glMap2, glMap2d, glMap2f - define a two-dimensional evaluator
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 );
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. 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. Specifies
the number of floats or doubles between the beginning of
control point R[i][j] 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. Specifies the dimension of the control
point array in the u axis. Must be positive. The initial
value is 1. 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. Specifies the number of
floats or doubles between the beginning of control point
R[i]j 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.
Specifies the dimension of the control point array in the
v axis. Must be positive. The initial value is 1. 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 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
n m p ( u hat , v hat ) = sum sum
B[i]^n(u hat) B[j]^m(v hat) R[ij]
i=0 j=0
where R[i]j is a control point, B[i] sup n ( u hat ) is
the ith Bernstein polynomial of degree n (uorder = n + 1)
B[i]^n(u hat) = n above i u hat^i(1 - u hat)^n-i
and B[j]^m ( v hat ) is the jth Bernstein polynomial of
degree m (vorder = m + 1) B[j]^m(v hat) = m above j v
hat^j(1 - v hat)^m-j
Recall that 0^0 = 1 and n above = 0 == 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: Each control point is three floating-point
values representing x, y, and z. Internal glVertex3()
commands are generated when the map is evaluated.
Each control point is four floating-point values representing
x, y, z, and w. Internal glVertex4() commands are
generated when the map is evaluated. 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. 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.
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. 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. 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. 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. 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) ].
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.
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.
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
glBegin(3), glColor(3), glEnable(3), glEvalCoord(3), glEvalMesh(3), glEvalPoint(3), glMap1(3), glMapGrid(3),
glNormal(3), glTexCoord(3), glVertex(3)
glMap(3G)
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