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 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 splines used in computer graphics: B-splines, Bezier curves, Hermite splines, and so on.

Evaluators define curves based on Bernstein polynomials. Define $\mathit{p}\left(\hat{\mathit{u}}\right)$ as

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

${{\mathit{B}}_{\mathit{i}}}^{\mathit{n}}\left(\hat{\mathit{u}}\right)=\left(\begin{array}{c}\mathit{n}\\ \mathit{i}\end{array}\right){\hat{\mathit{u}}}^{\mathit{i}}{\left(1-\hat{\mathit{u}}\right)}^{\mathit{n}-\mathit{i}}$

Recall that

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

glMap1 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. glEvalCoord1 evaluates the one-dimensional maps that are enabled. When glEvalCoord1 presents a value $\mathit{u}$, the Bernstein functions are evaluated using $\hat{\mathit{u}}$, where $\hat{\mathit{u}}=\frac{\mathit{u}-\mathit{u1}}{\mathit{u2}-\mathit{u1}}$

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:

stride, order, 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. order is the number of control points in the array. stride specifies how many float or double locations to advance the internal memory pointer to reach the next control point.

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 glMap1 before glMap1 returns. Changes to the contents of points have no effect after glMap1 is called.

Errors

GL_INVALID_ENUM is generated if target is not an accepted value.

GL_INVALID_VALUE is generated if u1 is equal to u2.

GL_INVALID_VALUE is generated if stride is less than the number of values in a control point.

GL_INVALID_VALUE is generated if order is less than 1 or greater than the return value of GL_MAX_EVAL_ORDER.

GL_INVALID_OPERATION is generated if glMap1 is executed between the execution of glBegin and the corresponding execution of glEnd.

GL_INVALID_OPERATION is generated if glMap1 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_MAP1_VERTEX_3

glIsEnabled with argument GL_MAP1_VERTEX_4

glIsEnabled with argument GL_MAP1_INDEX

glIsEnabled with argument GL_MAP1_COLOR_4

glIsEnabled with argument GL_MAP1_NORMAL

glIsEnabled with argument GL_MAP1_TEXTURE_COORD_1

glIsEnabled with argument GL_MAP1_TEXTURE_COORD_2

glIsEnabled with argument GL_MAP1_TEXTURE_COORD_3

glIsEnabled with argument GL_MAP1_TEXTURE_COORD_4

See Also

glBegin, glColor, glEnable, glEvalCoord, glEvalMesh, glEvalPoint, glMap2, glMapGrid, glNormal, glTexCoord, glVertex