Specifies the kind of values that are generated by the evaluator.
Symbolic constants
GL_MAP2_VERTEX_3,
GL_MAP2_VERTEX_4,
GL_MAP2_INDEX,
GL_MAP2_COLOR_4,
GL_MAP2_NORMAL,
GL_MAP2_TEXTURE_COORD_1,
GL_MAP2_TEXTURE_COORD_2,
GL_MAP2_TEXTURE_COORD_3, and
GL_MAP2_TEXTURE_COORD_4 are accepted.
u1, u2
Specify a linear mapping of $u$,
as presented to glEvalCoord2,
to $u hat$,
one of the two variables that are evaluated by the equations specified
by this command. Initially, u1 is 0 and u2 is 1.
ustride
Specifies the number of floats or doubles between
the beginning of control point
$R sub ij$
and the beginning of control point
$R sub { (i+1) j }$,
where $i$ and $j$ are the $u$ and $v$ control point indices, respectively.
This allows control points to be embedded in arbitrary data structures.
The only constraint is that the values for a particular control point
must occupy contiguous memory locations. The initial value of ustride is 0.
uorder
Specifies the dimension of the control point array in the $u$ axis.
Must be positive. The initial value is 1.
v1, v2
Specify a linear mapping of $v$,
as presented to glEvalCoord2,
to $v hat$,
one of the two variables that are evaluated by the equations specified
by this command. Initially, v1 is 0 and v2 is 1.
vstride
Specifies the number of floats or doubles between
the beginning of control point
$R sub ij$
and the beginning of control point
$R sub { i (j+1) }$,
where $i$ and $j$ are the $u$ and $v$ control point indices, respectively.
This allows control points to be embedded in arbitrary data structures.
The only constraint is that the values for a particular control point
must occupy contiguous memory locations. The initial value of vstride is 0.
vorder
Specifies the dimension of the control point array in the $v$ axis.
Must be positive. The initial value is 1.
points
Specifies a pointer to the array of control points.
DESCRIPTION
Evaluators provide a way to use polynomial or rational polynomial mapping
to produce vertices,
normals,
texture coordinates,
and colors.
The values produced by an evaluator are sent on to further stages
of GL processing just as if they had been presented using
glVertex,
glNormal,
glTexCoord, and
glColor commands,
except that the generated values do not update the current normal,
texture coordinates,
or color.
All polynomial or rational polynomial splines of any degree
(up to the maximum degree supported by the GL implementation)
can be described using evaluators.
These include almost all surfaces used in computer graphics,
including B-spline surfaces,
NURBS surfaces,
Bezier surfaces, and so on.
Evaluators define surfaces based on bivariate Bernstein polynomials.
Define $p ( u hat , v hat ) $ as
p ( u hat , v hat ) ~~=~~
down 30 {{size 18 {sum}} from {size 8 {i~=~0}} to {size 9 {n}} } ~
{{size 18 {sum}} from {size 8 {j~=~0}} to {size 9 {m}} } ~
up 15 { B sub i sup n ( u hat ) ~ B sub j sup m ( v hat ) ~ R sub ij }
where $R sub ij$ is a control point,
$B sub i sup n ( u hat )$
is the $i$th Bernstein polynomial of degree
$n$ (uorder = $n ~+~ 1$)
B sub i sup n ( u hat ) ~~=~~ left ( down 20 {cpile { n above i }} ~ right
) u hat sup i ( 1 - u hat ) sup { n - i }
and $B sub j sup m ( v hat )$
is the $j$th Bernstein polynomial of degree $m$ (vorder = $m ~+~ 1$)
B sub j sup m ( v hat ) ~~=~~ left ( ^down 20 {cpile { m above j }} ~^ right ) v hat sup j ( 1 - v hat ) sup { m - j }
Recall that
$0 sup 0 ~==~ 1 $ and $ left ( ^ down 20 {cpile { n above 0 }} ~^ right ) ~~==~~ 1 $
glMap2 is used to define the basis and to specify what kind of values
are produced.
Once defined,
a map can be enabled and disabled by calling glEnable and glDisable
with the map name, one of the nine predefined values for target,
described below.
When glEvalCoord2 presents values $u$ and $v$,
the bivariate Bernstein polynomials are evaluated using $u hat$ and $v hat$,
where
$u hat ~~=~~ {u ~-~ "u1"} over {"u2" ~-~ "u1"}$
$v hat ~~=~~ {v ~-~ "v1"} over {"v2" ~-~ "v1"}$
target is a symbolic constant that indicates what kind of control points
are provided in points,
and what output is generated when the map is evaluated.
It can assume one of nine predefined values:
GL_MAP2_VERTEX_3
Each control point is three floating-point values representing
$x$, $y$, and $z$.
Internal glVertex3 commands are generated when the map is evaluated.
GL_MAP2_VERTEX_4
Each control point is four floating-point values representing
$x$, $y$, $z$, and $w$.
Internal glVertex4 commands are generated when the map is evaluated.
GL_MAP2_INDEX
Each control point is a single floating-point value representing a color index.
Internal glIndex commands are generated when the map is evaluated
but the current index is not updated with the value of these
glIndex commands.
GL_MAP2_COLOR_4
Each control point is four floating-point values representing
red, green, blue, and alpha.
Internal glColor4 commands are generated when the map is
evaluated but the current color is not updated with the value of
these glColor4 commands.
GL_MAP2_NORMAL
Each control point is three floating-point values representing
the $x$, $y$, and $z$ components of a normal vector.
Internal glNormal commands are generated when the map is
evaluated but the current normal is not updated with the value of
these glNormal commands.
GL_MAP2_TEXTURE_COORD_1
Each control point is a single floating-point value representing
the $s$ texture coordinate.
Internal
glTexCoord1 commands are generated when the map is evaluated but
the current texture coordinates are not updated with the value
of these glTexCoord commands.
GL_MAP2_TEXTURE_COORD_2
Each control point is two floating-point values representing
the $s$ and $t$ texture coordinates.
Internal
glTexCoord2 commands are generated when the map is evaluated but
the current texture coordinates are not updated with the value
of these glTexCoord commands.
GL_MAP2_TEXTURE_COORD_3
Each control point is three floating-point values representing
the $s$, $t$, and $r$ texture coordinates.
Internal glTexCoord3 commands are generated when the map is
evaluated but the current texture coordinates are not updated with the value
of these glTexCoord commands.
GL_MAP2_TEXTURE_COORD_4
Each control point is four floating-point values representing
the $s$, $t$, $r$, and $q$ texture coordinates.
Internal
glTexCoord4 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value
of these glTexCoord commands.
ustride,
uorder,
vstride,
vorder, and
points define the array addressing for accessing the control points.
points is the location of the first control point,
which occupies one, two, three, or four contiguous memory locations,
depending on which map is being defined.
There are $ "uorder" ~times~ "vorder" $ control points in the array.
ustride specifies how many float or double locations are skipped to advance
the internal memory pointer from control point
$R sub {i j} $ to control point $R sub {(i+1) j} $.
vstride specifies how many float or double locations are skipped to advance
the internal memory pointer from control point
$R sub {i j} $ to control point $R sub {i (j+1) } $.
NOTES
As is the case with all GL commands that accept pointers to data,
it is as if the contents of points were copied by glMap2 before glMap2
returns.
Changes to the contents of points have no effect after glMap2 is called.
Initially, GL_AUTO_NORMAL is enabled. If GL_AUTO_NORMAL is enabled,
normal vectors are generated when either
GL_MAP2_VERTEX_3 or GL_MAP2_VERTEX_4 is used to generate
vertices.
ERRORS
GL_INVALID_ENUM is generated if target is not an accepted value.
GL_INVALID_VALUE is generated if u1 is equal to u2,
or if v1 is equal to v2.
GL_INVALID_VALUE is generated if either ustride or vstride
is less than the number of values in a control point.
GL_INVALID_VALUE is generated if either uorder or vorder
is less than 1 or greater than the return value of GL_MAX_EVAL_ORDER.
GL_INVALID_OPERATION is generated if glMap2
is executed between the execution of
glBegin
and the corresponding execution of glEnd.
When the GL_ARB_multitexture extension is supported,
GL_INVALID_OPERATION is generated if glMap2 is called and the value
of GL_ACTIVE_TEXTURE_ARB is not GL_TEXTURE0_ARB.
ASSOCIATED GETS
glGetMap glGet with argument GL_MAX_EVAL_ORDER glIsEnabled with argument GL_MAP2_VERTEX_3 glIsEnabled with argument GL_MAP2_VERTEX_4 glIsEnabled with argument GL_MAP2_INDEX glIsEnabled with argument GL_MAP2_COLOR_4 glIsEnabled with argument GL_MAP2_NORMAL glIsEnabled with argument GL_MAP2_TEXTURE_COORD_1 glIsEnabled with argument GL_MAP2_TEXTURE_COORD_2 glIsEnabled with argument GL_MAP2_TEXTURE_COORD_3 glIsEnabled with argument GL_MAP2_TEXTURE_COORD_4
