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glMap(3G)							     glMap(3G)

NAME
       glMap2, glMap2d, glMap2f - define a two-dimensional evaluator

SYNOPSIS
       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
       Specifies  the kind of values that are generated by the evaluator. Sym‐
       bolic  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_TEX‐
       TURE_COORD_2, GL_MAP2_TEXTURE_COORD_3, and GL_MAP2_TEXTURE_COORD_4  are
       accepted.   Specify  a  linear  mapping of u, as presented to glEvalCo‐
       ord2(), to u hat, one of the two variables that are  evaluated  by  the
       equations  specified  by	 this command. Initially, u1 is 0 and u2 is 1.
       Specifies the number of floats or doubles between the beginning of con‐
       trol point R[i][j] and the beginning of control point R sub [(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.  Specifies the dimension of the control  point  array  in	the  u
       axis.  Must be positive. The initial value is 1.	 Specify a linear map‐
       ping of v, as presented to glEvalCoord2(), to v hat,  one  of  the  two
       variables  that	are  evaluated by the equations specified by this com‐
       mand. Initially, v1 is 0 and v2 is 1.  Specifies the number  of	floats
       or  doubles between the beginning of control point R[i]j and the begin‐
       ning of control point R sub [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.  Specifies the  dimension
       of  the	control point array in the v axis.  Must be positive. The ini‐
       tial value is 1.	 Specifies a pointer to the array of control points.

DESCRIPTION
       Evaluators provide a way to use polynomial or rational polynomial  map‐
       ping 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(), glNor‐
       mal(), 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 hat , v hat )  as
			      n	  m p ( u hat , v hat )	 =  sum	 sum  B[i]^n(u
       hat) B[j]^m(v hat) R[ij]
			     i=0 j=0

       where  R[i]j  is a control point, B[i] sup n ( u hat ) is the ith Bern‐
       stein polynomial of degree n (uorder = n + 1) B[i]^n(u hat) = n above i
       u hat^i(1 - u hat)^n-i

       and  B[j]^m  (  v  hat  )  is  the jth Bernstein polynomial of degree m
       (vorder = m + 1) B[j]^m(v hat) = m above j v hat^j(1 - v hat)^m-j

       Recall that 0^0 = 1 and n above = 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 call‐
       ing glEnable() and glDisable() with the map name, one of the nine  pre‐
       defined	 values	 for  target,  described  below.  When	glEvalCoord2()
       presents values u and v, the bivariate Bernstein polynomials are evalu‐
       ated using u hat and v hat, where u hat = {u - u1} over {u2 - u1} v hat
       = {v - v1} over {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:  Each
       control	point is three floating-point values representing x, y, and z.
       Internal glVertex3() commands are generated when the map is  evaluated.
       Each  control point is four floating-point values representing x, y, z,
       and w.  Internal glVertex4() commands are generated  when  the  map  is
       evaluated.   Each control point is a single floating-point value repre‐
       senting 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.  Each control point is  four	float‐
       ing-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() com‐
       mands.  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.  Each con‐
       trol 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.  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.	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.	Each control point is four floating-point val‐
       ues 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 address‐
       ing 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" times "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 sub [i][ j]	to control point R sub
       [(i+1)[ j]] .  vstride specifies how many float or double locations are
       skipped to advance the internal memory pointer from control point R sub
       [i][ j]	to control point R sub [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().

       When  the GL_ARB_multitexture extension is supported, GL_INVALID_OPERA‐
       TION is generated if glMap2() is called and the value of GL_ACTIVE_TEX‐
       TURE_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(3),  glColor(3),	 glEnable(3),  glEvalCoord(3),	glEvalMesh(3),
       glEvalPoint(3), glMap1(3),  glMapGrid(3),  glNormal(3),	glTexCoord(3),
       glVertex(3)

								     glMap(3G)
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