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GLMAP2(3gl)							   GLMAP2(3gl)

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 evalua‐
		tor.  Symbolic constants  GL_MAP2_VERTEX_3,  GL_MAP2_VERTEX_4,
		GL_MAP2_INDEX,	GL_MAP2_COLOR_4,  GL_MAP2_NORMAL, GL_MAP2_TEX‐
		TURE_COORD_1,	   GL_MAP2_TEXTURE_COORD_2,	  GL_MAP2_TEX‐
		TURE_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 equa‐
		tions  specified by this command. Initially, u1 is 0 and u2 is
		1.

       ustride	Specifies the number of floats or doubles between  the	begin‐
		ning  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, 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	begin‐
		ning  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 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, 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)=iΣ0jΣ0Bi(u)Bj(v)Rij

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

				 Bi(u)=⎝ ⎠ui(1−u)n−i

					i

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

				 Bj(v)=⎝ ⎠vj(1−v)m−j

					j

       Recall that			     n

				   00≡1 and ⎝ ⎠≡1

					     0

       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	prede‐
       fined  values  for target, described below.  When glEvalCoord2 presents
       values u and v, the bivariate Bernstein polynomials are evaluated using
       u and v, where

				       u=_____

				       v=_____

       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 val‐
				ues  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 val‐
				ues 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  com‐
				mands  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 coor‐
				dinates	 are  not  updated  with  the value of
				these glTexCoord commands.

       GL_MAP2_TEXTURE_COORD_2	Each control point is two floating-point  val‐
				ues  representing  the s and t texture coordi‐
				nates.	Internal
				glTexCoord2 commands are  generated  when  the
				map is evaluated but the current texture coor‐
				dinates 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 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 coor‐
				dinates	 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×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 spec‐
       ifies  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.

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

				   15 Mar 97			   GLMAP2(3gl)
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