glMap1d(3)
NAME
glMap1d, glMap1f - define a one-dimensional evaluator
C SPECIFICATION
void glMap1d( GLenum target,
GLdouble u1,
GLdouble u2,
GLint stride,
GLint order,
const GLdouble *points )
void glMap1f( GLenum target,
GLfloat u1,
GLfloat u2,
GLint stride,
GLint order,
const GLfloat *points )
delim $$
PARAMETERS
target Specifies the kind of values that are generated by the evalua-
tor. Symbolic constants GL_MAP1_VERTEX_3, GL_MAP1_VERTEX_4,
GL_MAP1_INDEX, GL_MAP1_COLOR_4, GL_MAP1_NORMAL,
GL_MAP1_TEXTURE_COORD_1, GL_MAP1_TEXTURE_COORD_2,
GL_MAP1_TEXTURE_COORD_3, and GL_MAP1_TEXTURE_COORD_4 are
accepted.
u1, u2 Specify a linear mapping of $u$, as presented to glEvalCoord1,
to $u hat$, the variable that is evaluated by the equations
specified by this command.
stride Specifies the number of floats or doubles between the beginning
of one control point and the beginning of the next one in the
data structure referenced in points. 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.
order Specifies the number of control points. Must be positive.
points Specifies a pointer to the array of control points.
DESCRIPTION
Evaluators provide a way to use polynomial or rational polynomial map-
ping to produce vertices, normals, texture coordinates, and colors.
The values produced by an evaluator are sent 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 splines used in computer
graphics: B-splines, Bezier curves, Hermite splines, and so on.
Evaluators define curves based on Bernstein polynomials. Define $p ( u
hat ^) $ as
$p ( u hat ^) ~~=~~ up 10 { sum from i=0 to n } B sub i sup n ( u hat
^) R sub i$
where $R sub i$ is a control point and $B sub i sup n ( u hat ^)$ is
the $i$th Bernstein polynomial of degree $n$ (order = $n ~+~ 1$):
$B sub i sup n ( u hat ^) ~~=~~ left ( down 20 {cpile { n above i }} ~~
right ) u hat sup i ( 1 - u hat ^) sup { n - i }$
Recall that
$0 sup 0 ~==~ 1 $ and $ left ( down 20 {cpile { n above ~0 }} ~~ right
) ~~==~~ 1 $
glMap1 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 call-
ing glEnable and glDisable with the map name, one of the nine prede-
fined values for target described below. glEvalCoord1 evaluates the
one-dimensional maps that are enabled. When
glEvalCoord1 presents a value $u$, the Bernstein functions are evalu-
ated using $u hat$, where
$u hat ~~=~~ {u ~-~ "u1"} over {"u2" ~-~ "u1"}$
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_MAP1_VERTEX_3 Each control point is three floating-point
values representing $x$, $y$, and $z$. Inter-
nal glVertex3 commands are generated when the
map is evaluated.
GL_MAP1_VERTEX_4 Each control point is four floating-point val-
ues representing $x$, $y$, $z$, and $w$.
Internal glVertex4 commands are generated when
the map is evaluated.
GL_MAP1_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_MAP1_COLOR_4 Each control point is four floating-point val-
ues 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_MAP1_NORMAL Each control point is three floating-point
values representing the $x$, $y$, and $z$ com-
ponents of a normal vector. Internal glNormal
commands are generated when the map is evalu-
ated but the current normal is not updated
with the value of these glNormal commands.
GL_MAP1_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 coor-
dinates are not updated with the value of
these glTexCoord commands.
GL_MAP1_TEXTURE_COORD_2 Each control point is two floating-point val-
ues representing the $s$ and $t$ texture coor-
dinates. Internal
glTexCoord2 commands are generated when the
map is evaluated but the current texture coor-
dinates are not updated with the value of
these glTexCoord commands.
GL_MAP1_TEXTURE_COORD_3 Each control point is three floating-point
values representing the $s$, $t$, and $r$ tex-
ture coordinates. Internal glTexCoord3 com-
mands are generated when the map is evaluated
but the current texture coordinates are not
updated with the value of these glTexCoord
commands.
GL_MAP1_TEXTURE_COORD_4 Each control point is four floating-point val-
ues representing the $s$, $t$, $r$, and $q$
texture coordinates. Internal
glTexCoord4 commands are generated when the
map is evaluated but the current texture coor-
dinates are not updated with the value of
these glTexCoord commands.
stride, order, 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. order is the number of con-
trol points in the array. stride specifies how many float or double
locations to advance the internal memory pointer to reach the next con-
trol point.
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 glMap1 before glMap1
returns. Changes to the contents of points have no effect after glMap1
is called.
ERRORS
GL_INVALID_ENUM is generated if target is not an accepted value.
GL_INVALID_VALUE is generated if u1 is equal to u2.
GL_INVALID_VALUE is generated if stride is less than the number of val-
ues in a control point.
GL_INVALID_VALUE is generated if order is less than 1 or greater than
the return value of GL_MAX_EVAL_ORDER.
GL_INVALID_OPERATION is generated if glMap1 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 glMap1 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_MAP1_VERTEX_3
glIsEnabled with argument GL_MAP1_VERTEX_4
glIsEnabled with argument GL_MAP1_INDEX
glIsEnabled with argument GL_MAP1_COLOR_4
glIsEnabled with argument GL_MAP1_NORMAL
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_1
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_2
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_3
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_4
SEE ALSO
glBegin(3G), glColor(3G), glEnable(3G), glEvalCoord(3G),
glEvalMesh(3G), glEvalPoint(3G), glMap2(3G), glMapGrid(3G),
glNormal(3G), glTexCoord(3G), glVertex(3G)
GLMAP1(3G)
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