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glMap1d, glMap1f - define a one-dimensional evaluator
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 )
eqn not supported
- target
- Specifies the kind of values that are
generated by the evaluator. 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.
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 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 calling glEnable and glDisable with
the map name, one of the nine predefined values for target described below.
glEvalCoord1 evaluates the one-dimensional maps that are enabled. When
glEvalCoord1 presents a value $u$, the Bernstein functions are evaluated
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 $z$. Internal
glVertex3 commands are generated when the map is evaluated.
- GL_MAP1_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_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
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_MAP1_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_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 coordinates are not updated with the value of these glTexCoord
commands.
- GL_MAP1_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_MAP1_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_MAP1_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.
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 control points in
the array. stride specifies how many float or double locations to advance
the internal memory pointer to reach the next control point.
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.
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 values 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.
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
glBegin(3G)
,
glColor(3G)
, glEnable(3G)
, glEvalCoord(3G)
, glEvalMesh(3G)
, glEvalPoint(3G)
,
glMap2(3G)
, glMapGrid(3G)
, glNormal(3G)
, glTexCoord(3G)
, glVertex(3G)
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