Static Sub Map2f ( Target As Integer, U1 As Float, U2 As Float, Ustride As Integer, Uorder As Integer, V1 As Float, V2 As Float, Vstride As Integer, Vorder As Integer, Points As Float[] )

Define a two-dimensional evaluator.

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 Gl.EvalCoord2, to $\hat{u}$ , 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 beginning of control point $R_{ij}$ 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 Gl.EvalCoord2, to $\hat{v}$ , 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 beginning of control point $R_{ij}$ and the beginning of control point $R_{i (j + 1)}$ , 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 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 Gl.Vertex, Gl.Normal, Gl.TexCoord, and Gl.Color 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 (\hat{u}, \hat{v})

p (\hat{u}, \hat{v}) Σ_{i 0}^{n} Σ_{j 0}^{m} {B_{i}}^{n} (\hat{u}) {B_{j}}^{m} (\hat{v}) R_{ij}

where

R_{ij}

is a control point,

{B_{i}}^{n} (\hat{u})

is the

i

th Bernstein polynomial of degree

n

(uorder =

n + 1

)

{B_{i}}^{n} (\hat{u}) (\begin{matrix} n \\ i \end{matrix}) {\hat{u}}^{i} {(1 - \hat{u})}^{n - i}

and

{B_{j}}^{m} (\hat{v})

is the

j

th Bernstein polynomial of degree

m

(vorder =

m + 1

)

{B_{j}}^{m} (\hat{v}) (\begin{matrix} m \\ j \end{matrix}) {\hat{v}}^{j} {(1 - \hat{v})}^{m - j}

Recall that

0^{0} 1

and

(\begin{matrix} n \\ 0 \end{matrix}) 1

Gl.Map2 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 Gl.Enable and Gl.Disable with the map name, one of the nine predefined values for target, described below. When Gl.EvalCoord2 presents values

u

and

v

, the bivariate Bernstein polynomials are evaluated using

\hat{u}

and

\hat{v}

, where

\hat{u} \frac{u - u1}{u2 - u1}

\hat{v} \frac{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 Gl.Vertex3 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 Gl.Vertex4 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 Gl.Index commands are generated when the map is evaluated but the current index is not updated with the value of these Gl.Index commands.
Gl.MAP2_COLOR_4: Each control point is four floating-point values representing red, green, blue, and alpha. Internal Gl.Color4 commands are generated when the map is evaluated but the current color is not updated with the value of these Gl.Color4 commands.
Gl.MAP2_NORMAL: Each control point is three floating-point values representing the $x$ , $y$ , and $z$ components of a normal vector. Internal Gl.Normal commands are generated when the map is evaluated but the current normal is not updated with the value of these Gl.Normal commands.
Gl.MAP2_TEXTURE_COORD_1: Each control point is a single floating-point value representing the $s$ texture coordinate. Internal Gl.TexCoord1 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these Gl.TexCoord commands.
Gl.MAP2_TEXTURE_COORD_2: Each control point is two floating-point values representing the $s$ and $t$ texture coordinates. Internal Gl.TexCoord2 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these Gl.TexCoord commands.
Gl.MAP2_TEXTURE_COORD_3: Each control point is three floating-point values representing the $s$ , $t$ , and $r$ texture coordinates. Internal Gl.TexCoord3 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these Gl.TexCoord commands.
Gl.MAP2_TEXTURE_COORD_4: Each control point is four floating-point values representing the $s$ , $t$ , $r$ , and $q$ texture coordinates. Internal Gl.TexCoord4 commands are generated when the map is evaluated but the current texture coordinates are not updated with the value of these Gl.TexCoord commands.

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 \times 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

R_{i j}

to control point

R_{(i + 1) j}

. vstride specifies how many float or double locations are skipped to advance the internal memory pointer from control point

R_{i j}

to control point

R_{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 Gl.Map2 before Gl.Map2 returns. Changes to the contents of points have no effect after Gl.Map2 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 Gl.Map2 is executed between the execution of Gl.Begin and the corresponding execution of Gl.End.

Gl.INVALID_OPERATION is generated if Gl.Map2 is called and the value of Gl.ACTIVE_TEXTURE is not Gl.TEXTURE0.

Associated Gets

Gl.GetMap

Gl.Get with argument Gl.MAX_EVAL_ORDER

Gl.IsEnabled with argument Gl.MAP2_VERTEX_3

Gl.IsEnabled with argument Gl.MAP2_VERTEX_4

Gl.IsEnabled with argument Gl.MAP2_INDEX

Gl.IsEnabled with argument Gl.MAP2_COLOR_4

Gl.IsEnabled with argument Gl.MAP2_NORMAL

Gl.IsEnabled with argument Gl.MAP2_TEXTURE_COORD_1

Gl.IsEnabled with argument Gl.MAP2_TEXTURE_COORD_2

Gl.IsEnabled with argument Gl.MAP2_TEXTURE_COORD_3

Gl.IsEnabled with argument Gl.MAP2_TEXTURE_COORD_4

Gl.Map2f (gb.opengl)

Parameters

Description

Notes

Errors

Associated Gets

See also