
<refentry id="glFrustum">
    <refmeta>
        <refmetainfo>
            <copyright>
                <year>1991-2006</year>
                <holder>Silicon Graphics, Inc.</holder>
            </copyright>
        </refmetainfo>
        <refentrytitle>glFrustum</refentrytitle>
        <manvolnum>3G</manvolnum>
    </refmeta>
    <refnamediv>
        <refname>glFrustum</refname>
        <refpurpose>multiply the current matrix by a perspective matrix</refpurpose>
    </refnamediv>
    <refsynopsisdiv><title>C Specification</title>
        <funcsynopsis>
            <funcprototype>
                <funcdef>void <function>glFrustum</function></funcdef>
                <paramdef>GLdouble <parameter>left</parameter></paramdef>
                <paramdef>GLdouble <parameter>right</parameter></paramdef>
                <paramdef>GLdouble <parameter>bottom</parameter></paramdef>
                <paramdef>GLdouble <parameter>top</parameter></paramdef>
                <paramdef>GLdouble <parameter>nearVal</parameter></paramdef>
                <paramdef>GLdouble <parameter>farVal</parameter></paramdef>
            </funcprototype>
        </funcsynopsis>
    </refsynopsisdiv>
    <!-- eqn: ignoring delim $$ -->
    <refsect1 id="parameters"><title>Parameters</title>
        <variablelist>
        <varlistentry>
            <term><parameter>left</parameter></term>
            <term><parameter>right</parameter></term>
            <listitem>
                <para>
                    Specify the coordinates for the left and right vertical clipping planes.
                </para>
            </listitem>
        </varlistentry>
        <varlistentry>
            <term><parameter>bottom</parameter></term>
            <term><parameter>top</parameter></term>
            <listitem>
                <para>
                    Specify the coordinates for the bottom and top horizontal clipping planes.
                </para>
            </listitem>
        </varlistentry>
        <varlistentry>
            <term><parameter>nearVal</parameter></term>
            <term><parameter>farVal</parameter></term>
            <listitem>
                <para>
                    Specify the distances to the near and far depth clipping planes.
                    Both distances must be positive.
                </para>
            </listitem>
        </varlistentry>
        </variablelist>
    </refsect1>
    <refsect1 id="description"><title>Description</title>
        <para>
            <function>glFrustum</function> describes a perspective matrix that produces a perspective projection.
            The current matrix (see <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>) is multiplied by this matrix
            and the result replaces the current matrix, as if
            <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> were called with the following matrix
            as its argument:
        </para>
        <para>
        </para>
        <para>
            <informalequation><mml:math>
                <!-- eqn:  left [      matrix {    ccol { {{2   nearVal} over {right  -  left}} above 0 above 0 above 0 }    ccol { 0 above {{2   nearVal} over {top  -  bottom}}   above 0 above 0 }    ccol { A      above B      above C      above -1     }    ccol { 0 above 0 above D above 0} }     right ]:-->
                <mml:mfenced open="[" close="]">
                    <mml:mtable>
                        <mml:mtr>
                            <mml:mtd>
                                <mml:mfenced open="" close="">
                                    <mml:mfrac>
                                        <mml:mfenced open="" close="">
                                            <mml:mrow>
                                                <mml:mn>2</mml:mn>
                                                <mml:mo>&it;</mml:mo>
                                                <mml:mi mathvariant="italic">nearVal</mml:mi>
                                            </mml:mrow>
                                        </mml:mfenced>
                                        <mml:mfenced open="" close="">
                                            <mml:mrow>
                                                <mml:mi mathvariant="italic">right</mml:mi>
                                                <mml:mo>-</mml:mo>
                                                <mml:mi mathvariant="italic">left</mml:mi>
                                            </mml:mrow>
                                        </mml:mfenced>
                                    </mml:mfrac>
                                </mml:mfenced>
                            </mml:mtd>
                            <mml:mtd>
                                <mml:mn>0</mml:mn>
                            </mml:mtd>
                            <mml:mtd>
                                <mml:mi mathvariant="italic">A</mml:mi>
                            </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:mfenced open="" close="">
                                    <mml:mfrac>
                                        <mml:mfenced open="" close="">
                                            <mml:mrow>
                                                <mml:mn>2</mml:mn>
                                                <mml:mo>&it;</mml:mo>
                                                <mml:mi mathvariant="italic">nearVal</mml:mi>
                                            </mml:mrow>
                                        </mml:mfenced>
                                        <mml:mfenced open="" close="">
                                            <mml:mrow>
                                                <mml:mi mathvariant="italic">top</mml:mi>
                                                <mml:mo>-</mml:mo>
                                                <mml:mi mathvariant="italic">bottom</mml:mi>
                                            </mml:mrow>
                                        </mml:mfenced>
                                    </mml:mfrac>
                                </mml:mfenced>
                            </mml:mtd>
                            <mml:mtd>
                                <mml:mi mathvariant="italic">B</mml:mi>
                            </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:mi mathvariant="italic">C</mml:mi>
                            </mml:mtd>
                            <mml:mtd>
                                <mml:mi mathvariant="italic">D</mml:mi>
                            </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>
        <para>
            <informalequation><mml:math>
                <!-- eqn:  A  =  {right  +  left} over {right  -  left}:-->
                <mml:mrow>
                    <mml:mi mathvariant="italic">A</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mfrac>
                        <mml:mfenced open="" close="">
                            <mml:mrow>
                                <mml:mi mathvariant="italic">right</mml:mi>
                                <mml:mo>+</mml:mo>
                                <mml:mi mathvariant="italic">left</mml:mi>
                            </mml:mrow>
                        </mml:mfenced>
                        <mml:mfenced open="" close="">
                            <mml:mrow>
                                <mml:mi mathvariant="italic">right</mml:mi>
                                <mml:mo>-</mml:mo>
                                <mml:mi mathvariant="italic">left</mml:mi>
                            </mml:mrow>
                        </mml:mfenced>
                    </mml:mfrac>
                </mml:mrow>
            </mml:math></informalequation>
        </para>
        <para>
            <informalequation><mml:math>
                <!-- eqn:  B  =  {top  +  bottom} over {top  -  bottom}:-->
                <mml:mrow>
                    <mml:mi mathvariant="italic">B</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mfrac>
                        <mml:mfenced open="" close="">
                            <mml:mrow>
                                <mml:mi mathvariant="italic">top</mml:mi>
                                <mml:mo>+</mml:mo>
                                <mml:mi mathvariant="italic">bottom</mml:mi>
                            </mml:mrow>
                        </mml:mfenced>
                        <mml:mfenced open="" close="">
                            <mml:mrow>
                                <mml:mi mathvariant="italic">top</mml:mi>
                                <mml:mo>-</mml:mo>
                                <mml:mi mathvariant="italic">bottom</mml:mi>
                            </mml:mrow>
                        </mml:mfenced>
                    </mml:mfrac>
                </mml:mrow>
            </mml:math></informalequation>
        </para>
        <para>
            <informalequation><mml:math>
                <!-- eqn:  C  =  -{{farVal  +  nearVal} over {farVal  -  nearVal}}:-->
                <mml:mrow>
                    <mml:mi mathvariant="italic">C</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mrow>
                        <mml:mo>-</mml:mo>
                        <mml:mfenced open="" close="">
                            <mml:mfrac>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mi mathvariant="italic">farVal</mml:mi>
                                        <mml:mo>+</mml:mo>
                                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mi mathvariant="italic">farVal</mml:mi>
                                        <mml:mo>-</mml:mo>
                                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                            </mml:mfrac>
                        </mml:mfenced>
                    </mml:mrow>
                </mml:mrow>
            </mml:math></informalequation>
        </para>
        <para>
            <informalequation><mml:math>
                <!-- eqn:  D  =  -{{2   farVal   nearVal} over {farVal  -  nearVal}}:-->
                <mml:mrow>
                    <mml:mi mathvariant="italic">D</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mrow>
                        <mml:mo>-</mml:mo>
                        <mml:mfenced open="" close="">
                            <mml:mfrac>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mn>2</mml:mn>
                                        <mml:mo>&it;</mml:mo>
                                        <mml:mi mathvariant="italic">farVal</mml:mi>
                                        <mml:mo>&it;</mml:mo>
                                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mi mathvariant="italic">farVal</mml:mi>
                                        <mml:mo>-</mml:mo>
                                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                            </mml:mfrac>
                        </mml:mfenced>
                    </mml:mrow>
                </mml:mrow>
            </mml:math></informalequation>
        </para>
        <para>
        </para>
        <para>
            Typically, the matrix mode is <constant>GL_PROJECTION</constant>, and
            <inlineequation><mml:math>
                <!-- eqn: (left, bottom,  -nearVal):-->
                <mml:mfenced open="(" close=")">
                    <mml:mi mathvariant="italic">left</mml:mi>
                    <mml:mi mathvariant="italic">bottom</mml:mi>
                    <mml:mrow>
                        <mml:mo>-</mml:mo>
                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                    </mml:mrow>
                </mml:mfenced>
            </mml:math></inlineequation>
            and 
            <inlineequation><mml:math>
                <!-- eqn: (right, top,  -nearVal):-->
                <mml:mfenced open="(" close=")">
                    <mml:mi mathvariant="italic">right</mml:mi>
                    <mml:mi mathvariant="italic">top</mml:mi>
                    <mml:mrow>
                        <mml:mo>-</mml:mo>
                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                    </mml:mrow>
                </mml:mfenced>
            </mml:math></inlineequation>
            specify the points on the near clipping plane that are mapped
            to the lower left and upper right corners of the window,
            assuming that the eye is located at (0, 0, 0).
            <inlineequation><mml:math>
                <!-- eqn: -farVal:-->
                <mml:mrow>
                    <mml:mo>-</mml:mo>
                    <mml:mi mathvariant="italic">farVal</mml:mi>
                </mml:mrow>
            </mml:math></inlineequation>
            specifies the location of the far clipping plane.
            Both <parameter>nearVal</parameter> and <parameter>farVal</parameter> must be positive.
        </para>
        <para>
            Use <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glPopMatrix</refentrytitle></citerefentry> to save and restore
            the current matrix stack.
        </para>
    </refsect1>
    <refsect1 id="notes"><title>Notes</title>
        <para>
            Depth buffer precision is affected by the values specified for
            <parameter>nearVal</parameter> and <parameter>farVal</parameter>.
            The greater the ratio of <parameter>farVal</parameter> to <parameter>nearVal</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  =  farVal over nearVal:-->
                <mml:mrow>
                    <mml:mi mathvariant="italic">r</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mfrac>
                        <mml:mi mathvariant="italic">farVal</mml:mi>
                        <mml:mi mathvariant="italic">nearVal</mml:mi>
                    </mml:mfrac>
                </mml:mrow>
            </mml:math></inlineequation>
        </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>&af;</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>nearVal</parameter> approaches 0,
            <parameter>nearVal</parameter> must never be set to 0.
        </para>
    </refsect1>
    <refsect1 id="errors"><title>Errors</title>
        <para>
            <constant>GL_INVALID_VALUE</constant> is generated if <parameter>nearVal</parameter> or <parameter>farVal</parameter> is not
            positive, or if <parameter>left</parameter> = <parameter>right</parameter>, or <parameter>bottom</parameter> = <parameter>top</parameter>,
            or <parameter>near</parameter> = <parameter>far</parameter>.
        </para>
        <para>
            <constant>GL_INVALID_OPERATION</constant> is generated if <function>glFrustum</function>
            is executed between the execution of <citerefentry><refentrytitle>glBegin</refentrytitle></citerefentry>
            and the corresponding execution of <citerefentry><refentrytitle>glEnd</refentrytitle></citerefentry>.
        </para>
    </refsect1>
    <refsect1 id="associatedgets"><title>Associated Gets</title>
        <para>
            <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MATRIX_MODE</constant>
        </para>
        <para>
            <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MODELVIEW_MATRIX</constant>
        </para>
        <para>
            <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_PROJECTION_MATRIX</constant>
        </para>
        <para>
            <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_TEXTURE_MATRIX</constant>
        </para>
        <para>
            <citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_COLOR_MATRIX</constant>
        </para>
    </refsect1>
    <refsect1 id="seealso"><title>See Also</title>
        <para>
            <citerefentry><refentrytitle>glOrtho</refentrytitle></citerefentry>,
            <citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>,
            <citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry>,
            <citerefentry><refentrytitle>glPushMatrix</refentrytitle></citerefentry>,
            <citerefentry><refentrytitle>glViewport</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>
