GLMAP2(3G)GLMAP2(3G)NAME
glMap2d, glMap2f - define a two-dimensional evaluator
C SPECIFICATION
void glMap2d( GLenum target,
GLdouble u1,
GLdouble u2,
GLint ustride,
GLint uorder,
GLdouble v1,
GLdouble v2,
GLint vstride,
GLint vorder,
const GLdouble *points )
void glMap2f( GLenum target,
GLfloat u1,
GLfloat u2,
GLint ustride,
GLint uorder,
GLfloat v1,
GLfloat v2,
GLint vstride,
GLint vorder,
const GLfloat *points )
delim $$
PARAMETERS
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.
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
SEE ALSOglBegin(3G), glColor(3G), glEnable(3G), glEvalCoord(3G),
glEvalMesh(3G), glEvalPoint(3G), glMap1(3G), glMapGrid(3G),
glNormal(3G), glTexCoord(3G), glVertex(3G)
March 1, 2011
