fglMap2(3G) OpenGL Reference fglMap2(3G)NAME
fglMap2d, fglMap2f - define a two-dimensional evaluator
FORTRAN SPECIFICATION
SUBROUTINE fglMap2d( INTEGER*4 target,
REAL*4 u1,
REAL*4 u2,
INTEGER*4 ustride,
INTEGER*4 uorder,
REAL*4 v1,
REAL*4 v2,
INTEGER*4 vstride,
INTEGER*4 vorder,
CHARACTER*8 points )
SUBROUTINE fglMap2f( INTEGER*4 target,
REAL*4 u1,
REAL*4 u2,
INTEGER*4 ustride,
INTEGER*4 uorder,
REAL*4 v1,
REAL*4 v2,
INTEGER*4 vstride,
INTEGER*4 vorder,
CHARACTER*8 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 fglEvalCoord2, 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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fglMap2(3G) OpenGL Reference fglMap2(3G)
v1, v2 Specify a linear mapping of v, as presented to fglEvalCoord2, 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.
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 fglVertex, fglNormal,
fglTexCoord, and fglColor 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(^,^) 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 n-i
B (^) = | |^ (1-^)
i
(i )
m
and B (^) is the jth Bernstein polynomial of degree m (vorder = m + 1)
j
( )
m m j m-j
B (^) = | |^ (1-^)
j
(j )
Recall that
( )
0 n
0 = 1 and | | = 1
(0 )
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fglMap2(3G) OpenGL Reference fglMap2(3G)
fglMap2 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
fglEnable and fglDisable with the map name, one of the nine predefined
values for target, described below. When fglEvalCoord2 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 floating-point
values representing x, y, and z. Internal
fglVertex3 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
fglVertex4 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
fglIndex commands are generated when the map is
evaluated but the current index is not updated
with the value of these fglIndex commands.
GL_MAP2_COLOR_4 Each control point is four floating-point values
representing red, green, blue, and alpha.
Internal fglColor4 commands are generated when
the map is evaluated but the current color is
not updated with the value of these fglColor4
commands.
GL_MAP2_NORMAL Each control point is three floating-point
values representing the x, y, and z components
of a normal vector. Internal fglNormal commands
are generated when the map is evaluated but the
current normal is not updated with the value of
these fglNormal commands.
GL_MAP2_TEXTURE_COORD_1 Each control point is a single floating-point
value representing the s texture coordinate.
Internal fglTexCoord1 commands are generated
when the map is evaluated but the current
texture coordinates are not updated with the
value of these fglTexCoord commands.
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fglMap2(3G) OpenGL Reference fglMap2(3G)
GL_MAP2_TEXTURE_COORD_2 Each control point is two floating-point values
representing the s and t texture coordinates.
Internal fglTexCoord2 commands are generated
when the map is evaluated but the current
texture coordinates are not updated with the
value of these fglTexCoord commands.
GL_MAP2_TEXTURE_COORD_3 Each control point is three floating-point
values representing the s, t, and r texture
coordinates. Internal fglTexCoord3 commands are
generated when the map is evaluated but the
current texture coordinates are not updated with
the value of these fglTexCoord commands.
GL_MAP2_TEXTURE_COORD_4 Each control point is four floating-point values
representing the s, t, r, and q texture
coordinates. Internal fglTexCoord4 commands are
generated when the map is evaluated but the
current texture coordinates are not updated with
the value of these fglTexCoord 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)
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 fglMap2 before fglMap2
returns. Changes to the contents of points have no effect after fglMap2
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.
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fglMap2(3G) OpenGL Reference fglMap2(3G)
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 fglMap2 is executed between the
execution of fglBegin and the corresponding execution of fglEnd.
ASSOCIATED GETS
fglGetMap
fglGet with argument GL_MAX_EVAL_ORDER
fglIsEnabled with argument GL_MAP2_VERTEX_3
fglIsEnabled with argument GL_MAP2_VERTEX_4
fglIsEnabled with argument GL_MAP2_INDEX
fglIsEnabled with argument GL_MAP2_COLOR_4
fglIsEnabled with argument GL_MAP2_NORMAL
fglIsEnabled with argument GL_MAP2_TEXTURE_COORD_1
fglIsEnabled with argument GL_MAP2_TEXTURE_COORD_2
fglIsEnabled with argument GL_MAP2_TEXTURE_COORD_3
fglIsEnabled with argument GL_MAP2_TEXTURE_COORD_4
SEE ALSO
fglBegin, fglColor, fglEnable, fglEvalCoord, fglEvalMesh, fglEvalPoint,
fglMap1, fglMapGrid, fglNormal, fglTexCoord, fglVertex
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