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850 lines
44 KiB
XML
850 lines
44 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="glMultTransposeMatrix">
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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>glMultTransposeMatrix</refentrytitle>
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<manvolnum>3G</manvolnum>
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</refmeta>
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<refnamediv>
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<refname>glMultTransposeMatrix</refname>
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<refpurpose>multiply the current matrix with the specified row-major ordered matrix</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>glMultTransposeMatrixd</function></funcdef>
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<paramdef>const GLdouble * <parameter>m</parameter></paramdef>
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</funcprototype>
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</funcsynopsis>
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<funcsynopsis>
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<funcprototype>
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<funcdef>void <function>glMultTransposeMatrixf</function></funcdef>
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<paramdef>const GLfloat * <parameter>m</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>m</parameter></term>
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<listitem>
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<para>
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Points to 16 consecutive values that are used as the elements of
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a
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<inlineequation><mml:math>
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<!-- eqn: 4 times 4:-->
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<mml:mrow>
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<mml:mn>4</mml:mn>
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<mml:mo>×</mml:mo>
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<mml:mn>4</mml:mn>
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</mml:mrow>
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</mml:math></inlineequation>
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row-major matrix.
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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>glMultTransposeMatrix</function> multiplies the current matrix with the one specified using <parameter>m</parameter>, and
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replaces the current matrix with the product.
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</para>
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<para>
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The current matrix is determined by the current matrix mode (see
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<citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>). It is either the projection matrix, modelview matrix,
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or the texture matrix.
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</para>
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</refsect1>
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<refsect1 id="examples"><title>Examples</title>
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<para>
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If the current matrix is
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<inlineequation><mml:math><mml:mi mathvariant="italic">C</mml:mi></mml:math></inlineequation>
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and the coordinates
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to be transformed are
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<inlineequation><mml:math>
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<!-- eqn: v = (v[0], v[1], v[2], v[3]):-->
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<mml:mrow>
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<mml:mi mathvariant="italic">v</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mfenced open="(" close=")">
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<mml:mrow>
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<mml:mi mathvariant="italic">v</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:mi mathvariant="italic">v</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:mi mathvariant="italic">v</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:mi mathvariant="italic">v</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>3</mml:mn>
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</mml:mfenced>
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</mml:mrow>
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</mml:mfenced>
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</mml:mrow>
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</mml:math></inlineequation>,
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then the current transformation is
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<inlineequation><mml:math>
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<!-- eqn: C times v:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">C</mml:mi>
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<mml:mo>×</mml:mo>
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<mml:mi mathvariant="italic">v</mml:mi>
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</mml:mrow>
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</mml:math></inlineequation>,
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or
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: left ( matrix { ccol { c[0] above c[1] above c[2] above c[3] } ccol { c[4] above c[5] above c[6] above c[7] } ccol { c[8] above c[9] above c[10] above c[11] } ccol { c[12] above c[13] above c[14] above c[15] } } right ) times left ( matrix { ccol { v[0] above v[1] above v[2] above v[3] } } right ):-->
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<mml:mrow>
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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">c</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>4</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>8</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>12</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: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">c</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>5</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>9</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>13</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: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">c</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:mrow>
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<mml:mi mathvariant="italic">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>6</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>10</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>14</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: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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>3</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>7</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>11</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>15</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:mtr>
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</mml:mtable>
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</mml:mfenced>
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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">v</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: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">v</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: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">v</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: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">v</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>3</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: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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Calling <function>glMultTransposeMatrix</function> with an argument of
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<inlineequation><mml:math>
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<!-- eqn: m = left { m[0], m[1], ..., m[15] right }:-->
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<mml:mrow>
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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:mn>16</mml:mn>
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</mml:mfenced>
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</mml:mrow>
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<mml:mo>=</mml:mo>
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<mml:mfenced open="{" close="}">
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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: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: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:mn>1</mml:mn>
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</mml:mfenced>
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</mml:mrow>
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<mml:mi mathvariant="italic">...</mml:mi>
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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:mn>15</mml:mn>
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</mml:mfenced>
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</mml:mrow>
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</mml:mfenced>
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</mml:mrow>
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</mml:math></inlineequation>
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replaces the current transformation with
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<inlineequation><mml:math>
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<!-- eqn: (C times M) times v:-->
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<mml:mrow>
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<mml:mfenced open="(" close=")">
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<mml:mrow>
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<mml:mi mathvariant="italic">C</mml:mi>
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<mml:mo>×</mml:mo>
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<mml:mi mathvariant="italic">M</mml:mi>
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</mml:mrow>
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</mml:mfenced>
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<mml:mo>×</mml:mo>
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<mml:mi mathvariant="italic">v</mml:mi>
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</mml:mrow>
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</mml:math></inlineequation>,
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or
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: left ( matrix { ccol { c[0] above c[1] above c[2] above c[3] } ccol { c[4] above c[5] above c[6] above c[7] } ccol { c[8] above c[9] above c[10] above c[11] } ccol { c[12] above c[13] above c[14] above c[15] } } right ) times left ( matrix { ccol { m[0] above m[4] above m[8] above m[12] } ccol { m[1] above m[5] above m[9] above m[13] } ccol { m[2] above m[6] above m[10] above m[14] } ccol { m[3] above m[7] above m[11] above m[15] } } right ) times left ( matrix { ccol { v[0] above v[1] above v[2] above v[3] } } right ):-->
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<mml:mrow>
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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">c</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>4</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>8</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">c</mml:mi>
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<mml:mo>⁡</mml:mo>
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<mml:mfenced open="[" close="]">
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<mml:mn>12</mml:mn>
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</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>1</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>5</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>9</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>13</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>2</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>6</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>10</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>14</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>3</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>7</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>11</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">c</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>15</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
</mml:mtable>
|
|
</mml:mfenced>
|
|
<mml:mo>×</mml:mo>
|
|
<mml:mfenced open="(" close=")">
|
|
<mml:mtable>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>0</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>1</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>2</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>3</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>4</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>5</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>6</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>7</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>8</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>9</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>10</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>11</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>12</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>13</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>14</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">m</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>15</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
</mml:mtable>
|
|
</mml:mfenced>
|
|
<mml:mo>×</mml:mo>
|
|
<mml:mfenced open="(" close=")">
|
|
<mml:mtable>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">v</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>0</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">v</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>1</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">v</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>2</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
<mml:mtr>
|
|
<mml:mtd>
|
|
<mml:mrow>
|
|
<mml:mi mathvariant="italic">v</mml:mi>
|
|
<mml:mo>⁡</mml:mo>
|
|
<mml:mfenced open="[" close="]">
|
|
<mml:mn>3</mml:mn>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:mtd>
|
|
</mml:mtr>
|
|
</mml:mtable>
|
|
</mml:mfenced>
|
|
</mml:mrow>
|
|
</mml:math></informalequation>
|
|
</para>
|
|
<para>
|
|
</para>
|
|
<para>
|
|
Where
|
|
<inlineequation><mml:math><mml:mi mathvariant="italic">v</mml:mi></mml:math></inlineequation>
|
|
is represented as a
|
|
<inlineequation><mml:math>
|
|
<!-- eqn: 4 times 1:-->
|
|
<mml:mrow>
|
|
<mml:mn>4</mml:mn>
|
|
<mml:mo>×</mml:mo>
|
|
<mml:mn>1</mml:mn>
|
|
</mml:mrow>
|
|
</mml:math></inlineequation>
|
|
matrix.
|
|
</para>
|
|
<para>
|
|
Calling <function>glMultTransposeMatrix</function> with matrix
|
|
<inlineequation><mml:math><mml:mi mathvariant="italic">M</mml:mi></mml:math></inlineequation>
|
|
is identical in operation to
|
|
<citerefentry><refentrytitle>glMultMatrix</refentrytitle></citerefentry> with
|
|
<inlineequation><mml:math>
|
|
<!-- eqn: M sup T:-->
|
|
<mml:msup><mml:mi mathvariant="italic">M</mml:mi>
|
|
<mml:mi mathvariant="italic">T</mml:mi>
|
|
</mml:msup>
|
|
</mml:math></inlineequation>,
|
|
where
|
|
<inlineequation><mml:math><mml:mi mathvariant="italic">T</mml:mi></mml:math></inlineequation>
|
|
represents the transpose.
|
|
</para>
|
|
</refsect1>
|
|
<refsect1 id="notes"><title>Notes</title>
|
|
<para>
|
|
<function>glMultTransposeMatrix</function> is available only if the GL version is 1.3 or greater.
|
|
</para>
|
|
<para>
|
|
While the elements of the matrix may be specified with
|
|
single or double precision, the GL may store or operate on these
|
|
values in less-than-single precision.
|
|
</para>
|
|
<para>
|
|
The order of the multiplication is important. For example, if the current
|
|
transformation is a rotation, and <function>glMultTransposeMatrix</function> is called with a translation matrix,
|
|
the translation is done directly on the coordinates to be transformed,
|
|
while the rotation is done on the results of that translation.
|
|
</para>
|
|
</refsect1>
|
|
<refsect1 id="errors"><title>Errors</title>
|
|
<para>
|
|
<constant>GL_INVALID_OPERATION</constant> is generated if <function>glMultTransposeMatrix</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_COLOR_MATRIX</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>
|
|
</refsect1>
|
|
<refsect1 id="seealso"><title>See Also</title>
|
|
<para>
|
|
<citerefentry><refentrytitle>glLoadIdentity</refentrytitle></citerefentry>,
|
|
<citerefentry><refentrytitle>glLoadMatrix</refentrytitle></citerefentry>,
|
|
<citerefentry><refentrytitle>glLoadTransposeMatrix</refentrytitle></citerefentry>,
|
|
<citerefentry><refentrytitle>glMatrixMode</refentrytitle></citerefentry>,
|
|
<citerefentry><refentrytitle>glPushMatrix</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>
|