glMap2(3G) OpenGL Reference glMap2(3G)
NAME
glMap2d, glMap2f - define a two-dimensional evaluator
C SPECIFICATION
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 )
PARAMETERS
target Specifies the kind of values that are generated by the
evaluator. Symbolic constants GLMAP2VERTEX3,
GLMAP2VERTEX4, GLMAP2INDEX, GLMAP2COLOR4,
GLMAP2NORMAL, GLMAP2TEXTURECOORD1,
GLMAP2TEXTURECOORD2, GLMAP2TEXTURECOORD3, and
GLMAP2TEXTURECOORD4 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.
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glMap2(3G) OpenGL Reference glMap2(3G)
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(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.
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.
DESCRIPTION
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
p(u',v') = sum from i=0 to n sum from j=0 to m B (u')*B (v')*R
i j ij
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 )
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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 u' and v',
where
u' = (u - u1) / (u2 - u1)
v' = (v - v1) / (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:
GLMAP2VERTEX3 Each control point is three floating-point
values representing x, y, and z. Internal
glVertex3 commands are generated when the map is
evaluated.
GLMAP2VERTEX4 Each control point is four floating-point values
representing x, y, z, and w. Internal glVertex4
commands are generated when the map is
evaluated.
GLMAP2INDEX 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.
GLMAP2COLOR4 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.
GLMAP2NORMAL 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.
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glMap2(3G) OpenGL Reference glMap2(3G)
GLMAP2TEXTURECOORD1 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.
GLMAP2TEXTURECOORD2 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.
GLMAP2TEXTURECOORD3 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.
GLMAP2TEXTURECOORD4 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
ij (i+1)j
float or double locations are skipped to advance the internal memory
pointer from control point R to control point R .
ij i(j+1)
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 glMap2 before it returned.
Changes to the contents of points have no effect after glMap2 is called.
ERRORS
GLINVALIDENUM is generated if target is not an accepted value.
GLINVALIDVALUE is generated if u1 is equal to u2, or if v1 is equal to
v2.
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glMap2(3G) OpenGL Reference glMap2(3G)
GLINVALIDVALUE is generated if either ustride or vstride is less than
the number of values in a control point.
GLINVALIDVALUE is generated if either uorder or vorder is less than one
or greater than GLMAXEVALORDER.
GLINVALIDOPERATION is generated if glMap2 is executed between the
execution of glBegin and the corresponding execution of glEnd.
ASSOCIATED GETS
glGetMap
glGet with argument GLMAXEVALORDER
glIsEnabled with argument GLMAP2VERTEX3
glIsEnabled with argument GLMAP2VERTEX4
glIsEnabled with argument GLMAP2INDEX
glIsEnabled with argument GLMAP2COLOR4
glIsEnabled with argument GLMAP2NORMAL
glIsEnabled with argument GLMAP2TEXTURECOORD1
glIsEnabled with argument GLMAP2TEXTURECOORD2
glIsEnabled with argument GLMAP2TEXTURECOORD3
glIsEnabled with argument GLMAP2TEXTURECOORD4
SEE ALSO
glBegin, glColor, glEnable, glEvalCoord, glEvalMesh, glEvalPoint, glMap1,
glMapGrid, glNormal, glTexCoord, glVertex
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