varlistentry>
  38             <term><parameter>i</parameter></term>
  39             <listitem>
  40                 <para>
  41                     Specifies the integer value for grid domain variable
  42                     <inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
  43                 </para>
  44             </listitem>
  45         </varlistentry>
  46         <varlistentry>
  47             <term><parameter>j</parameter></term>
  48             <listitem>
  49                 <para>
  50                     Specifies the integer value for grid domain variable
  51                     <inlineequation><mml:math><mml:mi mathvariant="italic">j</mml:mi></mml:math></inlineequation>
  52                     (<function>glEvalPoint2</function> only).
  53                 </para>
  54             </listitem>
  55         </varlistentry>
  56         </variablelist>
  57     </refsect1>
  58     <refsect1 id="description"><title>Description</title>
  59         <para>
  60             <citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry> are used in tandem to efficiently
  61             generate and evaluate a series of evenly spaced map domain values.
  62             <function>glEvalPoint</function> can be used to evaluate a single grid point in the same gridspace
  63             that is traversed by <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry>.
  64             Calling <function>glEvalPoint1</function> is equivalent to calling
  65             <programlisting>
  66 glEvalCoord1( <mml:math>
  67                   <!-- eqn: i \cdot DELTA u + u sub 1 :-->
  68                   <mml:mrow>
  69                       <mml:mrow>
  70                           <mml:mn>i</mml:mn>
  71                           <mml:mo>&CenterDot;</mml:mo>
  72                           <mml:mo>&Delta;</mml:mo>
  73                           <mml:mi mathvariant="italic">u</mml:mi>
  74                       </mml:mrow>
  75                       <mml:mo>+</mml:mo>
  76                       <mml:msub>
  77                           <mml:mi mathvariant="italic">u</mml:mi>
  78                           <mml:mn>1</mml:mn>
  79                       </mml:msub>
  80                   </mml:mrow>
  81               </mml:math> );
  82          </programlisting>
  83             where
  84             <informalequation><mml:math>
  85                 <!-- eqn: DELTA u  =  ( u sub 2 - u sub 1 )  /  n:-->
  86                 <mml:mrow>
  87                     <mml:mrow>
  88                         <mml:mo>&Delta;</mml:mo>
  89                         <mml:mi mathvariant="italic">u</mml:mi>
  90                     </mml:mrow>
  91                     <mml:mo>=</mml:mo>
  92                     <mml:mfrac>
  93                         <mml:mfenced open="(" close=")">
  94                             <mml:mrow>
  95                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
  96                                 <mml:mn>2</mml:mn>
  97                                 </mml:msub>
  98                                 <mml:mo>-</mml:mo>
  99                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 100                                 <mml:mn>1</mml:mn>
 101                                 </mml:msub>
 102                             </mml:mrow>
 103                         </mml:mfenced>
 104                         <mml:mi mathvariant="italic">n</mml:mi>
 105                     </mml:mfrac>
 106                 </mml:mrow>
 107             </mml:math></informalequation>
 108         </para>
 109         <para>
 110             and
 111             <inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
 112             <inlineequation><mml:math>
 113                 <!-- eqn: u sub 1:-->
 114                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 115                 <mml:mn>1</mml:mn>
 116                 </mml:msub>
 117             </mml:math></inlineequation>,
 118             and
 119             <inlineequation><mml:math>
 120                 <!-- eqn: u sub 2:-->
 121                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 122                 <mml:mn>2</mml:mn>
 123                 </mml:msub>
 124             </mml:math></inlineequation>
 125             are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid1</refentrytitle></citerefentry> command.
 126             The one absolute numeric requirement is that if
 127             <inlineequation><mml:math>
 128                 <!-- eqn: i = n:-->
 129                 <mml:mrow>
 130                     <mml:mi mathvariant="italic">i</mml:mi>
 131                     <mml:mo>=</mml:mo>
 132                     <mml:mi mathvariant="italic">n</mml:mi>
 133                 </mml:mrow>
 134             </mml:math></inlineequation>,
 135             then the value computed from
 136             <inlineequation><mml:math>
 137                 <!-- eqn: i  cdot  DELTA u  +  u sub 1:-->
 138                 <mml:mrow>
 139                     <mml:mrow>
 140                         <mml:mi mathvariant="italic">i</mml:mi>
 141                         <mml:mo>&CenterDot;</mml:mo>
 142                         <mml:mrow>
 143                             <mml:mo>&Delta;</mml:mo>
 144                             <mml:mi mathvariant="italic">u</mml:mi>
 145                         </mml:mrow>
 146                     </mml:mrow>
 147                     <mml:mo>+</mml:mo>
 148                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 149                     <mml:mn>1</mml:mn>
 150                     </mml:msub>
 151                 </mml:mrow>
 152             </mml:math></inlineequation>
 153             is exactly
 154             <inlineequation><mml:math>
 155                 <!-- eqn: u sub 2:-->
 156                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 157                 <mml:mn>2</mml:mn>
 158                 </mml:msub>
 159             </mml:math></inlineequation>.
 160         </para>
 161         <para>
 162             In the two-dimensional case, <function>glEvalPoint2</function>, let
 163         </para>
 164         <para>
 165             <informalequation><mml:math>
 166                 <!-- eqn: DELTA u  =    ( u sub 2 - u sub 1 )  /  n:-->
 167                 <mml:mrow>
 168                     <mml:mrow>
 169                         <mml:mo>&Delta;</mml:mo>
 170                         <mml:mi mathvariant="italic">u</mml:mi>
 171                     </mml:mrow>
 172                     <mml:mo>=</mml:mo>
 173                     <mml:mfrac>
 174                         <mml:mfenced open="(" close=")">
 175                             <mml:mrow>
 176                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 177                                 <mml:mn>2</mml:mn>
 178                                 </mml:msub>
 179                                 <mml:mo>-</mml:mo>
 180                                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 181                                 <mml:mn>1</mml:mn>
 182                                 </mml:msub>
 183                             </mml:mrow>
 184                         </mml:mfenced>
 185                         <mml:mi mathvariant="italic">n</mml:mi>
 186                     </mml:mfrac>
 187                 </mml:mrow>
 188             </mml:math></informalequation>
 189             <para>
 190                 <informalequation><mml:math>
 191                     <!-- eqn: DELTA v  =    ( v sub 2 - v sub 1 )  /  m:-->
 192                     <mml:mrow>
 193                         <mml:mrow>
 194                             <mml:mo>&Delta;</mml:mo>
 195                             <mml:mi mathvariant="italic">v</mml:mi>
 196                         </mml:mrow>
 197                         <mml:mo>=</mml:mo>
 198                         <mml:mfrac>
 199                             <mml:mfenced open="(" close=")">
 200                                 <mml:mrow>
 201                                     <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 202                                     <mml:mn>2</mml:mn>
 203                                     </mml:msub>
 204                                     <mml:mo>-</mml:mo>
 205                                     <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 206                                     <mml:mn>1</mml:mn>
 207                                     </mml:msub>
 208                                 </mml:mrow>
 209                             </mml:mfenced>
 210                             <mml:mi mathvariant="italic">m</mml:mi>
 211                         </mml:mfrac>
 212                     </mml:mrow>
 213                 </mml:math></informalequation>
 214             </para>
 215         </para>
 216         <para>
 217             where
 218             <inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
 219             <inlineequation><mml:math>
 220                 <!-- eqn: u sub 1:-->
 221                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 222                 <mml:mn>1</mml:mn>
 223                 </mml:msub>
 224             </mml:math></inlineequation>,
 225             <inlineequation><mml:math>
 226                 <!-- eqn: u sub 2:-->
 227                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 228                 <mml:mn>2</mml:mn>
 229                 </mml:msub>
 230             </mml:math></inlineequation>,
 231             <inlineequation><mml:math><mml:mi mathvariant="italic">m</mml:mi></mml:math></inlineequation>,
 232             <inlineequation><mml:math>
 233                 <!-- eqn: v sub 1:-->
 234                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 235                 <mml:mn>1</mml:mn>
 236                 </mml:msub>
 237             </mml:math></inlineequation>,
 238             and
 239             <inlineequation><mml:math>
 240                 <!-- eqn: v sub 2:-->
 241                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 242                 <mml:mn>2</mml:mn>
 243                 </mml:msub>
 244             </mml:math></inlineequation>
 245             are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid2</refentrytitle></citerefentry> command.
 246             Then the <function>glEvalPoint2</function> command is equivalent to calling
 247             <programlisting>
 248 glEvalCoord2( <mml:math>
 249                         <!-- i \cdot DELTA u + u sub 1 :-->
 250                         <mml:mrow>
 251                             <mml:mrow>
 252                                 <mml:mn>i</mml:mn>
 253                                 <mml:mo>&CenterDot;</mml:mo>
 254                                 <mml:mo>&Delta;</mml:mo>
 255                                 <mml:mi mathvariant="italic">u</mml:mi>
 256                             </mml:mrow>
 257                             <mml:mo>+</mml:mo>
 258                             <mml:msub>
 259                                 <mml:mi mathvariant="italic">u</mml:mi>
 260                                 <mml:mn>1</mml:mn>
 261                             </mml:msub>
 262                             <mml:mo>,</mml:mo>
 263                             <!-- j \cdot DELTA v + v sub 1 :-->
 264                             <mml:mrow>
 265                                 <mml:mn>j</mml:mn>
 266                                 <mml:mo>&CenterDot;</mml:mo>
 267                                 <mml:mo>&Delta;</mml:mo>
 268                                 <mml:mi mathvariant="italic">v</mml:mi>
 269
 270                             </mml:mrow>
 271                             <mml:mo>+</mml:mo>
 272                             <mml:msub>
 273                                 <mml:mi mathvariant="italic">v</mml:mi>
 274                                 <mml:mn>1</mml:mn>
 275                             </mml:msub>
 276                         </mml:mrow>
 277                     </mml:math> );
 278             </programlisting>
 279             The only absolute numeric requirements are that if
 280             <inlineequation><mml:math>
 281                 <!-- eqn: i = n:-->
 282                 <mml:mrow>
 283                     <mml:mi mathvariant="italic">i</mml:mi>
 284                     <mml:mo>=</mml:mo>
 285                     <mml:mi mathvariant="italic">n</mml:mi>
 286                 </mml:mrow>
 287             </mml:math></inlineequation>,
 288             then the value computed from
 289             <inlineequation><mml:math>
 290                 <!-- eqn: i  cdot DELTA u  +  u sub 1:-->
 291                 <mml:mrow>
 292                     <mml:mrow>
 293                         <mml:mi mathvariant="italic">i</mml:mi>
 294                         <mml:mo>&CenterDot;</mml:mo>
 295                         <mml:mrow>
 296                             <mml:mo>&Delta;</mml:mo>
 297                             <mml:mi mathvariant="italic">u</mml:mi>
 298                         </mml:mrow>
 299                     </mml:mrow>
 300                     <mml:mo>+</mml:mo>
 301                     <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 302                     <mml:mn>1</mml:mn>
 303                     </mml:msub>
 304                 </mml:mrow>
 305             </mml:math></inlineequation>
 306             is exactly
 307             <inlineequation><mml:math>
 308                 <!-- eqn: u sub 2:-->
 309                 <mml:msub><mml:mi mathvariant="italic">u</mml:mi>
 310                 <mml:mn>2</mml:mn>
 311                 </mml:msub>
 312             </mml:math></inlineequation>,
 313             and if
 314             <inlineequation><mml:math>
 315                 <!-- eqn: j = m:-->
 316                 <mml:mrow>
 317                     <mml:mi mathvariant="italic">j</mml:mi>
 318                     <mml:mo>=</mml:mo>
 319                     <mml:mi mathvariant="italic">m</mml:mi>
 320                 </mml:mrow>
 321             </mml:math></inlineequation>,
 322             then the value computed from
 323             <inlineequation><mml:math>
 324                 <!-- eqn: j  cdot DELTA v  +  v sub 1:-->
 325                 <mml:mrow>
 326                     <mml:mrow>
 327                         <mml:mi mathvariant="italic">j</mml:mi>
 328                         <mml:mo>&CenterDot;</mml:mo>
 329                         <mml:mrow>
 330                             <mml:mo>&Delta;</mml:mo>
 331                             <mml:mi mathvariant="italic">v</mml:mi>
 332                         </mml:mrow>
 333                     </mml:mrow>
 334                     <mml:mo>+</mml:mo>
 335                     <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 336                     <mml:mn>1</mml:mn>
 337                     </mml:msub>
 338                 </mml:mrow>
 339             </mml:math></inlineequation>
 340             is exactly
 341             <inlineequation><mml:math>
 342                 <!-- eqn: v sub 2:-->
 343                 <mml:msub><mml:mi mathvariant="italic">v</mml:mi>
 344                 <mml:mn>2</mml:mn>
 345                 </mml:msub>
 346             </mml:math></inlineequation>.
 347         </para>
 348     </refsect1>
 349     <refsect1 id="associatedgets"><title>Associated Gets</title>
 350         <para>
 351             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_DOMAIN</constant>
 352         </para>
 353         <para>
 354             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_DOMAIN</constant>
 355         </para>
 356         <para>
 357             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_SEGMENTS</constant>
 358         </para>
 359         <para>
 360             <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_SEGMENTS</constant>
 361         </para>
 362     </refsect1>
 363     <refsect1 id="seealso"><title>See Also</title>
 364         <para>
 365             <citerefentry><refentrytitle>glEvalCoord</refentrytitle></citerefentry>,
 366             <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry>,
 367             <citerefentry><refentrytitle>glMap1</refentrytitle></citerefentry>,
 368             <citerefentry><refentrytitle>glMap2</refentrytitle></citerefentry>,
 369             <citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry>
 370         </para>
 371     </refsect1>
 372     <refsect1 id="Copyright"><title>Copyright</title>
 373         <para>
 374             Copyright <trademark class="copyright"></trademark> 1991-2006
 375             Silicon Graphics, Inc. This document is licensed under the SGI
 376             Free Software B License. For details, see
 377             <ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>.
 378         </para>
 379     </refsect1>
 380 </refentry>