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<!DOCTYPE book PUBLIC "-//OASIS//DTD DocBook MathML Module V1.1b1//EN"
"http://www.oasis-open.org/docbook/xml/mathml/1.1CR1/dbmathml.dtd">
<refentry id="glFrustum">
<refmeta>
<refmetainfo>
<copyright>
<year>1991-2006</year>
<holder>Silicon Graphics, Inc.</holder>
</copyright>
</refmetainfo>
<refentrytitle>glFrustum</refentrytitle>
<manvolnum>3G</manvolnum>
</refmeta>
<refnamediv>
<refname>glFrustum</refname>
<refpurpose>multiply the current matrix by a perspective matrix</refpurpose>
</refnamediv>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>glFrustum</function></funcdef>
<paramdef>GLdouble <parameter>left</parameter></paramdef>
<paramdef>GLdouble <parameter>right</parameter></paramdef>
<paramdef>GLdouble <parameter>bottom</parameter></paramdef>
<paramdef>GLdouble <parameter>top</parameter></paramdef>
<paramdef>GLdouble <parameter>nearVal</parameter></paramdef>
<paramdef>GLdouble <parameter>farVal</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<!-- eqn: ignoring delim $$ -->
<refsect1 id="parameters"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>left</parameter></term>
<term><parameter>right</parameter></term>
<listitem>
<para>
Specify the coordinates for the left and right vertical clipping planes.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>bottom</parameter></term>
<term><parameter>top</parameter></term>
<listitem>
<para>
Specify the coordinates for the bottom and top horizontal clipping planes.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>nearVal</parameter></term>
<term><parameter>farVal</parameter></term>
<listitem>
<para>
Specify the distances to the near and far depth clipping planes.
Both distances must be positive.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsect1 id="description"><title>Description</title>
<para>
<function>glFrustum</function> describes a perspective matrix that produces a perspective projection.
The current matrix (see <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>) is multiplied by this matrix
and the result replaces the current matrix, as if
<citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the following matrix
as its argument:
</para>
<para>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: left [ matrix { ccol { {{2 nearVal} over {right - left}} above 0 above 0 above 0 } ccol { 0 above {{2 nearVal} over {top - bottom}} above 0 above 0 } ccol { A above B above C above -1 } ccol { 0 above 0 above D above 0} } right ]:-->
<mml:mfenced open="[" close="]">
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mfenced open="" close="">
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>⁢</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">right</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">left</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mfenced>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mfenced open="" close="">
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>⁢</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">top</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">bottom</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mfenced>
</mml:mtd>
<mml:mtd>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mi mathvariant="italic">C</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mi mathvariant="italic">D</mml:mi>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>-1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mfenced>
</mml:math></informalequation>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: A = {right + left} over {right - left}:-->
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">right</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">left</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">right</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">left</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: B = {top + bottom} over {top - bottom}:-->
<mml:mrow>
<mml:mi mathvariant="italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">top</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">bottom</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">top</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">bottom</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: C = -{{farVal + nearVal} over {farVal - nearVal}}:-->
<mml:mrow>
<mml:mi mathvariant="italic">C</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mfenced open="" close="">
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">farVal</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">farVal</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: D = -{{2 farVal nearVal} over {farVal - nearVal}}:-->
<mml:mrow>
<mml:mi mathvariant="italic">D</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mfenced open="" close="">
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>⁢</mml:mo>
<mml:mi mathvariant="italic">farVal</mml:mi>
<mml:mo>⁢</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">farVal</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
</para>
<para>
Typically, the matrix mode is <constant>GL_PROJECTION</constant>, and
<inlineequation><mml:math>
<!-- eqn: (left, bottom, -nearVal):-->
<mml:mfenced open="(" close=")">
<mml:mi mathvariant="italic">left</mml:mi>
<mml:mi mathvariant="italic">bottom</mml:mi>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:math></inlineequation>
and
<inlineequation><mml:math>
<!-- eqn: (right, top, -nearVal):-->
<mml:mfenced open="(" close=")">
<mml:mi mathvariant="italic">right</mml:mi>
<mml:mi mathvariant="italic">top</mml:mi>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:math></inlineequation>
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).
<inlineequation><mml:math>
<!-- eqn: -farVal:-->
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">farVal</mml:mi>
</mml:mrow>
</mml:math></inlineequation>
specifies the location of the far clipping plane.
Both <parameter>nearVal</parameter> and <parameter>farVal</parameter> must be positive.
</para>
<para>
Use <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glPopMatrix</refentrytitle></citerefentry> to save and restore
the current matrix stack.
</para>
</refsect1>
<refsect1 id="notes"><title>Notes</title>
<para>
Depth buffer precision is affected by the values specified for
<parameter>nearVal</parameter> and <parameter>farVal</parameter>.
The greater the ratio of <parameter>farVal</parameter> to <parameter>nearVal</parameter> is,
the less effective the depth buffer will be at distinguishing between
surfaces that are near each other.
If
</para>
<para>
<inlineequation><mml:math>
<!-- eqn: r = farVal over nearVal:-->
<mml:mrow>
<mml:mi mathvariant="italic">r</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mi mathvariant="italic">farVal</mml:mi>
<mml:mi mathvariant="italic">nearVal</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math></inlineequation>
</para>
<para>
roughly
<inlineequation><mml:math>
<!-- eqn: log sub 2 (r):-->
<mml:mrow>
<mml:msub><mml:mi mathvariant="italic">log</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mi mathvariant="italic">r</mml:mi>
</mml:mfenced>
</mml:mrow>
</mml:math></inlineequation>
bits of depth buffer precision are lost.
Because
<inlineequation><mml:math><mml:mi mathvariant="italic">r</mml:mi></mml:math></inlineequation>
approaches infinity as <parameter>nearVal</parameter> approaches 0,
<parameter>nearVal</parameter> must never be set to 0.
</para>
</refsect1>
<refsect1 id="errors"><title>Errors</title>
<para>
<constant>GL_INVALID_VALUE</constant> is generated if <parameter>nearVal</parameter> or <parameter>farVal</parameter> is not
positive, or if <parameter>left</parameter> = <parameter>right</parameter>, or <parameter>bottom</parameter> = <parameter>top</parameter>,
or <parameter>near</parameter> = <parameter>far</parameter>.
</para>
<para>
<constant>GL_INVALID_OPERATION</constant> is generated if <function>glFrustum</function>
is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry>
and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>.
</para>
</refsect1>
<refsect1 id="associatedgets"><title>Associated Gets</title>
<para>
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MATRIX_MODE</constant>
</para>
<para>
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MODELVIEW_MATRIX</constant>
</para>
<para>
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_PROJECTION_MATRIX</constant>
</para>
<para>
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_TEXTURE_MATRIX</constant>
</para>
<para>
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_COLOR_MATRIX</constant>
</para>
</refsect1>
<refsect1 id="seealso"><title>See Also</title>
<para>
<citerefentry><refentrytitle>glOrtho</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glViewport</refentrytitle></citerefentry>
</para>
</refsect1>
<refsect1 id="Copyright"><title>Copyright</title>
<para>
Copyright <trademark class="copyright"></trademark> 1991-2006
Silicon Graphics, Inc. This document is licensed under the SGI
Free Software B License. For details, see
<ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>.
</para>
</refsect1>
</refentry>