Parameters

Description

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 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 $\mathit{p}\left(\hat{\mathit{u}},\hat{\mathit{v}}\right)$ as

where ${\mathit{R}}_{\mathit{ij}}$ is a control point, ${{\mathit{B}}_{\mathit{i}}}^{\mathit{n}}\left(\hat{\mathit{u}}\right)$ is the $\mathit{i}$th Bernstein polynomial of degree $\mathit{n}$ (uorder = $\mathit{n}+1$)

and ${{\mathit{B}}_{\mathit{j}}}^{\mathit{m}}\left(\hat{\mathit{v}}\right)$ is the $\mathit{j}$th Bernstein polynomial of degree $\mathit{m}$ (vorder = $\mathit{m}+1$)

Recall that $0^0==1$ and $\left(\begin{array}{c}\mathit{n}\\ 0\end{array}\right)==1$

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 calling glEnable and glDisable with the map name, one of the nine predefined values for target, described below. When glEvalCoord2 presents values $\mathit{u}$ and $\mathit{v}$, the bivariate Bernstein polynomials are evaluated using $\hat{\mathit{u}}$ and $\hat{\mathit{v}}$, where

$\hat{\mathit{u}}=\frac{\mathit{u}-\mathit{u1}}{\mathit{u2}-\mathit{u1}}$

$\hat{\mathit{v}}=\frac{\mathit{v}-\mathit{v1}}{\mathit{v2}-\mathit{v1}}$

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:

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 $\mathit{uorder}\times \mathit{vorder}$ control points in the array. ustride specifies how many float or double locations are skipped to advance the internal memory pointer from control point ${\mathit{R}}_{\mathit{i}\mathit{j}}$ to control point ${\mathit{R}}_{\left(\mathit{i}+1\right)\mathit{j}}$. vstride specifies how many float or double locations are skipped to advance the internal memory pointer from control point ${\mathit{R}}_{\mathit{i}\mathit{j}}$ to control point ${\mathit{R}}_{\mathit{i}\left(\mathit{j}+1\right)}$.

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.

GL_INVALID_OPERATION is generated if glMap2 is called and the value of GL_ACTIVE_TEXTURE is not GL_TEXTURE0.

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