GLMAP2() MachTen Programmer’s Manual GLMAP2()

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 )

delim $$

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 $u hat$, one of the two vari-
ables that are evaluated by the equations speci-
fied 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 $R sub ij$ and the
beginning of control point $R sub { (i+1) j }$,
where $i$ and $j$ are the $u$ and $v$ control
point indices, respectively. This allows control
points to be embedded in arbitrary data struc-
tures. The only constraint is that the values
for a particular control point must occupy con-
tiguous 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
glEvalCoord2, to $v hat$, 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 $R sub ij$ and the
beginning of control point $R sub { i (j+1) }$,
where $i$ and $j$ are the $u$ and $v$ control
point indices, respectively. This allows control
points to be embedded in arbitrary data struc-
tures. The only constraint is that the values
for a particular control point must occupy con-
tiguous 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 evalu-
ator 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 gener-
ated 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 sur-
faces, and so on.

Evaluators define surfaces based on bivariate Bernstein
polynomials. Define $p ( u hat , v hat ) $ as

p ( u hat , v hat ^) ~~=~~ up 10 {sum from i=0 to n sum
from j=0 to m} B sub i sup n ( u hat ^) B sub j sup m ( v
hat ^) R sub ij

where $R sub ij$ is a control point, $B sub i sup n ( u
hat ^)$ is the $i$th Bernstein polynomial of degree
$n$ (uorder = $n + 1$)

B sub i sup n ( u hat ^) ~~=~~ left ( down 20 {cpile { n
above i }} ~~ right ) u hat sup i ( 1 - u hat ^) sup { n -
i }

and $B sub j sup m ( v hat ^)$ is the $j$th Bernstein
polynomial of degree $m$ (vorder = $m + 1$)

B sub j sup m ( v hat ^) ~~=~~ left ( down 20 {cpile { m
above j }} ~~ right ) v hat sup j ( 1 - v hat ^) sup { m -
j }

Recall that
$0 sup 0 ~==~ 1 $ and $ left ( down 20 {cpile { n above ~0
}} ~~ right ) ~~==~~ 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 val-
ues $u$ and $v$, the bivariate Bernstein polynomials are
evaluated using $u hat$ and $v hat$, where

$u hat ~~=~~ {u ~-~ "u1"} over {"u2" ~-~ "u1"}$

$v hat ~~=~~ {v ~-~ "v1"} over {"v2" ~-~ "v1"}$

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 represent-
ing $x$, $y$, and $z$. Internal
glVertex3 commands are generated
when the map is evaluated.

GL_MAP2_VERTEX_4 Each control point is four float-
ing-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
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 float-
ing-point values representing
red, green, blue, and alpha.
Internal glColor4 commands are
generated when the map is evalu-
ated but the current color is not
updated with the value of these
glColor4 commands.

GL_MAP2_NORMAL Each control point is three
floating-point values represent-
ing the $x$, $y$, and $z$ compo-
nents of a normal vector. Inter-
nal glNormal commands are gener-
ated 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 gener-
ated when the map is evaluated
but the current texture coordi-
nates are not updated with the
value of these glTexCoord com-
mands.

GL_MAP2_TEXTURE_COORD_2 Each control point is two float-
ing-point values representing the
$s$ and $t$ texture coordinates.
Internal
glTexCoord2 commands are gener-
ated when the map is evaluated
but the current texture coordi-
nates are not updated with the
value of these glTexCoord com-
mands.

GL_MAP2_TEXTURE_COORD_3 Each control point is three
floating-point values represent-
ing the $s$, $t$, and $r$ texture
coordinates. Internal glTexCo-
ord3 commands are generated when
the map is evaluated but the cur-
rent texture coordinates are not
updated with the value of these
glTexCoord commands.

GL_MAP2_TEXTURE_COORD_4 Each control point is four float-
ing-point values representing the
$s$, $t$, $r$, and $q$ texture
coordinates. Internal
glTexCoord4 commands are gener-
ated when the map is evaluated
but the current texture coordi-
nates are not updated with the
value of these glTexCoord com-
mands.

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" times "vorder" $ control points in the array.
ustride specifies how many float or double locations are
skipped to advance the internal memory pointer from con-
trol point $R sub {i j} $ to control point $R sub {(i+1)
j} $. vstride specifies how many float or double loca-
tions are skipped to advance the internal memory pointer
from control point $R sub {i j} $ to control point $R sub
{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 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
execution of glEnd.

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

SEE ALSO
glBegin, glColor, glEnable, glEvalCoord, glEvalMesh, glE-
valPoint, glMap1, glMapGrid, glNormal, glTexCoord, glVer-
tex

MachTen 5