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GLMAP2(3G)			 OpenGL Manual			    GLMAP2(3G)

NAME
       glMap2 - define a two-dimensional evaluator

C SPECIFICATION
       void glMap2f(GLenum target, GLfloat u1, GLfloat u2, GLint ustride,
		    GLint uorder, GLfloat v1, GLfloat v2, GLint vstride,
		    GLint vorder, const GLfloat * points);

       void glMap2d(GLenum target, GLdouble u1, GLdouble u2, GLint ustride,
		    GLint uorder, GLdouble v1, GLdouble v2, GLint vstride,
		    GLint vorder, const GLdouble * points);

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^, one of the two variables that are evaluated by the equations
	   specified 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 ij and the beginning of control point R 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
	   structures. The only constraint is that the values for a particular
	   control point must occupy contiguous 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^, 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 ij and the beginning of control point R 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
	   structures. The only constraint is that the values for a particular
	   control point must occupy contiguous 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 evaluator 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
       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 surfaces used in computer
       graphics, including B-spline surfaces, NURBS surfaces, Bezier surfaces,
       and so on.

       Evaluators define surfaces based on bivariate Bernstein polynomials.
       Define p ⁡ u^ v^ as

       p ⁡ u^ v^ = Σ i = 0 n Σ j = 0 m B i n ⁡ u^ ⁢ B j m ⁡ v^ ⁢ R ij

       where R ij is a control point, B i n ⁡ u^ is the ith Bernstein
       polynomial of degree n (uorder = n + 1)

       B i n ⁡ u^ = n i ⁢ u^ i ⁢ 1 - u^ n - i

       and B j m ⁡ v^ is the jth Bernstein polynomial of degree m (vorder = m
       + 1)

       B j m ⁡ v^ = m j ⁢ v^ j ⁢ 1 - v^ m - j

       Recall that 0 0 == 1 and n 0 == 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 values u and v, the bivariate Bernstein polynomials are
       evaluated using u^ and v^, where

       u^ = u - u1 u2 - u1

       v^ = v - v1 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 representing x,
	   y, and z. Internal glVertex3() commands are generated when the map
	   is evaluated.

       GL_MAP2_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_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 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_MAP2_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_MAP2_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_MAP2_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_MAP2_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_MAP2_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.

       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 × vorder control points in the array.  ustride
       specifies how many float or double locations are skipped to advance the
       internal memory pointer from control point R i ⁢ j to control point R i
       + 1 ⁢ j.	vstride specifies how many float or double locations are
       skipped to advance the internal memory pointer from control point R i ⁢
       j to control point R 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().

       GL_INVALID_OPERATION is generated if glMap2 is called and the value of
       GL_ACTIVE_TEXTURE is not GL_TEXTURE0.

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(),
       glEvalPoint(), glMap1(), glMapGrid(), glNormal(), glTexCoord(),
       glVertex()

COPYRIGHT
       Copyright © 1991-2006 Silicon Graphics, Inc. This document is licensed
       under the SGI Free Software B License. For details, see
       http://oss.sgi.com/projects/FreeB/.

AUTHORS
       opengl.org

opengl.org			  04/29/2014			    GLMAP2(3G)
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