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