GLMAP2(3G) UNIX Programmer's Manual 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 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 Rij and the begin-
ning of control point R(i+1)j, where i and j are
the u and v control point indices, respectively.
This allows control points to be embedded in arbi-
trary 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
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is 1.
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 Rij and the begin-
ning of control point Ri(j+1), where i and j are
the u and v control point indices, respectively.
This allows control points to be embedded in arbi-
trary 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.
DESCRIPTION
Evaluators provide a way to use polynomial or rational poly-
nomial mapping to produce vertices, normals, texture coordi-
nates, 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 implementa-
tion) 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(^,^) as m(^) Rij
n m n(^) Bj
p(^,^) = ≥̅ ≥̅n(^)iis the ith Bernstein
polynomialiofadegreeolipoint, Bi0
n (uorder = n + 1) |n |
n(^) = |i |^i(1-^)n-i
m(^) is the jth Bernstein polynomial of degree m
(_v_or_d_er = m + 1)
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|m |
m(^) = |j |^j(1-^)m-j
Bj | |
Recall that |n |
00 _ 1 and |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 ^
and ^, where
______1_
^ = _2__-__v_1_
^ = 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 com-
mands 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
floating-point values representing
red, green, blue, and alpha. Inter-
nal glColor4 commands are generated
when the map is evaluated but the
current color is not updated with
the value of these glColor4 com-
mands.
GL_MAP2_NORMAL Each control point is three
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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_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 but the
current texture coordinates are not
updated with the value of these
glTexCoord commands.
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 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
floating-point values representing
the s, t, and r texture coordi-
nates. Internal glTexCoord3 com-
mands are generated when the map is
evaluated but the current texture
coordinates are not updated with
the value of these glTexCoord com-
mands.
GL_MAP2_TEXTURE_COORD_4 Each control point is four
floating-point values representing
the s, t, r, and q texture coordi-
nates. 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
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control points in the array. ustride specifies how many
float or double locations are skipped to advance the inter-
nal memory pointer from control point Rij to control point
R(i+1)j. vstride specifies how many float or double loca-
tions are skipped to advance the internal memory pointer
from control point Rij to control point Ri(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 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.
ERRORS
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 exe-
cution 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.
ASSOCIATED GETS
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
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SEE ALSO
glBegin(3G), glColor(3G), glEnable(3G), glEvalCoord(3G),
glEvalMesh(3G), glEvalPoint(3G), glMap1(3G), glMapGrid(3G),
glNormal(3G), glTexCoord(3G), glVertex(3G)
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