GLMAP2(3G)																GLMAP2(3G)

NAME

       glMap2d, glMap2f - define a two-dimensional evaluator

C SPECIFICATION

       void glMap2d( GLenum target,
		     GLdouble u1,
		     GLdouble u2,
		     GLint ustride,
		     GLint uorder,
		     GLdouble v1,
		     GLdouble v2,
		     GLint vstride,
		     GLint vorder,
		     const GLdouble *points )
       void glMap2f( GLenum target,
		     GLfloat u1,
		     GLfloat u2,
		     GLint ustride,
		     GLint uorder,
		     GLfloat v1,
		     GLfloat v2,
		     GLint vstride,
		     GLint vorder,
		     const GLfloat *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 hat, one of the two variables that are evaluated by the equa-
		tions 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 Rij 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 hat, one of the two variables that are evaluated by the equa-
		tions 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 Rij and the beginning of control  point  Ri(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 sur-
       faces, and so on.

       Evaluators define surfaces based on bivariate Bernstein polynomials.  Define p ( u hat , v hat ) as

				      p(u hat, v hat) = Sum(i=0 to n) Sum(j=0 to n)  Bi^n (u hat) Bj^m (v hat) Rij

       where Rij is a control point, Bi^n(u hat) is the ith Bernstein polynomial of degree
       n (uorder = n + 1)

						  Bi^n ( u hat ) = (n,i) (u hat)^i (1 - u hat) ^ (n-1)

       and Bj^m ( v hat ) is the jth Bernstein polynomial of degree m (vorder = m + 1)

						  Bj^m ( u hat ) = (m,j) (v hat)^j (1 - b hat) ^ (m-j)

       Recall that

								0^0 == 1  and (0,n) == 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 hat and v hat, where

								 u hat = (u-u1)/(u2-u1)

								 v hat = (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 gen-
				erated 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 com-
				mands  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 Rij 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 Rij to control point Ri(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.

       When  the  GL_ARB_multitexture  extension  is  supported,  GL_INVALID_OPERATION	is  generated  if  glMap2  is  called  and  the  value	of
       GL_ACTIVE_TEXTURE_ARB is not GL_TEXTURE0_ARB.

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

																	GLMAP2(3G)