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GLMAP2() GLMAP2() 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 ) delim $$ 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_TEXTURE_CO- ORD_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 equations 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 $R sub ij$ 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. 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 equations 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 $R sub ij$ and the beginning 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. 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 us- ing 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 ^) ~~=~~ up 10 {sum from i=0 to n sum from j=0 to m} B sub i sup n ( u hat ^) B sub j sup m ( v hat ^) R sub ij where $R sub ij$ is a control point, $B sub i sup n ( u hat ^)$ is the $i$th Bernstein polynomial of degree $n$ (uorder = $n + 1$) B sub i sup n ( u hat ^) ~~=~~ left ( down 20 {cpile { n above i }} ~~ right ) u hat sup i ( 1 - u hat ^) sup { n - i } and $B sub j sup m ( v hat ^)$ is the $j$th Bernstein polynomial of de- gree $m$ (vorder = $m + 1$) B sub j sup m ( v hat ^) ~~=~~ left ( down 20 {cpile { m above j }} ~~ right ) v hat sup j ( 1 - v hat ^) sup { m - j } Recall that $0 sup 0 ~==~ 1 $ and $ left ( down 20 {cpile { n above ~0 }} ~~ right ) ~~==~~ 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 prede- fined 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 $u hat ~~=~~ {u ~-~ "u1"} over {"u2" ~-~ "u1"}$ $v hat ~~=~~ {v ~-~ "v1"} over {"v2" ~-~ "v1"}$ 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: GL_MAP2_VERTEX_3 Each control point is three floating-point values representing $x$, $y$, and $z$. Inter- nal 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 $w$. In- ternal 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 $z$ com- ponents of a normal vector. Internal glNormal commands are generated when the map is evalu- ated 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 coor- dinates. 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 $r$ tex- ture coordinates. Internal glTexCoord3 com- mands 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" times "vorder" $ control points in the array. ustride speci- fies how many float or double locations are skipped to advance the in- ternal 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 con- trol 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 re- turns. 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 ex- ecution 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 GLMAP2()
NAME | C SPECIFICATION | PARAMETERS | DESCRIPTION | NOTES | ERRORS | ASSOCIATED GETS | SEE ALSO
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