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,v)=∑18i=08n9∑18j=08m9Bin(u)Bjm(v)Rij
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 = $n ~+~ 1$)
Bin(u)=(ni)ui(1-u)n-i
and $B sub j sup m ( v hat )$ is the $j$th Bernstein polynomial of degree $m$ (
vorder = $m ~+~ 1$)
Bjm(v)=(mj)vj(1-v)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.