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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="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="&DoubleVerticalBar;" close="&DoubleVerticalBar;">
                                <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>&Prime;</mml:mo>
                    </mml:msup>
                    <mml:mo>=</mml:mo>
                    <mml:mfrac>
                        <mml:mi mathvariant="italic">UP</mml:mi>
                        <mml:mfenced open="" close="">
                            <mml:mfenced open="&DoubleVerticalBar;" close="&DoubleVerticalBar;">
                                <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>&times;</mml:mo>
                        <mml:msup><mml:mi mathvariant="italic">UP</mml:mi>
                        <mml:mo>&Prime;</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>&times;</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>&af;</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>&af;</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>&af;</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>&af;</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>&af;</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>&af;</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>&af;</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>&af;</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>&af;</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>
