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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="gluLookAt">
<refmeta>
<refmetainfo>
<copyright>
<year>1991-2006</year>
<holder>Silicon Graphics, Inc.</holder>
</copyright>
</refmetainfo>
<refentrytitle>gluLookAt</refentrytitle>
<manvolnum>3G</manvolnum>
</refmeta>
<refnamediv>
<refname>gluLookAt</refname>
<refpurpose>define a viewing transformation</refpurpose>
</refnamediv>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>gluLookAt</function></funcdef>
<paramdef>GLdouble <parameter>eyeX</parameter></paramdef>
<paramdef>GLdouble <parameter>eyeY</parameter></paramdef>
<paramdef>GLdouble <parameter>eyeZ</parameter></paramdef>
<paramdef>GLdouble <parameter>centerX</parameter></paramdef>
<paramdef>GLdouble <parameter>centerY</parameter></paramdef>
<paramdef>GLdouble <parameter>centerZ</parameter></paramdef>
<paramdef>GLdouble <parameter>upX</parameter></paramdef>
<paramdef>GLdouble <parameter>upY</parameter></paramdef>
<paramdef>GLdouble <parameter>upZ</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<!-- eqn: ignoring delim $$ -->
<refsect1 id="parameters"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>eyeX</parameter></term>
<term><parameter>eyeY</parameter></term>
<term><parameter>eyeZ</parameter></term>
<listitem>
<para>
Specifies the position of the eye point.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>centerX</parameter></term>
<term><parameter>centerY</parameter></term>
<term><parameter>centerZ</parameter></term>
<listitem>
<para>
Specifies the position of the reference point.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>upX</parameter></term>
<term><parameter>upY</parameter></term>
<term><parameter>upZ</parameter></term>
<listitem>
<para>
Specifies the direction of the <emphasis>up</emphasis> vector.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsect1 id="description"><title>Description</title>
<para>
<function>gluLookAt</function> creates a viewing matrix derived from an eye point, a reference
point indicating the center of the scene, and an <emphasis>UP</emphasis> vector.
</para>
<para>
The matrix
maps the reference point to the negative <emphasis>z</emphasis> axis and the
eye point to the origin.
When a typical projection matrix is used,
the center of the scene therefore maps to the center of the viewport.
Similarly, the direction described by the <emphasis>UP</emphasis>
vector projected onto the viewing plane is mapped to the positive <emphasis>y</emphasis>
axis so that it points upward in the viewport.
The <emphasis>UP</emphasis> vector must not be parallel to the line of sight from the
eye point to the reference point.
</para>
<para>
Let
</para>
<para>
<informalequation><mml:math>
<!-- eqn: F = left ( matrix { ccol { centerX - eyeX above centerY - eyeY above centerZ - eyeZ } } right ):-->
<mml:mrow>
<mml:mi mathvariant="italic">F</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">centerX</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">eyeX</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">centerY</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">eyeY</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">centerZ</mml:mi>
<mml:mo>-</mml:mo>
<mml:mi mathvariant="italic">eyeZ</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mfenced>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
</para>
<para>
Let <emphasis>UP</emphasis> be the vector
<inlineequation><mml:math>
<!-- eqn: (upX, upY, upZ):-->
<mml:mfenced open="(" close=")">
<mml:mi mathvariant="italic">upX</mml:mi>
<mml:mi mathvariant="italic">upY</mml:mi>
<mml:mi mathvariant="italic">upZ</mml:mi>
</mml:mfenced>
</mml:math></inlineequation>.
</para>
<para>
Then normalize as follows:
<informalequation><mml:math>
<!-- eqn: f = F over {|| F ||}:-->
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mi mathvariant="italic">F</mml:mi>
<mml:mfenced open="" close="">
<mml:mfenced open="∥" close="∥">
<mml:mi mathvariant="italic">F</mml:mi>
</mml:mfenced>
</mml:mfenced>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
<informalequation><mml:math>
<!-- eqn: UP sup prime = UP over {|| UP ||}:-->
<mml:mrow>
<mml:msup><mml:mi mathvariant="italic">UP</mml:mi>
<mml:mo>″</mml:mo>
</mml:msup>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mi mathvariant="italic">UP</mml:mi>
<mml:mfenced open="" close="">
<mml:mfenced open="∥" close="∥">
<mml:mi mathvariant="italic">UP</mml:mi>
</mml:mfenced>
</mml:mfenced>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
</para>
<para>
Finally, let
<inlineequation><mml:math>
<!-- eqn: s = f times UP sup prime:-->
<mml:mrow>
<mml:mi mathvariant="italic">s</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>×</mml:mo>
<mml:msup><mml:mi mathvariant="italic">UP</mml:mi>
<mml:mo>″</mml:mo>
</mml:msup>
</mml:mrow>
</mml:mrow>
</mml:math></inlineequation>,
and
<inlineequation><mml:math>
<!-- eqn: u = s times f:-->
<mml:mrow>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">s</mml:mi>
<mml:mo>×</mml:mo>
<mml:mi mathvariant="italic">f</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math></inlineequation>.
</para>
<para>
</para>
<para>
M is then constructed as follows:
<informalequation><mml:math>
<!-- eqn: M = left ( matrix { ccol { s[0] above u[0] above -f[0] above 0 } ccol { s[1] above u[1] above -f[1] above 0 } ccol { s[2] above u[2] above -f[2] above 0 } ccol { 0 above 0 above 0 above 1 } } right ):-->
<mml:mrow>
<mml:mi mathvariant="italic">M</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">s</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>0</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">s</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>1</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">s</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>2</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>0</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>1</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>2</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>0</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>1</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mo>⁡</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mn>2</mml:mn>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</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:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mfenced>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
and <function>gluLookAt</function> is equivalent to
<programlisting>
glMultMatrixf(M);
glTranslated(-eyex, -eyey, -eyez);
</programlisting>
</para>
</refsect1>
<refsect1 id="seealso"><title>See Also</title>
<para>
<citerefentry><refentrytitle>gluPerspective</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glFrustum</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>