glMap2(3G) OpenGL Reference glMap2(3G)
glMap2d, glMap2f  define a twodimensional 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
^, 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 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. 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.
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glMap2(3G) OpenGL Reference glMap2(3G)
v1, v2 Specify a linear mapping of v, as presented to glEvalCoord2, to
^, 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 and the beginning of control point R ,
ij 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.
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 Bspline surfaces, NURBS surfaces, Bezier surfaces, and so on.
Evaluators define surfaces based on bivariate Bernstein polynomials.
Define p(^,^) as
m n m
n B (^) B (^) R
p(^,^) = R i j ij
R
j = 0
i = 0
n
where R is a control point, B (^) is the ith Bernstein polynomial of
ij i
degree
n (uorder = n + 1)
( )
n n i ni
B (^) =  ^ (1^)
i
(i )
m
and B (^) is the jth Bernstein polynomial of degree m (vorder = m + 1)
j
( )
m m j mj
B (^) =  ^ (1^)
j
(j )
Recall that
( )
0 n
0 = 1 and   = 1
(0 )
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glMap2(3G) OpenGL Reference glMap2(3G)
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 ^ and ^,
where
_______
^ =
u2  u1
_______
^ =
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 floatingpoint
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 floatingpoint 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 floatingpoint
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 floatingpoint 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 floatingpoint
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 floatingpoint
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.
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glMap2(3G) OpenGL Reference glMap2(3G)
GL_MAP2_TEXTURE_COORD_2 Each control point is two floatingpoint 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 floatingpoint
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 floatingpoint 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 x 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 to control point R . vstride
ij (i+1)j
specifies how many float 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 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.
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glMap2(3G) OpenGL Reference glMap2(3G)
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
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