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<?xml version="1.0" encoding="UTF-8"?>
<!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="gluPerspective">
<refmeta>
<refmetainfo>
<copyright>
<year>1991-2006</year>
<holder>Silicon Graphics, Inc.</holder>
</copyright>
</refmetainfo>
<refentrytitle>gluPerspective</refentrytitle>
<manvolnum>3G</manvolnum>
</refmeta>
<refnamediv>
<refname>gluPerspective</refname>
<refpurpose>set up a perspective projection matrix</refpurpose>
</refnamediv>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>gluPerspective</function></funcdef>
<paramdef>GLdouble <parameter>fovy</parameter></paramdef>
<paramdef>GLdouble <parameter>aspect</parameter></paramdef>
<paramdef>GLdouble <parameter>zNear</parameter></paramdef>
<paramdef>GLdouble <parameter>zFar</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<!-- eqn: ignoring delim $$ -->
<refsect1 id="parameters"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>fovy</parameter></term>
<listitem>
<para>
Specifies the field of view angle, in degrees, in the <emphasis>y</emphasis> direction.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>aspect</parameter></term>
<listitem>
<para>
Specifies the aspect ratio that determines
the field of view in the <emphasis>x</emphasis> direction.
The aspect ratio is the ratio of <emphasis>x</emphasis> (width) to <emphasis>y</emphasis> (height).
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>zNear</parameter></term>
<listitem>
<para>
Specifies the distance from the viewer to the near clipping plane
(always positive).
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>zFar</parameter></term>
<listitem>
<para>
Specifies the distance from the viewer to the far clipping plane
(always positive).
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsect1 id="description"><title>Description</title>
<para>
<function>gluPerspective</function> specifies a viewing frustum into the world coordinate system.
In general, the aspect ratio in <function>gluPerspective</function> should match the aspect ratio
of the associated viewport. For example,
<inlineequation><mml:math>
<!-- eqn: aspect = 2.0:-->
<mml:mrow>
<mml:mi mathvariant="italic">aspect</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>2.0</mml:mn>
</mml:mrow>
</mml:math></inlineequation>
means
the viewer's
angle of view is twice as wide in <emphasis>x</emphasis> as it is in <emphasis>y</emphasis>.
If the viewport is
twice as wide as it is tall, it displays the image without distortion.
</para>
<para>
The matrix generated by <function>gluPerspective</function> is multipled by the current matrix,
just as if <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the generated matrix.
To load the perspective matrix onto the current matrix stack instead,
precede the call to <function>gluPerspective</function> with a call to <citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>.
</para>
<para>
Given <emphasis>f</emphasis> defined as follows:
</para>
<para>
<informalequation><mml:math>
<!-- eqn: f = cotangent(fovy over 2):-->
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">cotangent</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mfrac>
<mml:mi mathvariant="italic">fovy</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math></informalequation>
The generated matrix is
</para>
<para>
<informalequation><mml:math>
<!-- 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 ):-->
<mml:mfenced open="(" close=")">
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mfrac>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mi mathvariant="italic">aspect</mml:mi>
</mml:mfrac>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</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:mi mathvariant="italic">f</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</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:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">zFar</mml:mi>
<mml:mo>+</mml:mo>
<mml:mi mathvariant="italic">zNear</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">zNear</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">zFar</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</mml:mtd>
<mml:mtd>
<mml:mfrac>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>×</mml:mo>
<mml:mi mathvariant="italic">zFar</mml:mi>
<mml:mo>×</mml:mo>
<mml:mi mathvariant="italic">zNear</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mfenced open="" close="">
<mml:mrow>
<mml:mi mathvariant="italic">zNear</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">zFar</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mfrac>
</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>
</refsect1>
<refsect1 id="notes"><title>Notes</title>
<para>
Depth buffer precision is affected by the values specified for
<parameter>zNear</parameter> and <parameter>zFar</parameter>.
The greater the ratio of <parameter>zFar</parameter> to <parameter>zNear</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 = zFar over zNear:-->
<mml:mrow>
<mml:mi mathvariant="italic">r</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mi mathvariant="italic">zFar</mml:mi>
<mml:mi mathvariant="italic">zNear</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math></inlineequation>
</para>
<para>
</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>zNear</parameter> approaches 0,
<parameter>zNear</parameter> must never be set to 0.
</para>
</refsect1>
<refsect1 id="seealso"><title>See Also</title>
<para>
<citerefentry><refentrytitle>gluOrtho2D</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glFrustum</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glMultMatrix</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>