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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 V1.78.1" /></head><body><div class="refentry"><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" class="funcprototype-table" summary="Function synopsis" style="cellspacing: 0; cellpadding: 0;"><tr><td><code class="funcdef">void <strong class="fsfunc">glFrustumf</strong>(</code></td><td>GLfloat <var class="pdparam">left</var>, </td></tr><tr><td> </td><td>GLfloat <var class="pdparam">right</var>, </td></tr><tr><td> </td><td>GLfloat <var class="pdparam">bottom</var>, </td></tr><tr><td> </td><td>GLfloat <var class="pdparam">top</var>, </td></tr><tr><td> </td><td>GLfloat <var class="pdparam">near</var>, </td></tr><tr><td> </td><td>GLfloat <var class="pdparam">far</var><code>)</code>;</td></tr></table><div class="funcprototype-spacer"> </div><table border="0" class="funcprototype-table" summary="Function synopsis" style="cellspacing: 0; cellpadding: 0;"><tr><td><code class="funcdef">void <strong class="fsfunc">glFrustumx</strong>(</code></td><td>GLfixed <var class="pdparam">left</var>, </td></tr><tr><td> </td><td>GLfixed <var class="pdparam">right</var>, </td></tr><tr><td> </td><td>GLfixed <var class="pdparam">bottom</var>, </td></tr><tr><td> </td><td>GLfixed <var class="pdparam">top</var>, </td></tr><tr><td> </td><td>GLfixed <var class="pdparam">near</var>, </td></tr><tr><td> </td><td>GLfixed <var class="pdparam">far</var><code>)</code>;</td></tr></table><div class="funcprototype-spacer"> </div></div></div><div class="refsect1"><a id="parameters"></a><h2>Parameters</h2><div class="variablelist"><dl class="variablelist"><dt><span class="term">
		<em class="parameter"><code>left</code></em>,
		<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>,
		<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>near</code></em>,
		<em class="parameter"><code>far</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"><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><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">near</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">near</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">far</mml:mi>
                                        <mml:mo>+</mml:mo>
                                        <mml:mi mathvariant="italic">near</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mi mathvariant="italic">far</mml:mi>
                                        <mml:mo>-</mml:mo>
                                        <mml:mi mathvariant="italic">near</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">far</mml:mi>
                                        <mml:mo>⁢</mml:mo>
                                        <mml:mi mathvariant="italic">near</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                                <mml:mfenced open="" close="">
                                    <mml:mrow>
                                        <mml:mi mathvariant="italic">far</mml:mi>
                                        <mml:mo>-</mml:mo>
                                        <mml:mi mathvariant="italic">near</mml:mi>
                                    </mml:mrow>
                                </mml:mfenced>
                            </mml:mfrac>
                        </mml:mfenced>
                    </mml:mrow>
                </mml:mrow>
            </mml:math></div><p>
        </p><p>Typically, the matrix mode is
	<code class="constant">GL_PROJECTION</code>, and
	(<em class="parameter"><code>left</code></em>, <em class="parameter"><code>bottom</code></em>,
	-<em class="parameter"><code>near</code></em>) and
	(<em class="parameter"><code>right</code></em>, <em class="parameter"><code>top</code></em>,
	-<em class="parameter"><code>near</code></em>)
	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).
	-<em class="parameter"><code>far</code></em>
	specifies the location of the far clipping plane. Both
	<em class="parameter"><code>near</code></em> and
	<em class="parameter"><code>far</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"><a id="notes"></a><h2>Notes</h2><p>Depth buffer precision is affected by the values
	specified for <em class="parameter"><code>near</code></em> and
	<em class="parameter"><code>far</code></em>. The greater the ratio of
	<em class="parameter"><code>far</code></em> to
	<em class="parameter"><code>near</code></em>
	is, the less effective the depth buffer will be at
	distinguishing between surfaces that are near each other. If</p><div class="informalequation"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mtable>
	    <mml:mtr><mml:mtd>
		<mml:mi>r</mml:mi>
		<mml:mo>=</mml:mo>
		<mml:mfrac><mml:mi>far</mml:mi><mml:mi>near</mml:mi></mml:mfrac>
	    </mml:mtd></mml:mtr>
	</mml:mtable></mml:math></div><p>roughly
	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
	    <mml:msub><mml:mo>log</mml:mo><mml:mn>2</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo>
	</mml:math>
	bits of depth buffer precision are lost. Because
	<em class="replaceable"><code>r</code></em> approaches infinity as
	<em class="parameter"><code>near</code></em> approaches 0,
	<em class="parameter"><code>near</code></em> must never be set to 0.</p></div><div class="refsect1"><a id="errors"></a><h2>Errors</h2><p>
	    <code class="constant">GL_INVALID_VALUE</code> is generated if
	    <em class="parameter"><code>near</code></em> or <em class="parameter"><code>far</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></div><div class="refsect1"><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"><a id="copyright"></a><h2>Copyright</h2><p>
	    Copyright <span class="trademark"></span>© 2003-2004
	    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>