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421 lines
20 KiB
XML
421 lines
20 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE book PUBLIC "-//OASIS//DTD DocBook MathML Module V1.1b1//EN"
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"http://www.oasis-open.org/docbook/xml/mathml/1.1CR1/dbmathml.dtd">
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<refentry id="glFrustum">
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<refmeta>
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<refmetainfo>
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<copyright>
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<year>1991-2006</year>
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<holder>Silicon Graphics, Inc.</holder>
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</copyright>
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</refmetainfo>
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<refentrytitle>glFrustum</refentrytitle>
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<manvolnum>3G</manvolnum>
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</refmeta>
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<refnamediv>
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<refname>glFrustum</refname>
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<refpurpose>multiply the current matrix by a perspective matrix</refpurpose>
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</refnamediv>
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<refsynopsisdiv><title>C Specification</title>
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<funcsynopsis>
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<funcprototype>
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<funcdef>void <function>glFrustum</function></funcdef>
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<paramdef>GLdouble <parameter>left</parameter></paramdef>
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<paramdef>GLdouble <parameter>right</parameter></paramdef>
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<paramdef>GLdouble <parameter>bottom</parameter></paramdef>
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<paramdef>GLdouble <parameter>top</parameter></paramdef>
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<paramdef>GLdouble <parameter>nearVal</parameter></paramdef>
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<paramdef>GLdouble <parameter>farVal</parameter></paramdef>
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</funcprototype>
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</funcsynopsis>
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</refsynopsisdiv>
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<!-- eqn: ignoring delim $$ -->
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<refsect1 id="parameters"><title>Parameters</title>
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<variablelist>
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<varlistentry>
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<term><parameter>left</parameter></term>
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<term><parameter>right</parameter></term>
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<listitem>
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<para>
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Specify the coordinates for the left and right vertical clipping planes.
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</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><parameter>bottom</parameter></term>
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<term><parameter>top</parameter></term>
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<listitem>
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<para>
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Specify the coordinates for the bottom and top horizontal clipping planes.
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</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><parameter>nearVal</parameter></term>
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<term><parameter>farVal</parameter></term>
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<listitem>
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<para>
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Specify the distances to the near and far depth clipping planes.
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Both distances must be positive.
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</para>
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</listitem>
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</varlistentry>
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</variablelist>
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</refsect1>
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<refsect1 id="description"><title>Description</title>
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<para>
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<function>glFrustum</function> describes a perspective matrix that produces a perspective projection.
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The current matrix (see <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>) is multiplied by this matrix
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and the result replaces the current matrix, as if
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<citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the following matrix
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as its argument:
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</para>
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<para>
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</para>
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<para>
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<informalequation><mml:math>
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<!-- 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 ]:-->
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<mml:mfenced open="[" close="]">
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<mml:mtable>
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<mml:mtr>
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<mml:mtd>
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<mml:mfenced open="" close="">
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mn>2</mml:mn>
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<mml:mo>⁢</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">right</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">left</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mfenced>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mi mathvariant="italic">A</mml:mi>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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</mml:mtr>
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<mml:mtr>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mfenced open="" close="">
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mn>2</mml:mn>
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<mml:mo>⁢</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">top</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">bottom</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mfenced>
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</mml:mtd>
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<mml:mtd>
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<mml:mi mathvariant="italic">B</mml:mi>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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</mml:mtr>
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<mml:mtr>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mi mathvariant="italic">C</mml:mi>
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</mml:mtd>
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<mml:mtd>
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<mml:mi mathvariant="italic">D</mml:mi>
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</mml:mtd>
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</mml:mtr>
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<mml:mtr>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>-1</mml:mn>
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</mml:mtd>
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<mml:mtd>
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<mml:mn>0</mml:mn>
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</mml:mtd>
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</mml:mtr>
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</mml:mtable>
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</mml:mfenced>
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</mml:math></informalequation>
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: A = {right + left} over {right - left}:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">A</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">right</mml:mi>
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<mml:mo>+</mml:mo>
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<mml:mi mathvariant="italic">left</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">right</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">left</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mrow>
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</mml:math></informalequation>
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: B = {top + bottom} over {top - bottom}:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">B</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">top</mml:mi>
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<mml:mo>+</mml:mo>
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<mml:mi mathvariant="italic">bottom</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">top</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">bottom</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mrow>
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</mml:math></informalequation>
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: C = -{{farVal + nearVal} over {farVal - nearVal}}:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">C</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mrow>
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<mml:mo>-</mml:mo>
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<mml:mfenced open="" close="">
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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<mml:mo>+</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mfenced>
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</mml:mrow>
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</mml:mrow>
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</mml:math></informalequation>
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: D = -{{2 farVal nearVal} over {farVal - nearVal}}:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">D</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mrow>
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<mml:mo>-</mml:mo>
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<mml:mfenced open="" close="">
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<mml:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mn>2</mml:mn>
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<mml:mo>⁢</mml:mo>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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<mml:mo>⁢</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:mfrac>
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</mml:mfenced>
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</mml:mrow>
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</mml:mrow>
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</mml:math></informalequation>
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</para>
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<para>
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</para>
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<para>
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Typically, the matrix mode is <constant>GL_PROJECTION</constant>, and
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<inlineequation><mml:math>
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<!-- eqn: (left, bottom, -nearVal):-->
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<mml:mfenced open="(" close=")">
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<mml:mi mathvariant="italic">left</mml:mi>
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<mml:mi mathvariant="italic">bottom</mml:mi>
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<mml:mrow>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:math></inlineequation>
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and
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<inlineequation><mml:math>
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<!-- eqn: (right, top, -nearVal):-->
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<mml:mfenced open="(" close=")">
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<mml:mi mathvariant="italic">right</mml:mi>
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<mml:mi mathvariant="italic">top</mml:mi>
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<mml:mrow>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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</mml:math></inlineequation>
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specify the points on the near clipping plane that are mapped
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to the lower left and upper right corners of the window,
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assuming that the eye is located at (0, 0, 0).
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<inlineequation><mml:math>
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<!-- eqn: -farVal:-->
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<mml:mrow>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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</mml:mrow>
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</mml:math></inlineequation>
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specifies the location of the far clipping plane.
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Both <parameter>nearVal</parameter> and <parameter>farVal</parameter> must be positive.
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</para>
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<para>
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Use <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glPopMatrix</refentrytitle></citerefentry> to save and restore
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the current matrix stack.
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</para>
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</refsect1>
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<refsect1 id="notes"><title>Notes</title>
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<para>
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Depth buffer precision is affected by the values specified for
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<parameter>nearVal</parameter> and <parameter>farVal</parameter>.
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The greater the ratio of <parameter>farVal</parameter> to <parameter>nearVal</parameter> is,
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the less effective the depth buffer will be at distinguishing between
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surfaces that are near each other.
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If
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</para>
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<para>
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<inlineequation><mml:math>
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<!-- eqn: r = farVal over nearVal:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">r</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mi mathvariant="italic">farVal</mml:mi>
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<mml:mi mathvariant="italic">nearVal</mml:mi>
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</mml:mfrac>
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</mml:mrow>
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</mml:math></inlineequation>
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</para>
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<para>
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roughly
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<inlineequation><mml:math>
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<!-- eqn: log sub 2 (r):-->
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<mml:mrow>
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<mml:msub><mml:mi mathvariant="italic">log</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="(" close=")">
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<mml:mi mathvariant="italic">r</mml:mi>
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</mml:mfenced>
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</mml:mrow>
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</mml:math></inlineequation>
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bits of depth buffer precision are lost.
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Because
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<inlineequation><mml:math><mml:mi mathvariant="italic">r</mml:mi></mml:math></inlineequation>
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approaches infinity as <parameter>nearVal</parameter> approaches 0,
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<parameter>nearVal</parameter> must never be set to 0.
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</para>
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</refsect1>
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<refsect1 id="errors"><title>Errors</title>
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<para>
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<constant>GL_INVALID_VALUE</constant> is generated if <parameter>nearVal</parameter> or <parameter>farVal</parameter> is not
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positive, or if <parameter>left</parameter> = <parameter>right</parameter>, or <parameter>bottom</parameter> = <parameter>top</parameter>,
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or <parameter>near</parameter> = <parameter>far</parameter>.
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</para>
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<para>
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<constant>GL_INVALID_OPERATION</constant> is generated if <function>glFrustum</function>
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is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry>
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and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>.
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</para>
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</refsect1>
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<refsect1 id="associatedgets"><title>Associated Gets</title>
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<para>
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<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MATRIX_MODE</constant>
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</para>
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<para>
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<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MODELVIEW_MATRIX</constant>
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</para>
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<para>
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<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_PROJECTION_MATRIX</constant>
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</para>
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<para>
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<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_TEXTURE_MATRIX</constant>
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</para>
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<para>
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<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_COLOR_MATRIX</constant>
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</para>
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</refsect1>
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<refsect1 id="seealso"><title>See Also</title>
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<para>
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<citerefentry><refentrytitle>glOrtho</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glViewport</refentrytitle></citerefentry>
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</para>
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</refsect1>
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<refsect1 id="Copyright"><title>Copyright</title>
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<para>
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Copyright <trademark class="copyright"></trademark> 1991-2006
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Silicon Graphics, Inc. This document is licensed under the SGI
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Free Software B License. For details, see
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<ulink url="http://oss.sgi.com/projects/FreeB/">http://oss.sgi.com/projects/FreeB/</ulink>.
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</para>
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</refsect1>
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</refentry>
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