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<HTML><BODY><PRE>     <STRONG>NAME</STRONG>	  <STRONG>glMap2d,</STRONG> <STRONG>glMap2f</STRONG> - define a two-dimensional evaluator     <STRONG>C</STRONG> <STRONG>SPECIFICATION</STRONG>	  void <STRONG>glMap2d</STRONG>(	GLenum <EM>target</EM>,			GLdouble <EM>u1</EM>,			GLdouble <EM>u2</EM>,			GLint <EM>ustride</EM>,			GLint <EM>uorder</EM>,			GLdouble <EM>v1</EM>,			GLdouble <EM>v2</EM>,			GLint <EM>vstride</EM>,			GLint <EM>vorder</EM>,			const GLdouble *<EM>points</EM> )	  void <STRONG>glMap2f</STRONG>(	GLenum <EM>target</EM>,			GLfloat	<EM>u1</EM>,			GLfloat	<EM>u2</EM>,			GLint <EM>ustride</EM>,			GLint <EM>uorder</EM>,			GLfloat	<EM>v1</EM>,			GLfloat	<EM>v2</EM>,			GLint <EM>vstride</EM>,			GLint <EM>vorder</EM>,			const GLfloat *<EM>points</EM> )     <STRONG>PARAMETERS</STRONG>	  <EM>target</EM>   Specifies the kind of values	that are generated by		   the evaluator.  Symbolic constants		   <STRONG>GL_MAP2_VERTEX_3</STRONG>, <STRONG>GL_MAP2_VERTEX_4</STRONG>, <STRONG>GL_MAP2_INDEX</STRONG>,		   <STRONG>GL_MAP2_COLOR_4</STRONG>, <STRONG>GL_MAP2_NORMAL</STRONG>,		   <STRONG>GL_MAP2_TEXTURE_COORD_1</STRONG>, <STRONG>GL_MAP2_TEXTURE_COORD_2</STRONG>,		   <STRONG>GL_MAP2_TEXTURE_COORD_3</STRONG>, and		   <STRONG>GL_MAP2_TEXTURE_COORD_4</STRONG> are accepted.	  <EM>u1</EM>, <EM>u2</EM>   Specify a linear mapping of u, as presented to		   <STRONG>glEvalCoord2</STRONG>, to <STRONG>^</STRONG>, one of the two variables	that		   are evaluated by the	equations specified by this		   command. Initially, <EM>u1</EM> is 0 and <EM>u2</EM> is 1.	  <EM>ustride</EM>  Specifies the number	of floats or doubles between		   the beginning of control point R   and the		   beginning of	control	point R	   ij, where i and j		   are the u and v control poin<STRONG>t</STRONG>i<STRONG>indi</STRONG>ces,		   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 <EM>ustride</EM> is 0.	  <EM>uorder</EM>   Specifies the dimension of the control point	array		   in the u axis.  Must	be positive. The initial value		   is 1.	  <EM>v1</EM>, <EM>v2</EM>   Specify a linear mapping of v, as presented to		   <STRONG>glEvalCoord2</STRONG>, to <STRONG>^</STRONG>, one of the two variables	that		   are evaluated by the	equations specified by this		   command. Initially, <EM>v1</EM> is 0 and <EM>v2</EM> is 1.	  <EM>vstride</EM>  Specifies the number	of floats or doubles between		   the beginning of control point R   and the		   beginning of	control	point R	   ij, where i and j		   are the u and v control poin<STRONG>t</STRONG>(<STRONG>indi</STRONG>ces,		   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 <EM>vstride</EM> is 0.	  <EM>vorder</EM>   Specifies the dimension of the control point	array		   in the v axis.  Must	be positive. The initial value		   is 1.	  <EM>points</EM>   Specifies a pointer to the array of control points.     <STRONG>DESCRIPTION</STRONG>	  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 <STRONG>glVertex</STRONG>, <STRONG>glNormal</STRONG>,	  <STRONG>glTexCoord</STRONG>, and <STRONG>glColor</STRONG> 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(<STRONG>^</STRONG>,<STRONG>^</STRONG>) as				     n	m				     R	R  n	m			 p(<STRONG>^</STRONG>,<STRONG>^</STRONG>)	 =  i=0j=0Bi(<STRONG>^</STRONG>)Bj(<STRONG>^</STRONG>)Rij	  where	R   is a control point,	Bn(<STRONG>^</STRONG>) is the ith Bernstein	  polynom<STRONG>ia</STRONG>l of	degree		 i	  n (<EM>uorder</EM> = n+1)			    n	     (n	 ) i	 n-i			   Bi(<STRONG>^</STRONG>)  =  |	 |<STRONG>^</STRONG> (1-<STRONG>^</STRONG>)				     (i	 )	  and Bm(<STRONG>^</STRONG>) is the jth Bernstein polynomial of degree m	  (<EM>vord</EM><STRONG><</STRONG>EM>er</EM> = m+1)			    m	     (m	 ) j	 m-j			   Bj(<STRONG>^</STRONG>)  =  |	 |<STRONG>^</STRONG> (1-<STRONG>^</STRONG>)				     (j	 )	  Recall that			     0	       (n   )			    0  <EM>=</EM> 1 and |    |  <EM>=</EM>  1				       ( 0  )	  <STRONG>glMap2</STRONG> 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 <STRONG>glEnable</STRONG> and <STRONG>glDisable</STRONG> with the map	  name,	one of the nine	predefined values for <EM>target</EM>,	  described below.  When <STRONG>glEvalCoord2</STRONG> presents values u	and v,	  the bivariate	Bernstein polynomials are evaluated using <STRONG>^</STRONG>	  and <STRONG>^</STRONG>, where				 <STRONG>^</STRONG>  =  _<STRONG>_</STRONG>_<STRONG>_</STRONG>_<STRONG>__</STRONG>				       u2 - u1				 <STRONG>^</STRONG>  =  _<STRONG>_</STRONG>_<STRONG>_</STRONG>_<STRONG>__</STRONG>				       v2 - v1	  <EM>target</EM> is a symbolic constant	that indicates what kind of	  control points are provided in <EM>points</EM>, and what output is	  generated when the map is evaluated.	It can assume one of	  nine predefined values:	  <STRONG>GL_MAP2_VERTEX_3</STRONG>	   Each	control	point is three				   floating-point values representing				   x, y, and z.	 Internal <STRONG>glVertex3</STRONG>				   commands are	generated when the map				   is evaluated.	  <STRONG>GL_MAP2_VERTEX_4</STRONG>	   Each	control	point is four				   floating-point values representing				   x, y, z, and	w.  Internal <STRONG>glVertex4</STRONG>				   commands are	generated when the map				   is evaluated.	  <STRONG>GL_MAP2_INDEX</STRONG>		   Each	control	point is a single				   floating-point value	representing a				   color index.	 Internal <STRONG>glIndex</STRONG>				   commands are	generated when the map				   is evaluated	but the	current	index				   is not updated with the value of				   these <STRONG>glIndex</STRONG> commands.	  <STRONG>GL_MAP2_COLOR_4</STRONG>	   Each	control	point is four				   floating-point values representing				   red,	green, blue, and alpha.				   Internal <STRONG>glColor4</STRONG> commands are				   generated when the map is evaluated				   but the current color is not				   updated with	the value of these				   <STRONG>glColor4</STRONG> commands.	  <STRONG>GL_MAP2_NORMAL</STRONG>	   Each	control	point is three				   floating-point values representing				   the x, y, and z components of a				   normal vector.  Internal <STRONG>glNormal</STRONG>				   commands are	generated when the map				   is evaluated	but the	current	normal				   is not updated with the value of				   these <STRONG>glNormal</STRONG> commands.	  <STRONG>GL_MAP2_TEXTURE_COORD_1</STRONG>  Each	control	point is a single				   floating-point value	representing				   the s texture coordinate.  Internal				   <STRONG>glTexCoord1</STRONG> commands	are generated				   when	the map	is evaluated but the				   current texture coordinates are not				   updated with	the value of these				   <STRONG>glTexCoord</STRONG> commands.	  <STRONG>GL_MAP2_TEXTURE_COORD_2</STRONG>  Each	control	point is two				   floating-point values representing				   the s and t texture coordinates.				   Internal				   <STRONG>glTexCoord2</STRONG> commands	are generated				   when	the map	is evaluated but the				   current texture coordinates are not				   updated with	the value of these				   <STRONG>glTexCoord</STRONG> commands.	  <STRONG>GL_MAP2_TEXTURE_COORD_3</STRONG>  Each	control	point is three				   floating-point values representing				   the s, t, and r texture				   coordinates.	 Internal <STRONG>glTexCoord3</STRONG>				   commands are	generated when the map				   is evaluated	but the	current				   texture coordinates are not updated				   with	the value of these <STRONG>glTexCoord</STRONG>				   commands.	  <STRONG>GL_MAP2_TEXTURE_COORD_4</STRONG>  Each	control	point is four				   floating-point values representing				   the s, t, r,	and q texture				   coordinates.	 Internal				   <STRONG>glTexCoord4</STRONG> commands	are generated				   when	the map	is evaluated but the				   current texture coordinates are not				   updated with	the value of these				   <STRONG>glTexCoord</STRONG> commands.	  <EM>ustride</EM>, <EM>uorder</EM>, <EM>vstride</EM>, <EM>vorder</EM>, and	<EM>points</EM> define the	  array	addressing for accessing the control points.  <EM>points</EM>	  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	  uorderxvorder	control	points in the array.  <EM>ustride</EM>	  specifies how	many float or double locations are skipped to	  advance the internal memory pointer from control point R	  to control point R	  .  <EM>vstride</EM> specifies how many	fl<STRONG>oa</STRONG>t	  or double location<STRONG>s</STRONG>i<STRONG>are</STRONG>jskipped to advance the internal	  memory pointer from control point R	to control point	  R	 .			     ij	   i(j+1)     <STRONG>NOTES</STRONG>	  As is	the case with all GL commands that accept pointers to	  data,	it is as if the	contents of <EM>points</EM> were	copied by	  <STRONG>glMap2</STRONG> before	<STRONG>glMap2</STRONG> returns.	 Changes to the	contents of	  <EM>points</EM> have no effect	after <STRONG>glMap2</STRONG> is	called.	  Initially, <STRONG>GL_AUTO_NORMAL</STRONG> is enabled.	If <STRONG>GL_AUTO_NORMAL</STRONG> is	  enabled, normal vectors are generated	when either	  <STRONG>GL_MAP2_VERTEX_3</STRONG> or <STRONG>GL_MAP2_VERTEX_4</STRONG> is used to generate	  vertices.     <STRONG>ERRORS</STRONG>	  <STRONG>GL_INVALID_ENUM</STRONG> is generated if <EM>target</EM> is not	an accepted	  value.	  <STRONG>GL_INVALID_VALUE</STRONG> is generated	if <EM>u1</EM> is equal to <EM>u2</EM>, or if <EM>v1</EM>	  is equal to <EM>v2</EM>.	  <STRONG>GL_INVALID_VALUE</STRONG> is generated	if either <EM>ustride</EM> or <EM>vstride</EM>	  is less than the number of values in a control point.	  <STRONG>GL_INVALID_VALUE</STRONG> is generated	if either <EM>uorder</EM> or <EM>vorder</EM> is	  less than 1 or greater than the return value of	  <STRONG>GL_MAX_EVAL_ORDER</STRONG>.	  <STRONG>GL_INVALID_OPERATION</STRONG> is generated if <STRONG>glMap2</STRONG> is executed	  between the execution	of <STRONG>glBegin</STRONG> and the corresponding	  execution of <STRONG>glEnd</STRONG>.     <STRONG>ASSOCIATED</STRONG>	<STRONG>GETS</STRONG>	  <STRONG>glGetMap</STRONG>	  <STRONG>glGet</STRONG>	with argument <STRONG>GL_MAX_EVAL_ORDER</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_VERTEX_3</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_VERTEX_4</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_INDEX</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_COLOR_4</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_NORMAL</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_TEXTURE_COORD_1</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_TEXTURE_COORD_2</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_TEXTURE_COORD_3</STRONG>	  <STRONG>glIsEnabled</STRONG> with argument <STRONG>GL_MAP2_TEXTURE_COORD_4</STRONG>     <STRONG>SEE</STRONG> <STRONG>ALSO</STRONG>	  <STRONG>glBegin</STRONG>, <STRONG>glColor</STRONG>, <STRONG>glEnable</STRONG>, <STRONG>glEvalCoord</STRONG>, <STRONG>glEvalMesh</STRONG>,	  <STRONG>glEvalPoint</STRONG>, <STRONG>glMap1</STRONG>, <STRONG>glMapGrid</STRONG>, <STRONG>glNormal</STRONG>, <STRONG>glTexCoord</STRONG>,	  <STRONG>glVertex</STRONG></PRE></BODY></HTML>
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