NAME¶

glFrustum - multiply the current matrix by a perspective matrix

C SPECIFICATION¶

void glFrustum( GLdouble left,

	GLdouble right,
	GLdouble bottom,
	GLdouble top,
	GLdouble near_val,
	GLdouble far_val )

PARAMETERS¶

left, right

Specify the coordinates for the left and right vertical clipping planes.

bottom, top

Specify the coordinates for the bottom and top horizontal clipping planes.

near_val, far_val

Specify the distances to the near and far depth clipping planes. Both distances must be positive.

DESCRIPTION¶

glFrustum describes a perspective matrix that produces a perspective projection. The current matrix (see glMatrixMode) is multiplied by this matrix and the result replaces the current matrix, as if glMultMatrix were called with the following matrix as its argument:

$\left[\begin{array}{cccc}\frac{2\mathrm{near\_val}}{\mathrm{right}-\mathrm{left}}& 0& A& 0\\ 0& \frac{2\mathrm{near\_val}}{\mathrm{top}-\mathrm{bottom}}& B& 0\\ 0& 0& C& D\\ 0& 0& -1& 0\end{array}\right]$

$A=\frac{\mathrm{right}+\mathrm{left}}{\mathrm{right}-\mathrm{left}}$

$B=\frac{\mathrm{top}+\mathrm{bottom}}{\mathrm{top}-\mathrm{bottom}}$

$C=-\frac{\mathrm{far\_val}+\mathrm{near\_val}}{\mathrm{far\_val}-\mathrm{near\_val}}$

$D=-\frac{2\mathrm{far\_val}\mathrm{near\_val}}{\mathrm{far\_val}-\mathrm{near\_val}}$

Typically, the matrix mode is GL_PROJECTION, and (left, bottom, -near_val) and (right, top, -near_val) specify the points on the near clipping plane that are mapped to the lower left and upper right corners of the window, assuming that the eye is located at (0, 0, 0). -far_val specifies the location of the far clipping plane. Both near_val and far_val must be positive.

Use glPushMatrix and glPopMatrix to save and restore the current matrix stack.

NOTES¶

Depth buffer precision is affected by the values specified for near_val and far_val. The greater the ratio of far_val to near_val is, the less effective the depth buffer will be at distinguishing between surfaces that are near each other. If

$r=\frac{\mathrm{far\_val}}{\mathrm{near\_val}}$

roughly ${\log }_2\left(r\right)$ bits of depth buffer precision are lost. Because $r$ approaches infinity as near_val approaches 0, near_val must never be set to 0.

ERRORS¶

GL_INVALID_VALUE is generated if near_val or far_val is not positive, or if left = right, or bottom = top.

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

ASSOCIATED GETS¶

glGet with argument GL_MATRIX_MODE
glGet with argument GL_MODELVIEW_MATRIX
glGet with argument GL_PROJECTION_MATRIX
glGet with argument GL_TEXTURE_MATRIX
glGet with argument GL_COLOR_MATRIX

SEE ALSO¶

glOrtho(3G), glMatrixMode(3G), glMultMatrix(3G), glPushMatrix(3G), glViewport(3G)