GLdoublevoidu1, GLdoubleu2, GLintustride, GLintuorder, GLdoublev1, GLdoublev2, GLintvstride, GLintvorder, const GLdouble*points)

GLfloatu1, GLfloatu2, GLintustride, GLintuorder, GLfloatv1, GLfloatv2, GLintvstride, GLintvorder, const GLfloat*points)

**eqn not supported**

*target*- 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.

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

**eqn not supported**

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* = $n ~+~ 1$)

**eqn not supported**

and $B sub j sup m ( v hat )$
is the $j$th Bernstein polynomial of degree $m$ (*vorder* = $m ~+~ 1$)

**eqn
not supported**

Recall that

**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

*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) } $.

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.

**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**.