GLMAP1() MachTen Programmer’s Manual GLMAP1()

NAME
glMap1d, glMap1f - define a one-dimensional evaluator

C SPECIFICATION
void glMap1d( GLenum target,
GLdouble u1,
GLdouble u2,
GLint stride,
GLint order,
const GLdouble *points )
void glMap1f( GLenum target,
GLfloat u1,
GLfloat u2,
GLint stride,
GLint order,
const GLfloat *points )

delim $$

PARAMETERS
target Specifies the kind of values that are generated by
the evaluator. Symbolic constants
GL_MAP1_VERTEX_3, GL_MAP1_VERTEX_4, GL_MAP1_INDEX,
GL_MAP1_COLOR_4, GL_MAP1_NORMAL,
GL_MAP1_TEXTURE_COORD_1, GL_MAP1_TEXTURE_COORD_2,
GL_MAP1_TEXTURE_COORD_3, and
GL_MAP1_TEXTURE_COORD_4 are accepted.

u1, u2 Specify a linear mapping of $u$, as presented to
glEvalCoord1, to $u hat$, the variable that is
evaluated by the equations specified by this com-
mand.

stride Specifies the number of floats or doubles between
the beginning of one control point and the begin-
ning of the next one in the data structure refer-
enced in points. 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 loca-
tions.

order Specifies the number of control points. 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 evalu-
ator are sent 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 splines used in computer graphics: B-
splines, Bezier curves, Hermite splines, and so on.

Evaluators define curves based on Bernstein polynomials.
Define $p ( u hat ^) $ as

$p ( u hat ^) ~~=~~ up 10 { sum from i=0 to n } B sub i
sup n ( u hat ^) R sub i$

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

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

Recall that

$0 sup 0 ~==~ 1 $ and $ left ( down 20 {cpile { n above ~0
}} ~~ right ) ~~==~~ 1 $

glMap1 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. glEvalCoord1 evaluates the one-
dimensional maps that are enabled. When
glEvalCoord1 presents a value $u$, the Bernstein functions
are evaluated using $u hat$, where

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

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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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.

stride, order, 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. order is the number of control
points in the array. stride specifies how many float or
double locations to advance the internal memory pointer to
reach the next control point.

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
glMap1 before glMap1 returns. Changes to the contents of
points have no effect after glMap1 is called.

ERRORS
GL_INVALID_ENUM is generated if target is not an accepted
value.

GL_INVALID_VALUE is generated if u1 is equal to u2.

GL_INVALID_VALUE is generated if stride is less than the
number of values in a control point.

GL_INVALID_VALUE is generated if order is less than 1 or
greater than the return value of GL_MAX_EVAL_ORDER.

GL_INVALID_OPERATION is generated if glMap1 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_MAP1_VERTEX_3
glIsEnabled with argument GL_MAP1_VERTEX_4
glIsEnabled with argument GL_MAP1_INDEX
glIsEnabled with argument GL_MAP1_COLOR_4
glIsEnabled with argument GL_MAP1_NORMAL
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_1
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_2
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_3
glIsEnabled with argument GL_MAP1_TEXTURE_COORD_4

SEE ALSO
glBegin, glColor, glEnable, glEvalCoord, glEvalMesh, glE-
valPoint, glMap2, glMapGrid, glNormal, glTexCoord, glVer-
tex

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