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<?xml-stylesheet type="text/xsl" href="mathml.xsl"?><html xmlns="http://www.w3.org/1999/xhtml" xmlns:pref="http://www.w3.org/2002/Math/preference" pref:renderer="mathplayer-dl"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>glFrustum</title><meta name="generator" content="DocBook XSL Stylesheets V1.73.2" /></head><body><div class="refentry" lang="en" xml:lang="en"><a id="glFrustum"></a><div class="titlepage"></div><div class="refnamediv"><h2>Name</h2><p>glFrustum — multiply the current matrix by a perspective matrix</p></div><div class="refsynopsisdiv"><h2>C Specification</h2><div class="funcsynopsis"><table border="0" summary="Function synopsis" cellspacing="0" cellpadding="0"><tr><td><code class="funcdef">void <b class="fsfunc">glFrustum</b>(</code></td><td>GLdouble  </td><td><var class="pdparam">left</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">right</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">bottom</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">top</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">nearVal</var>, </td></tr><tr><td> </td><td>GLdouble  </td><td><var class="pdparam">farVal</var><code>)</code>;</td></tr></table></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="parameters"></a><h2>Parameters</h2><div class="variablelist"><dl><dt><span class="term"><em class="parameter"><code>left</code></em>, </span><span class="term"><em class="parameter"><code>right</code></em></span></dt><dd><p>
                    Specify the coordinates for the left and right vertical clipping planes.
                </p></dd><dt><span class="term"><em class="parameter"><code>bottom</code></em>, </span><span class="term"><em class="parameter"><code>top</code></em></span></dt><dd><p>
                    Specify the coordinates for the bottom and top horizontal clipping planes.
                </p></dd><dt><span class="term"><em class="parameter"><code>nearVal</code></em>, </span><span class="term"><em class="parameter"><code>farVal</code></em></span></dt><dd><p>
                    Specify the distances to the near and far depth clipping planes.
                    Both distances must be positive.
                </p></dd></dl></div></div><div class="refsect1" lang="en" xml:lang="en"><a id="description"></a><h2>Description</h2><p>
            <code class="function">glFrustum</code> describes a perspective matrix that produces a perspective projection.
            The current matrix (see <a class="citerefentry" href="glMatrixMode.xml"><span class="citerefentry"><span class="refentrytitle">glMatrixMode</span></span></a>) is multiplied by this matrix
            and the result replaces the current matrix, as if
            <a class="citerefentry" href="glMultMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glMultMatrix</span></span></a> were called with the following matrix
            as its argument:
        </p><p>
        </p><p>
            </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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>⁢</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>⁢</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></div><p>
        </p><p>
            </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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></div><p>
        </p><p>
            </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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></div><p>
        </p><p>
            </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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></div><p>
        </p><p>
            </p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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>⁢</mml:mo>
                                        <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></div><p>
        </p><p>
        </p><p>
            Typically, the matrix mode is <code class="constant">GL_PROJECTION</code>, and
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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>
            and 
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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>
            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).
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <mml:mrow>
                    <mml:mo>-</mml:mo>
                    <mml:mi mathvariant="italic">farVal</mml:mi>
                </mml:mrow>
            </mml:math>
            specifies the location of the far clipping plane.
            Both <em class="parameter"><code>nearVal</code></em> and <em class="parameter"><code>farVal</code></em> must be positive.
        </p><p>
            Use <a class="citerefentry" href="glPushMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPushMatrix</span></span></a> and <a class="citerefentry" href="glPopMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPopMatrix</span></span></a> to save and restore
            the current matrix stack.
        </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="notes"></a><h2>Notes</h2><p>
            Depth buffer precision is affected by the values specified for
            <em class="parameter"><code>nearVal</code></em> and <em class="parameter"><code>farVal</code></em>.
            The greater the ratio of <em class="parameter"><code>farVal</code></em> to <em class="parameter"><code>nearVal</code></em> is,
            the less effective the depth buffer will be at distinguishing between
            surfaces that are near each other.
            If
        </p><p>
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <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>
        </p><p>
            roughly 
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
                
                <mml:mrow>
                    <mml:msub><mml:mi mathvariant="italic">log</mml:mi>
                    <mml:mn>2</mml:mn>
                    </mml:msub>
                    <mml:mo>⁡</mml:mo>
                    <mml:mfenced open="(" close=")">
                        <mml:mi mathvariant="italic">r</mml:mi>
                    </mml:mfenced>
                </mml:mrow>
            </mml:math>
            bits of depth buffer precision are lost.
            Because 
            <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">r</mml:mi></mml:math>
            approaches infinity as <em class="parameter"><code>nearVal</code></em> approaches 0,
            <em class="parameter"><code>nearVal</code></em> must never be set to 0.
        </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="errors"></a><h2>Errors</h2><p>
            <code class="constant">GL_INVALID_VALUE</code> is generated if <em class="parameter"><code>nearVal</code></em> or <em class="parameter"><code>farVal</code></em> is not
            positive, or if <em class="parameter"><code>left</code></em> = <em class="parameter"><code>right</code></em>, or <em class="parameter"><code>bottom</code></em> = <em class="parameter"><code>top</code></em>,
            or <em class="parameter"><code>near</code></em> = <em class="parameter"><code>far</code></em>.
        </p><p>
            <code class="constant">GL_INVALID_OPERATION</code> is generated if <code class="function">glFrustum</code>
            is executed between the execution of <a class="citerefentry" href="glBegin.xml"><span class="citerefentry"><span class="refentrytitle">glBegin</span></span></a>
            and the corresponding execution of <a class="citerefentry" href="glEnd.xml"><span class="citerefentry"><span class="refentrytitle">glEnd</span></span></a>.
        </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="associatedgets"></a><h2>Associated Gets</h2><p>
            <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MATRIX_MODE</code>
        </p><p>
            <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_MODELVIEW_MATRIX</code>
        </p><p>
            <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_PROJECTION_MATRIX</code>
        </p><p>
            <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_TEXTURE_MATRIX</code>
        </p><p>
            <a class="citerefentry" href="glGet.xml"><span class="citerefentry"><span class="refentrytitle">glGet</span></span></a> with argument <code class="constant">GL_COLOR_MATRIX</code>
        </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="seealso"></a><h2>See Also</h2><p>
            <a class="citerefentry" href="glOrtho.xml"><span class="citerefentry"><span class="refentrytitle">glOrtho</span></span></a>,
            <a class="citerefentry" href="glMatrixMode.xml"><span class="citerefentry"><span class="refentrytitle">glMatrixMode</span></span></a>,
            <a class="citerefentry" href="glMultMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glMultMatrix</span></span></a>,
            <a class="citerefentry" href="glPushMatrix.xml"><span class="citerefentry"><span class="refentrytitle">glPushMatrix</span></span></a>,
            <a class="citerefentry" href="glViewport.xml"><span class="citerefentry"><span class="refentrytitle">glViewport</span></span></a>
        </p></div><div class="refsect1" lang="en" xml:lang="en"><a id="Copyright"></a><h2>Copyright</h2><p>
            Copyright <span class="trademark"></span>© 1991-2006
            Silicon Graphics, Inc. This document is licensed under the SGI
            Free Software B License. For details, see
            <a class="ulink" href="http://oss.sgi.com/projects/FreeB/" target="_top">http://oss.sgi.com/projects/FreeB/</a>.
        </p></div></div></body></html>
