'\" te
'\"! tbl|eqn | mmdoc
'\"macro stdmacro
.ds Vn Version 1.2
.ds Dt 24 September 1999
.ds Re Release 1.2.1
.ds Dp Jan 14 18:30
.ds Dm 01 map1.gl -
.ds Xs 15186 10 map1.gl
.TH GLMAP1 3G
.SH NAME
.B "glMap1d, glMap1f
\- define a one-dimensional evaluator

.SH C SPECIFICATION
void \f3glMap1d\fP(
GLenum \fItarget\fP,
.nf
.ta \w'\f3void \fPglMap1d( 'u
	GLdouble \fIu1\fP,
	GLdouble \fIu2\fP,
	GLint \fIstride\fP,
	GLint \fIorder\fP,
	const GLdouble \fI*points\fP )
.fi
void \f3glMap1f\fP(
GLenum \fItarget\fP,
.nf
.ta \w'\f3void \fPglMap1f( 'u
	GLfloat \fIu1\fP,
	GLfloat \fIu2\fP,
	GLint \fIstride\fP,
	GLint \fIorder\fP,
	const GLfloat \fI*points\fP )
.fi

.EQ
delim $$
.EN
.SH PARAMETERS
.TP \w'\f2target\fP\ \ 'u 
\f2target\fP
Specifies the kind of values that are generated by the evaluator.
Symbolic constants
\%\f3GL_MAP1_VERTEX_3\fP,
\%\f3GL_MAP1_VERTEX_4\fP,
\%\f3GL_MAP1_INDEX\fP,
\%\f3GL_MAP1_COLOR_4\fP,
\%\f3GL_MAP1_NORMAL\fP,
\%\f3GL_MAP1_TEXTURE_COORD_1\fP,
\%\f3GL_MAP1_TEXTURE_COORD_2\fP,
\%\f3GL_MAP1_TEXTURE_COORD_3\fP, and
\%\f3GL_MAP1_TEXTURE_COORD_4\fP are accepted.
.TP
\f2u1\fP, \f2u2\fP
Specify a linear mapping of $u$,
as presented to \%\f3glEvalCoord1\fP,
to $u hat$,
the variable that is evaluated by the equations specified by this command.
.TP
\f2stride\fP
Specifies the number of floats or doubles between
the beginning of one control point and the beginning of the next one
in the data structure referenced in \f2points\fP.
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.
.TP
\f2order\fP
Specifies the number of control points.
Must be positive.
.TP
\f2points\fP
Specifies a pointer to the array of control points.

.SH 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 to further stages
of GL processing just as if they had been presented using
\%\f3glVertex\fP,
\%\f3glNormal\fP,
\%\f3glTexCoord\fP, and
\%\f3glColor\fP commands,
except that the generated values do not update the current normal,
texture coordinates,
or color.
.P
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.  
.P
Evaluators define curves based on Bernstein polynomials.
Define $p ( u hat ^) $ as
.sp
.ce
$p ( u hat ^) ~~=~~ up 10 { sum from i=0 to n } B sub i sup n ( u hat ^) R sub i$
.sp
where
$R sub i$
is a control point and
$B sub i sup n ( u hat ^)$
is the $i$th Bernstein polynomial of degree $n$ (\f2order\fP = $n ~+~ 1$):
.sp
.ce
$B sub i sup n ( u hat ^) ~~=~~ left ( down 20 {cpile { n above i }} ~~ right ) u hat sup i ( 1 - u hat ^) sup { n - i }$
.sp
Recall that 
.sp
.ce
$0 sup 0 ~==~ 1 $ and $ left ( down 20 {cpile { n above ~0 }} ~~ right ) ~~==~~ 1 $
.P
\%\f3glMap1\fP 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 \%\f3glEnable\fP and \%\f3glDisable\fP
with the map name, one of the nine predefined values for \f2target\fP
described below.
\%\f3glEvalCoord1\fP evaluates the one-dimensional maps that are enabled.
When 
.br
\%\f3glEvalCoord1\fP presents a value $u$,
the Bernstein functions are evaluated using $u hat$, where
.br

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

.br
.P
\f2target\fP is a symbolic constant that indicates what kind of control points
are provided in \f2points\fP,
and what output is generated when the map is evaluated.
It can assume one of nine predefined values:
.TP 25
\%\f3GL_MAP1_VERTEX_3\fP
Each control point is three floating-point values representing
$x$, $y$, and $z$.
Internal \%\f3glVertex3\fP commands are generated when the map is evaluated.
.TP
\%\f3GL_MAP1_VERTEX_4\fP
Each control point is four floating-point values representing
$x$, $y$, $z$, and $w$.
Internal \%\f3glVertex4\fP commands are generated when the map is evaluated.
.TP
\%\f3GL_MAP1_INDEX\fP
Each control point is a single floating-point value representing a color index.
Internal \%\f3glIndex\fP commands are generated when the map is evaluated
but the current index is not updated with the value of these \%\f3glIndex\fP
commands.
.TP
\%\f3GL_MAP1_COLOR_4\fP
Each control point is four floating-point values representing
red, green, blue, and alpha.
Internal \%\f3glColor4\fP commands are generated when the map is
evaluated but the current color is not updated with the value of these
\%\f3glColor4\fP commands.
.TP
\%\f3GL_MAP1_NORMAL\fP
Each control point is three floating-point values representing
the $x$, $y$, and $z$ components of a normal vector.
Internal \%\f3glNormal\fP commands are generated when the map is
evaluated but the current normal is not updated with the value of
these \%\f3glNormal\fP commands.
.TP 
\%\f3GL_MAP1_TEXTURE_COORD_1\fP
Each control point is a single floating-point value representing
the $s$ texture coordinate.
Internal 
.br
\%\f3glTexCoord1\fP commands are generated when the map is
evaluated but the current texture coordinates are not updated with the value
of these \%\f3glTexCoord\fP commands.
.TP
\%\f3GL_MAP1_TEXTURE_COORD_2\fP
Each control point is two floating-point values representing
the $s$ and $t$ texture coordinates.
Internal 
.br
\%\f3glTexCoord2\fP commands are generated when the map is
evaluated but the current texture coordinates are not updated with the value
of these \%\f3glTexCoord\fP commands.
.TP
\%\f3GL_MAP1_TEXTURE_COORD_3\fP
Each control point is three floating-point values representing
the $s$, $t$, and $r$ texture coordinates.
Internal \%\f3glTexCoord3\fP commands are generated when the map is
evaluated but the current texture coordinates are not updated with the value
of these \%\f3glTexCoord\fP commands.
.TP
\%\f3GL_MAP1_TEXTURE_COORD_4\fP
Each control point is four floating-point values representing
the $s$, $t$, $r$, and $q$ texture coordinates.
Internal 
.br
\%\f3glTexCoord4\fP commands are generated when the map is evaluated but
the current texture coordinates are not updated with the value 
of these \%\f3glTexCoord\fP commands.
.P
\f2stride\fP,
\f2order\fP, and
\f2points\fP define the array addressing for accessing the control points.
\f2points\fP 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.
\f2order\fP is the number of control points in the array.
\f2stride\fP specifies how many float or double locations to advance the internal
memory pointer to reach the next control point.
.SH NOTES
As is the case with all GL commands that accept pointers to data,
it is as if the contents of \f2points\fP were copied by \%\f3glMap1\fP before \%\f3glMap1\fP
returns.
Changes to the contents of \f2points\fP have no effect after \%\f3glMap1\fP is called.
.SH ERRORS
\%\f3GL_INVALID_ENUM\fP is generated if \f2target\fP is not an accepted value.
.P
\%\f3GL_INVALID_VALUE\fP is generated if \f2u1\fP is equal to \f2u2\fP.
.P
\%\f3GL_INVALID_VALUE\fP is generated if \f2stride\fP is less than the number
of values in a control point.
.P
\%\f3GL_INVALID_VALUE\fP is generated if \f2order\fP is less than 1 or
greater than the return value of \%\f3GL_MAX_EVAL_ORDER\fP.
.P
\%\f3GL_INVALID_OPERATION\fP is generated if \%\f3glMap1\fP
is executed between the execution of
\%\f3glBegin\fP
and the corresponding execution of \%\f3glEnd\fP.
.P
When the \%\f3GL_ARB_multitexture\fP extension is supported,
\%\f3GL_INVALID_OPERATION\fP is generated if \%\f3glMap1\fP is called and the value
of \%\f3GL_ACTIVE_TEXTURE_ARB\fP is not \%\f3GL_TEXTURE0_ARB\fP.
.SH ASSOCIATED GETS
\%\f3glGetMap\fP
.br
\%\f3glGet\fP with argument \%\f3GL_MAX_EVAL_ORDER\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_VERTEX_3\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_VERTEX_4\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_INDEX\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_COLOR_4\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_NORMAL\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_TEXTURE_COORD_1\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_TEXTURE_COORD_2\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_TEXTURE_COORD_3\fP
.br
\%\f3glIsEnabled\fP with argument \%\f3GL_MAP1_TEXTURE_COORD_4\fP
.SH SEE ALSO
\%\f3glBegin(3G)\fP,
\%\f3glColor(3G)\fP,
\%\f3glEnable(3G)\fP,
\%\f3glEvalCoord(3G)\fP,
\%\f3glEvalMesh(3G)\fP,
\%\f3glEvalPoint(3G)\fP,
\%\f3glMap2(3G)\fP,
\%\f3glMapGrid(3G)\fP,
\%\f3glNormal(3G)\fP,
\%\f3glTexCoord(3G)\fP,
\%\f3glVertex(3G)\fP
