Function glMap1d

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 p(û) as

p(û) = n∑i=0 𝐁ᵢⁿ(û) 𝐑ᵢ

where 𝐑ᵢ is a control point and 𝐁ᵢⁿ(û) is the 𝐢ᵗʰ Bernstein polynomial of degree 𝐧 (order = 𝐧 + 1):

𝐁ᵢⁿ(û) = (𝐧ㅤㅤi)ûⁱ ( 1− û) ^ 𝐧−i

Recall that

0⁰ == 1 and (𝐧ㅤㅤ0) == 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 𝐮, the Bernstein functions are evaluated using û, where û = (𝐮 − 𝐮1 / 𝐮2 − 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:

• GL_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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_MAP1_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 coordinates are not updated with the value of these glTexCoord commands.

• GL_MAP1_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 commands.

• GL_MAP1_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_MAP1_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 commands.

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.

Summary

define a one-dimensional evaluator

See

glMap1