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 )
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,
one of the two variables that is evaluated by the equations
specified by this command.
ustride Specifies the number of floats or doubles between the beginning of
control point R and the beginning of control point R ,
ij (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.
uorder Specifies the dimension of the control point array in the u axis.
Must be positive.
v1, v2 Specify a linear mapping of v, as presented to glEvalCoord2, to v,
one of the two variables that is evaluated by the equations
specified by this command.
vstride Specifies the number of floats or doubles between the beginning of
control point R and the beginning of control point R ,
ij (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.
vorder Specifies the dimension of the control point array in the v axis.
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 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,v) as
n m
--- ---
\ \ n m
p(u,v) = \ \ B (u)B (v) R
/ / i j ij
/ /
--- ---
i=0 j=0
n
where R is a control point, B (u) is the ith Bernstein polynomial of
ij i
degree n (uorder = n+1)
n |n| i n-i
B (u) = | |u (1-u)
i |i|
m
and B (v') is the jth Bernstein polynomial of degree m (vorder = m+1)
j
m |m| j m-j
B (v) = | |v (1-v)
j |j|
Recall that
0 |n|
0 = 1 and | | = 1
|0|
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 and v, where
u - u1
u = -------
u2 - u1
v - v1
v = -------
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. The current index is not updated with
the value of these glIndex commands, however.
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. The current color is not
updated with the value of these glColor4 commands,
however.
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. The current
normal is not updated with the value of these
glNormal commands, however.
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. The current texture
coordinates are not updated with the value of
these glTexCoord commands, however.
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. The current texture
coordinates are not updated with the value of
these glTexCoord commands, however.
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. The current texture
coordinates are not updated with the value of
these glTexCoord commands, however.
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. The current
texture coordinates are not updated with the value
of these glTexCoord commands, however.
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
uorderxvorder control points in the array. ustride tells how many float or
double locations are skipped to advance the internal memory pointer from
control point R to control point R . vstride tells how many float
ij (i+1)j
or double locations are skipped to advance the internal memory pointer from
control point R to control point R .
ij 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 it returned. Changes to the contents of points have no effect after glMap2 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, 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 one or greater than GL_MAX_EVAL_ORDER. GL_INVALID_OPERATION is generated if glMap2 is executed between the execution of glBegin and the corresponding execution of glEnd.
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, glColor, glEnable, glEvalCoord, glEvalMesh, glEvalPoint, glMap1, glMapGrid, glNormal, glTexCoord, glVertex
Introduction | Alphabetic | Specification
Last Edited: Mon, May 22, 1995