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<STRONG>NAME</STRONG>
<STRONG>glMap1d,</STRONG> <STRONG>glMap1f</STRONG> - define a one-dimensional evaluator
<STRONG>C</STRONG> <STRONG>SPECIFICATION</STRONG>
void <STRONG>glMap1d</STRONG>( GLenum <EM>target</EM>,
GLdouble <EM>u1</EM>,
GLdouble <EM>u2</EM>,
GLint <EM>stride</EM>,
GLint <EM>order</EM>,
const GLdouble *<EM>points</EM> )
void <STRONG>glMap1f</STRONG>( GLenum <EM>target</EM>,
GLfloat <EM>u1</EM>,
GLfloat <EM>u2</EM>,
GLint <EM>stride</EM>,
GLint <EM>order</EM>,
const GLfloat *<EM>points</EM> )
<STRONG>PARAMETERS</STRONG>
<EM>target</EM> Specifies the kind of values that are generated by
the evaluator. Symbolic constants <STRONG>GL_MAP1_VERTEX_3</STRONG>,
<STRONG>GL_MAP1_VERTEX_4</STRONG>, <STRONG>GL_MAP1_INDEX</STRONG>, <STRONG>GL_MAP1_COLOR_4</STRONG>,
<STRONG>GL_MAP1_NORMAL</STRONG>, <STRONG>GL_MAP1_TEXTURE_COORD_1</STRONG>,
<STRONG>GL_MAP1_TEXTURE_COORD_2</STRONG>, <STRONG>GL_MAP1_TEXTURE_COORD_3</STRONG>,
and <STRONG>GL_MAP1_TEXTURE_COORD_4</STRONG> are accepted.
<EM>u1</EM>, <EM>u2</EM> Specify a linear mapping of u, as presented to
<STRONG>glEvalCoord1</STRONG>, to <STRONG>^</STRONG>, the variable that is evaluated
by the equations specified by this command.
<EM>stride</EM> 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
<EM>points</EM>. 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.
<EM>order</EM> Specifies the number of control points. Must be
positive.
<EM>points</EM> Specifies a pointer to the array of control points.
<STRONG>DESCRIPTION</STRONG>
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 <STRONG>glVertex</STRONG>, <STRONG>glNormal</STRONG>,
<STRONG>glTexCoord</STRONG>, and <STRONG>glColor</STRONG> 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 splines used in computer graphics: B-
splines, Bezier curves, Hermite splines, and so on.
Evaluators define curves based on Bernstein polynomials.
Define p(<STRONG>^</STRONG>) as
n
R n
p(<STRONG>^</STRONG>) = i=0Bi(<STRONG>^</STRONG>)Ri
where R is a control point and Bn(<STRONG>^</STRONG>) is the ith Bernstein
polynom<STRONG>i</STRONG>al of degree n (<EM>order</EM> = n<STRONG>+</STRONG>1):
n (n ) i n-i
Bi(<STRONG>^</STRONG>) = | |<STRONG>^</STRONG> (1-<STRONG>^</STRONG>)
(i )
Recall that
0 (n )
0 <EM>=</EM> 1 and | | <EM>=</EM> 1
( 0 )
<STRONG>glMap1</STRONG> 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 <STRONG>glEnable</STRONG> and <STRONG>glDisable</STRONG> with the map
name, one of the nine predefined values for <EM>target</EM> described
below. <STRONG>glEvalCoord1</STRONG> evaluates the one-dimensional maps that
are enabled. When
<STRONG>glEvalCoord1</STRONG> presents a value u, the Bernstein functions are
evaluated using <STRONG>^</STRONG>, where
<STRONG>^</STRONG> = _<STRONG>_</STRONG>_<STRONG>_</STRONG>_<STRONG>__</STRONG>
u2 - u1
<EM>target</EM> is a symbolic constant that indicates what kind of
control points are provided in <EM>points</EM>, and what output is
generated when the map is evaluated. It can assume one of
nine predefined values:
<STRONG>GL_MAP1_VERTEX_3</STRONG> Each control point is three
floating-point values representing
x, y, and z. Internal <STRONG>glVertex3</STRONG>
commands are generated when the map
is evaluated.
<STRONG>GL_MAP1_VERTEX_4</STRONG> Each control point is four
floating-point values representing
x, y, z, and w. Internal <STRONG>glVertex4</STRONG>
commands are generated when the map
is evaluated.
<STRONG>GL_MAP1_INDEX</STRONG> Each control point is a single
floating-point value representing a
color index. Internal <STRONG>glIndex</STRONG>
commands are generated when the map
is evaluated but the current index
is not updated with the value of
these <STRONG>glIndex</STRONG> commands.
<STRONG>GL_MAP1_COLOR_4</STRONG> Each control point is four
floating-point values representing
red, green, blue, and alpha.
Internal <STRONG>glColor4</STRONG> commands are
generated when the map is evaluated
but the current color is not
updated with the value of these
<STRONG>glColor4</STRONG> commands.
<STRONG>GL_MAP1_NORMAL</STRONG> Each control point is three
floating-point values representing
the x, y, and z components of a
normal vector. Internal <STRONG>glNormal</STRONG>
commands are generated when the map
is evaluated but the current normal
is not updated with the value of
these <STRONG>glNormal</STRONG> commands.
<STRONG>GL_MAP1_TEXTURE_COORD_1</STRONG> Each control point is a single
floating-point value representing
the s texture coordinate. Internal
<STRONG>glTexCoord1</STRONG> commands are generated
when the map is evaluated but the
current texture coordinates are not
updated with the value of these
<STRONG>glTexCoord</STRONG> commands.
<STRONG>GL_MAP1_TEXTURE_COORD_2</STRONG> Each control point is two
floating-point values representing
the s and t texture coordinates.
Internal
<STRONG>glTexCoord2</STRONG> commands are generated
when the map is evaluated but the
current texture coordinates are not
updated with the value of these
<STRONG>glTexCoord</STRONG> commands.
<STRONG>GL_MAP1_TEXTURE_COORD_3</STRONG> Each control point is three
floating-point values representing
the s, t, and r texture
coordinates. Internal <STRONG>glTexCoord3</STRONG>
commands are generated when the map
is evaluated but the current
texture coordinates are not updated
with the value of these <STRONG>glTexCoord</STRONG>
commands.
<STRONG>GL_MAP1_TEXTURE_COORD_4</STRONG> Each control point is four
floating-point values representing
the s, t, r, and q texture
coordinates. Internal
<STRONG>glTexCoord4</STRONG> commands are generated
when the map is evaluated but the
current texture coordinates are not
updated with the value of these
<STRONG>glTexCoord</STRONG> commands.
<EM>stride</EM>, <EM>order</EM>, and <EM>points</EM> define the array addressing for
accessing the control points. <EM>points</EM> 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. <EM>order</EM> is the number of control points in the
array. <EM>stride</EM> specifies how many float or double locations
to advance the internal memory pointer to reach the next
control point.
<STRONG>NOTES</STRONG>
As is the case with all GL commands that accept pointers to
data, it is as if the contents of <EM>points</EM> were copied by
<STRONG>glMap1</STRONG> before <STRONG>glMap1</STRONG> returns. Changes to the contents of
<EM>points</EM> have no effect after <STRONG>glMap1</STRONG> is called.
<STRONG>ERRORS</STRONG>
<STRONG>GL_INVALID_ENUM</STRONG> is generated if <EM>target</EM> is not an accepted
value.
<STRONG>GL_INVALID_VALUE</STRONG> is generated if <EM>u1</EM> is equal to <EM>u2</EM>.
<STRONG>GL_INVALID_VALUE</STRONG> is generated if <EM>stride</EM> is less than the
number of values in a control point.
<STRONG>GL_INVALID_VALUE</STRONG> is generated if <EM>order</EM> is less than 1 or
greater than the return value of <STRONG>GL_MAX_EVAL_ORDER</STRONG>.
<STRONG>GL_INVALID_OPERATION</STRONG> is generated if <STRONG>glMap1</STRONG> is executed
between the execution of <STRONG>glBegin</STRONG> and the corresponding
execution of <STRONG>glEnd</STRONG>.
<STRONG>ASSOCIATED</STRONG> <STRONG>GETS</STRONG>
<STRONG>glGetMap</STRONG>
<STRONG>glGet</STRONG> with argument <STRONG>GL_MAX_EVAL_ORDER</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_VERTEX_3</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_VERTEX_4</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_INDEX</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_COLOR_4</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_NORMAL</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_TEXTURE_COORD_1</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_TEXTURE_COORD_2</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_TEXTURE_COORD_3</STRONG>
<STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP1_TEXTURE_COORD_4</STRONG>
<STRONG>SEE</STRONG> <STRONG>ALSO</STRONG>
<STRONG>glBegin</STRONG>, <STRONG>glColor</STRONG>, <STRONG>glEnable</STRONG>, <STRONG>glEvalCoord</STRONG>, <STRONG>glEvalMesh</STRONG>,
<STRONG>glEvalPoint</STRONG>, <STRONG>glMap2</STRONG>, <STRONG>glMapGrid</STRONG>, <STRONG>glNormal</STRONG>, <STRONG>glTexCoord</STRONG>,
<STRONG>glVertex</STRONG>
</PRE>
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