<!DOCTYPE refentry [ <!ENTITY % mathent SYSTEM "math.ent"> %mathent; ]>

<!-- Converted by db4-upgrade version 1.1 -->

<refentry xmlns="http://docbook.org/ns/docbook" version="5.0" xml:id="refract">
    <info>
        <copyright>
            <year>2011-2014</year>
            <holder>Khronos Group</holder>
        </copyright>
    </info>
    <refmeta>
        <refentrytitle>refract</refentrytitle>
        <manvolnum>3G</manvolnum>
    </refmeta>
    <refnamediv>
        <refname>refract</refname>
        <refpurpose>calculate the refraction direction for an incident vector</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Declaration</title>
        <funcsynopsis>
            <funcprototype>
                <funcdef>genType <function>refract</function></funcdef>
                <paramdef>genType <parameter>I</parameter></paramdef>
                <paramdef>genType <parameter>N</parameter></paramdef>
                <paramdef>float <parameter>eta</parameter></paramdef>
            </funcprototype>
        </funcsynopsis>
    </refsynopsisdiv>
    <refsect1 xml:id="parameters"><title>Parameters</title>
        <variablelist>
        <varlistentry>
            <term><parameter>I</parameter></term>
            <listitem>
                <para>
                    Specifies the incident vector.
                </para>
            </listitem>
        </varlistentry>
        <varlistentry>
            <term><parameter>N</parameter></term>
            <listitem>
                <para>
                    Specifies the normal vector.
                </para>
            </listitem>
        </varlistentry>
        <varlistentry>
            <term><parameter>eta</parameter></term>
            <listitem>
                <para>
                    Specifies the ratio of indices of refraction.
                </para>
            </listitem>
        </varlistentry>
        </variablelist>
    </refsect1>
    <refsect1 xml:id="description"><title>Description</title>
        <para>
            For a given incident vector <parameter>I</parameter>, surface normal <parameter>N</parameter> and ratio of
            indices of refraction, <parameter>eta</parameter>, <function>refract</function> returns the refraction vector,
            <parameter>R</parameter>.
        </para>
        <para>
            <parameter>R</parameter> is calculated as:
        </para>
        <para>
            <programlisting>    k = 1.0 - eta * eta * (1.0 - dot(N, I) * dot(N, I));
    if (k &lt; 0.0)
        R = genType(0.0);       // or genDType(0.0)
    else
        R = eta * I - (eta * dot(N, I) + sqrt(k)) * N;</programlisting>
        </para>
        <para>
            The input parameters <parameter>I</parameter> and <parameter>N</parameter> should be normalized in order to achieve the desired result.
        </para>
    </refsect1>
    <refsect1 xml:id="versions"><title>Version Support</title>
        <informaltable>
            <tgroup cols="4" align="left">
                <xi:include xmlns:xi="http://www.w3.org/2001/XInclude" href="funchead.xml" xpointer="xpointer(/*/*)"/>
                <tbody>
                    <row>
                        <entry>refract (genType)</entry>
                        <xi:include xmlns:xi="http://www.w3.org/2001/XInclude" href="version.xml" xpointer="xpointer(/*/*[@role='es10']/*)"/>
                    </row>
                </tbody>
            </tgroup>
        </informaltable>
    </refsect1>
    <refsect1 xml:id="seealso"><title>See Also</title>
        <para>
            <citerefentry><refentrytitle>dot</refentrytitle></citerefentry>,
            <citerefentry><refentrytitle>reflect</refentrytitle></citerefentry>
        </para>
    </refsect1>
    <refsect1 xml:id="Copyright"><title>Copyright</title>
        <para>
            Copyright <trademark class="copyright"/> 2011-2014 Khronos Group.
            This material may be distributed subject to the terms and conditions set forth in
            the Open Publication License, v 1.0, 8 June 1999.
            <link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://opencontent.org/openpub/">http://opencontent.org/openpub/</link>.
        </para>
    </refsect1>
</refentry>
