glMap1d, glMap1f − define a one-dimensional evaluator
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 ) |
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 command. | ||
stride |
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 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 locations. | ||
order |
Specifies the number of control points. Must be positive. | ||
points |
Specifies a pointer to the array of control points. |
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 glVertex, glNormal, glTexCoord, and glColor 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 ( 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 representing $x$, $y$, and $z$. Internal glVertex3 commands are generated when the map is evaluated. | ||
GL_MAP1_VERTEX_4 |
Each control point is four floating-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 floating-point values representing red, green, blue, and alpha. Internal glColor4 commands are generated when the map is evaluated 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 representing the $x$, $y$, and $z$ components of a normal vector. Internal glNormal commands are generated 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 generated when the map is evaluated but the current texture coordinates are not updated with the value of these glTexCoord commands.
GL_MAP1_TEXTURE_COORD_2 |
Each control point is two floating-point values representing the $s$ and $t$ texture coordinates. Internal |
glTexCoord2 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these glTexCoord commands.
GL_MAP1_TEXTURE_COORD_3 |
Each control point is three floating-point values representing the $s$, $t$, and $r$ texture coordinates. Internal glTexCoord3 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these glTexCoord commands. | ||
GL_MAP1_TEXTURE_COORD_4 |
Each control point is four floating-point values representing the $s$, $t$, $r$, and $q$ texture coordinates. Internal |
glTexCoord4 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these glTexCoord commands.
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.
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.
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.
When the GL_ARB_multitexture extension is supported, GL_INVALID_OPERATION is generated if glMap1 is called and the value of GL_ACTIVE_TEXTURE_ARB is not GL_TEXTURE0_ARB.
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
glBegin(3G), glColor(3G), glEnable(3G), glEvalCoord(3G), glEvalMesh(3G), glEvalPoint(3G), glMap2(3G), glMapGrid(3G), glNormal(3G), glTexCoord(3G), glVertex(3G)
Personal Opportunity - Free software gives you access to billions of dollars of software at no cost. Use this software for your business, personal use or to develop a profitable skill. Access to source code provides access to a level of capabilities/information that companies protect though copyrights. Open source is a core component of the Internet and it is available to you. Leverage the billions of dollars in resources and capabilities to build a career, establish a business or change the world. The potential is endless for those who understand the opportunity.
Business Opportunity - Goldman Sachs, IBM and countless large corporations are leveraging open source to reduce costs, develop products and increase their bottom lines. Learn what these companies know about open source and how open source can give you the advantage.
Free Software provides computer programs and capabilities at no cost but more importantly, it provides the freedom to run, edit, contribute to, and share the software. The importance of free software is a matter of access, not price. Software at no cost is a benefit but ownership rights to the software and source code is far more significant.
Free Office Software - The Libre Office suite provides top desktop productivity tools for free. This includes, a word processor, spreadsheet, presentation engine, drawing and flowcharting, database and math applications. Libre Office is available for Linux or Windows.
The Free Books Library is a collection of thousands of the most popular public domain books in an online readable format. The collection includes great classical literature and more recent works where the U.S. copyright has expired. These books are yours to read and use without restrictions.
Source Code - Want to change a program or know how it works? Open Source provides the source code for its programs so that anyone can use, modify or learn how to write those programs themselves. Visit the GNU source code repositories to download the source.
Study at Harvard, Stanford or MIT - Open edX provides free online courses from Harvard, MIT, Columbia, UC Berkeley and other top Universities. Hundreds of courses for almost all major subjects and course levels. Open edx also offers some paid courses and selected certifications.
Linux Manual Pages - A man or manual page is a form of software documentation found on Linux/Unix operating systems. Topics covered include computer programs (including library and system calls), formal standards and conventions, and even abstract concepts.