NAME
fglMap2d, fglMap2f - define a two-dimensional evaluator
FORTRAN SPECIFICATION
SUBROUTINE fglMap2d( INTEGER*4 target,
REAL*8 u1,
REAL*8 u2,
INTEGER*4 ustride,
INTEGER*4 uorder,
REAL*8 v1,
REAL*8 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, where i and j
are the u and v control pointiindices,
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.
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, 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
n m
R R n m
p(^,^) = i=0j=0Bi(^)Bj(^)Rij
where R is a control point, Bn(^) is the ith Bernstein
polynomial of degree i
n (uorder = n+1)
n (n ) i n-i
Bi(^) = | |^ (1-^)
(i )
and Bm(^) is the jth Bernstein polynomial of degree m
(vord<EM>er = m+1)
m (m ) j m-j
Bj(^) = | |^ (1-^)
(j )
Recall that
0 (n )
0 = 1 and | | = 1
( 0 )
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.
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
uorderxvorder 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 specifies how many float
or double locationsiarejskipped 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.
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