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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  vari-ables variables
                ables  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 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 vari-ables variables
                ables 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 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,  nor-mals, normals,
       mals,  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 coordi-nates, coordinates,
       nates, 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

                   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 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  com-mands. commands.
                                mands.

       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 tex-ture texture
                                ture 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 com-mands. commands.
                                mands.

       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  com-mands. commands.
                                mands.

       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  com-mands. commands.
                                mands.

       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 con-trol control
       trol 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 speci-fies specifies
       fies how many float or double locations are skipped to advance the internal memory pointer from  con-trol control
       trol 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 cor-responding corresponding
       responding 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(3G), glColor(3G),  glEnable(3G),  glEvalCoord(3G),  glEvalMesh(3G),  glEvalPoint(3G),  glMap1(3G),  glMapGrid(3G),  glNormal(3G),
       glTexCoord(3G), glVertex(3G)




                                                                                                  GLMAP2(3G)