_C_ License Applicability. Except to the extent portions of this file are
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_C_ Software License B, Version 1.1 (the "License"), the contents of this
_C_ file are subject only to the provisions of the License. You may not use
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_C_ 
_C_ Original Code. The Original Code is: OpenGL Sample Implementation,
_C_ Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
_C_ Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
_C_ Copyright in any portions created by third parties is as indicated
_C_ elsewhere herein. All Rights Reserved.
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_C_ Additional Notice Provisions: The application programming interfaces
_C_ established by SGI in conjunction with the Original Code are The
_C_ OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
_C_ April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
_C_ 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
_C_ Window System(R) (Version 1.3), released October 19, 1998. This software
_C_ was created using the OpenGL(R) version 1.2.1 Sample Implementation
_C_ published by SGI, but has not been independently verified as being
_C_ compliant with the OpenGL(R) version 1.2.1 Specification.
_C_
_C_ $Date$ $Revision$
_C_ The first character in this file must be an '_'!
_C_ Anything on a line after _C_ is ignored
_define(_filters,eqn)_C_
_C_      eqn is automatically replaced with neqn for nroff
_header(EvalMesh, compute a one- or two-dimensional grid of points or lines)
_names(EvalMesh1)
.EQ
delim $$
.EN
.SH PARAMETERS
_phead(_param1)
In _cmnd(EvalMesh1), specifies whether to compute a one-dimensional mesh of points or lines.
Symbolic constants
_const(POINT) and
_const(LINE) are accepted.
_phead(_param2 _param3)
Specify the first and last integer values for grid domain variable $i$.
_names(EvalMesh2)
.SH PARAMETERS
_phead(_param1)
In _cmnd(EvalMesh2), specifies whether to compute a two-dimensional mesh of points, lines,
or polygons.
Symbolic constants
_const(POINT),
_const(LINE), and
_const(FILL) are accepted.
_phead(_param2 _param3)
Specify the first and last integer values for grid domain variable $i$.
_phead(_param4 _param5)
Specify the first and last integer values for grid domain variable $j$.
.SH DESCRIPTION
_cmnd(MapGrid) and _cmnd are used in tandem to efficiently
generate and evaluate a series of evenly-spaced map domain values.
_cmnd steps through the integer domain of a one- or two-dimensional grid,
whose range is the domain of the evaluation maps specified by
_cmnd(Map1) and _cmnd(Map2).
_param1(1) determines whether the resulting vertices are connected as
points,
lines,
or filled polygons.
.P
In the one-dimensional case,
_cmnd(EvalMesh1),
the mesh is generated as if the following code fragment were executed:
.nf
.IP
\f7
glBegin( \f2type\f7 );
for ( i = _param2; i <= _param3; i += 1 )
   glEvalCoord1( i$^cdot^DELTA u ~+~ u sub 1$ );
glEnd();
\fP
.RE
.fi
where
.sp
.in
$ DELTA u ~=~ (u sub 2 ~-~ u sub 1 ) ^/^ n$
.sp
.in 0
.P
and $n$, $u sub 1$, and $u sub 2$ are the arguments to the most recent
_cmnd(MapGrid1) command.
\f2type\fP is _const(POINTS) if _param1(1) is _const(POINT),
or _const(LINES) if _param1(1) is _const(LINE).
.P
The one absolute numeric requirement is that if $i ~=~ n$, then the
value computed from $ i^cdot^DELTA u ~+~ u sub 1$ is exactly $u sub 2$.
.P
In the two-dimensional case, _cmnd(EvalMesh2), let 
.nf
.IP
$ DELTA u ~=~ mark ( u sub 2 ~-~ u sub 1 ) ^/^ n$
.sp
$ DELTA v ~=~ lineup ( v sub 2 ~-~ v sub 1 ) ^/^ m$,
.fi
.RE
.P
where $n$, $u sub 1$, $u sub 2$, $m$, $v sub 1$, and $v sub 2$ are the
arguments to the most recent _cmnd(MapGrid2) command.  Then, if
_param1(2) is _const(FILL), the _cmnd(EvalMesh2) command is equivalent
to:
.nf
.IP
\f7
for ( j = _param4; j < _param5; j += 1 ) {
   glBegin( GL_QUAD_STRIP );
   for ( i = _param2; i <= _param3; i += 1 ) {
      glEvalCoord2( i$^cdot^DELTA u ~+~ u sub 1$, j$^cdot^DELTA v ~+~ v sub 1$ );
      glEvalCoord2( i$^cdot^DELTA u ~+~ u sub 1$, (j+1)$^cdot^DELTA v ~+~ v sub 1$ );
   }
   glEnd();
}
\fP
.RE
.fi
.P
If _param1 is _const(LINE), then a call to _cmnd(EvalMesh2) is equivalent to:
.nf
.IP
\f7
for ( j = _param4; j <= _param5; j += 1 ) {
   glBegin( GL_LINE_STRIP );
   for ( i = _param2; i <= _param3; i += 1 )
      glEvalCoord2( i$^cdot^DELTA u ~+~ u sub 1$, j$^cdot^DELTA v ~+~ v sub 1$ );
   glEnd();
}
.sp
for ( i = _param2;  i <= _param3; i += 1 ) {
   glBegin( GL_LINE_STRIP );
   for ( j = _param4; j <= _param4; j += 1 )
      glEvalCoord2( i$^cdot^DELTA u ~+~ u sub 1$, j$^cdot^DELTA v ~+~ v sub 1 $ );
   glEnd();
}
\fP
.RE
.fi
.P
And finally, if _param1 is _const(POINT), then a call to
_cmnd(EvalMesh2) is equivalent to:
.nf
.IP
\f7
glBegin( GL_POINTS );
for ( j = _param4; j <= _param5; j += 1 )
   for ( i = _param2; i <= _param3; i += 1 )
      glEvalCoord2( i$^cdot^DELTA u ~+~ u sub 1$, j$^cdot^DELTA v ~+~ v sub 1$ );
glEnd();
\fP
.RE
.fi
.P
In all three cases, the only absolute numeric requirements are that if $i~=~n$,
then the value computed from $i^cdot^DELTA u ~+~ u sub 1$ is exactly $u
sub 2$, and if $j~=~m$, then the value computed from
$j ^cdot^ DELTA v ~+~ v sub 1$ is exactly $v sub 2$.
.SH ERRORS
_const(INVALID_ENUM) is generated if _param1 is not an accepted value.
.P
_const(INVALID_OPERATION) is generated if _cmnd
is executed between the execution of _cmnd(Begin)
and the corresponding execution of _cmnd(End).
.SH ASSOCIATED GETS
_cmnd(Get) with argument _const(MAP1_GRID_DOMAIN)
.br
_cmnd(Get) with argument _const(MAP2_GRID_DOMAIN)
.br
_cmnd(Get) with argument _const(MAP1_GRID_SEGMENTS)
.br
_cmnd(Get) with argument _const(MAP2_GRID_SEGMENTS)
.SH SEE ALSO
_cmnd(Begin),
_cmnd(EvalCoord),
_cmnd(EvalPoint),
_cmnd(Map1),
_cmnd(Map2),
_cmnd(MapGrid)
