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282 lines
13 KiB
XML
282 lines
13 KiB
XML
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<?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="gluPerspective">
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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>gluPerspective</refentrytitle>
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<manvolnum>3G</manvolnum>
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</refmeta>
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<refnamediv>
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<refname>gluPerspective</refname>
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<refpurpose>set up a perspective projection 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>gluPerspective</function></funcdef>
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<paramdef>GLdouble <parameter>fovy</parameter></paramdef>
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<paramdef>GLdouble <parameter>aspect</parameter></paramdef>
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<paramdef>GLdouble <parameter>zNear</parameter></paramdef>
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<paramdef>GLdouble <parameter>zFar</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>fovy</parameter></term>
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<listitem>
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<para>
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Specifies the field of view angle, in degrees, in the <emphasis>y</emphasis> direction.
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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>aspect</parameter></term>
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<listitem>
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<para>
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Specifies the aspect ratio that determines
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the field of view in the <emphasis>x</emphasis> direction.
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The aspect ratio is the ratio of <emphasis>x</emphasis> (width) to <emphasis>y</emphasis> (height).
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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>zNear</parameter></term>
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<listitem>
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<para>
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Specifies the distance from the viewer to the near clipping plane
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(always positive).
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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>zFar</parameter></term>
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<listitem>
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<para>
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Specifies the distance from the viewer to the far clipping plane
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(always 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>gluPerspective</function> specifies a viewing frustum into the world coordinate system.
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In general, the aspect ratio in <function>gluPerspective</function> should match the aspect ratio
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of the associated viewport. For example,
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<inlineequation><mml:math>
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<!-- eqn: aspect = 2.0:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">aspect</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mn>2.0</mml:mn>
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</mml:mrow>
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</mml:math></inlineequation>
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means
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the viewer's
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angle of view is twice as wide in <emphasis>x</emphasis> as it is in <emphasis>y</emphasis>.
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If the viewport is
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twice as wide as it is tall, it displays the image without distortion.
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</para>
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<para>
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The matrix generated by <function>gluPerspective</function> is multipled by the current matrix,
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just as if <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the generated matrix.
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To load the perspective matrix onto the current matrix stack instead,
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precede the call to <function>gluPerspective</function> with a call to <citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>.
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</para>
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<para>
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Given <emphasis>f</emphasis> defined as follows:
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: f = cotangent(fovy over 2):-->
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<mml:mrow>
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<mml:mi mathvariant="italic">f</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mrow>
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<mml:mi mathvariant="italic">cotangent</mml:mi>
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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:mi mathvariant="italic">fovy</mml:mi>
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<mml:mn>2</mml:mn>
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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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The generated matrix is
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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 { f over aspect above 0 above 0 above 0 } ccol { 0 above f above 0 above 0 } ccol { 0 above 0 above {zFar + zNear} over {zNear - zFar} above -1 } ccol { 0 above 0 above {2 * zFar * zNear} over {zNear - zFar} 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:mfrac>
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<mml:mi mathvariant="italic">f</mml:mi>
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<mml:mi mathvariant="italic">aspect</mml:mi>
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</mml:mfrac>
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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>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: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:mi mathvariant="italic">f</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: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:mfrac>
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<mml:mfenced open="" close="">
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<mml:mrow>
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<mml:mi mathvariant="italic">zFar</mml:mi>
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<mml:mo>+</mml:mo>
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<mml:mi mathvariant="italic">zNear</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">zNear</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">zFar</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:mtd>
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<mml:mtd>
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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">zFar</mml:mi>
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<mml:mo>×</mml:mo>
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<mml:mi mathvariant="italic">zNear</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">zNear</mml:mi>
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<mml:mo>-</mml:mo>
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<mml:mi mathvariant="italic">zFar</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: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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</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>zNear</parameter> and <parameter>zFar</parameter>.
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The greater the ratio of <parameter>zFar</parameter> to <parameter>zNear</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 = zFar over zNear:-->
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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">zFar</mml:mi>
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<mml:mi mathvariant="italic">zNear</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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</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>zNear</parameter> approaches 0,
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<parameter>zNear</parameter> must never be set to 0.
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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>gluOrtho2D</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glFrustum</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>,
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<citerefentry><refentrytitle>glMultMatrix</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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