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381 lines
16 KiB
XML
381 lines
16 KiB
XML
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<?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="glEvalPoint">
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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>glEvalPoint</refentrytitle>
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<manvolnum>3G</manvolnum>
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</refmeta>
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<refnamediv>
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<refname>glEvalPoint</refname>
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<refpurpose>generate and evaluate a single point in a mesh</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>glEvalPoint1</function></funcdef>
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<paramdef>GLint <parameter>i</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>glEvalPoint2</function></funcdef>
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<paramdef>GLint <parameter>i</parameter></paramdef>
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<paramdef>GLint <parameter>j</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>i</parameter></term>
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<listitem>
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<para>
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Specifies the integer value for grid domain variable
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<inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
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</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><parameter>j</parameter></term>
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<listitem>
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<para>
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Specifies the integer value for grid domain variable
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<inlineequation><mml:math><mml:mi mathvariant="italic">j</mml:mi></mml:math></inlineequation>
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(<function>glEvalPoint2</function> only).
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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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<citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry> are used in tandem to efficiently
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generate and evaluate a series of evenly spaced map domain values.
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<function>glEvalPoint</function> can be used to evaluate a single grid point in the same gridspace
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that is traversed by <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry>.
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Calling <function>glEvalPoint1</function> is equivalent to calling
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<programlisting>
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glEvalCoord1( <mml:math>
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<!-- eqn: i \cdot DELTA u + u sub 1 :-->
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<mml:mrow>
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<mml:mrow>
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<mml:mn>i</mml:mn>
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<mml:mo>·</mml:mo>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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<mml:mo>+</mml:mo>
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<mml:msub>
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<mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:math> );
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</programlisting>
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where
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<informalequation><mml:math>
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<!-- eqn: DELTA u = ( u sub 2 - u sub 1 ) / n:-->
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<mml:mrow>
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<mml:mrow>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mfenced open="(" close=")">
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<mml:mrow>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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<mml:mo>-</mml:mo>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:mfenced>
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<mml:mi mathvariant="italic">n</mml:mi>
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</mml:mfrac>
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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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and
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<inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
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<inlineequation><mml:math>
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<!-- eqn: u sub 1:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>,
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and
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<inlineequation><mml:math>
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<!-- eqn: u sub 2:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>
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are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid1</refentrytitle></citerefentry> command.
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The one absolute numeric requirement is that if
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<inlineequation><mml:math>
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<!-- eqn: i = n:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">i</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mi mathvariant="italic">n</mml:mi>
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</mml:mrow>
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</mml:math></inlineequation>,
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then the value computed from
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<inlineequation><mml:math>
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<!-- eqn: i cdot DELTA u + u sub 1:-->
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<mml:mrow>
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<mml:mrow>
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<mml:mi mathvariant="italic">i</mml:mi>
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<mml:mo>·</mml:mo>
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<mml:mrow>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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</mml:mrow>
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<mml:mo>+</mml:mo>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:math></inlineequation>
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is exactly
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<inlineequation><mml:math>
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<!-- eqn: u sub 2:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>.
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</para>
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<para>
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In the two-dimensional case, <function>glEvalPoint2</function>, let
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</para>
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<para>
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<informalequation><mml:math>
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<!-- eqn: DELTA u = ( u sub 2 - u sub 1 ) / n:-->
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<mml:mrow>
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<mml:mrow>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mfenced open="(" close=")">
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<mml:mrow>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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<mml:mo>-</mml:mo>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:mfenced>
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<mml:mi mathvariant="italic">n</mml:mi>
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</mml:mfrac>
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</mml:mrow>
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</mml:math></informalequation>
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<para>
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<informalequation><mml:math>
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<!-- eqn: DELTA v = ( v sub 2 - v sub 1 ) / m:-->
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<mml:mrow>
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<mml:mrow>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">v</mml:mi>
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</mml:mrow>
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<mml:mo>=</mml:mo>
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<mml:mfrac>
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<mml:mfenced open="(" close=")">
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<mml:mrow>
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<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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<mml:mo>-</mml:mo>
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<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:mfenced>
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<mml:mi mathvariant="italic">m</mml:mi>
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</mml:mfrac>
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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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where
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<inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
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<inlineequation><mml:math>
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<!-- eqn: u sub 1:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>,
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<inlineequation><mml:math>
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<!-- eqn: u sub 2:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>,
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<inlineequation><mml:math><mml:mi mathvariant="italic">m</mml:mi></mml:math></inlineequation>,
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<inlineequation><mml:math>
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<!-- eqn: v sub 1:-->
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<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>,
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and
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<inlineequation><mml:math>
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<!-- eqn: v sub 2:-->
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<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>
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are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid2</refentrytitle></citerefentry> command.
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Then the <function>glEvalPoint2</function> command is equivalent to calling
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<programlisting>
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glEvalCoord2( <mml:math>
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<!-- i \cdot DELTA u + u sub 1 :-->
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<mml:mrow>
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<mml:mrow>
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<mml:mn>i</mml:mn>
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<mml:mo>·</mml:mo>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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<mml:mo>+</mml:mo>
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<mml:msub>
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<mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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<mml:mo>,</mml:mo>
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<!-- j \cdot DELTA v + v sub 1 :-->
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<mml:mrow>
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<mml:mn>j</mml:mn>
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<mml:mo>·</mml:mo>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">v</mml:mi>
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</mml:mrow>
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<mml:mo>+</mml:mo>
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<mml:msub>
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<mml:mi mathvariant="italic">v</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:math> );
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</programlisting>
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The only absolute numeric requirements are that if
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<inlineequation><mml:math>
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<!-- eqn: i = n:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">i</mml:mi>
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<mml:mo>=</mml:mo>
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<mml:mi mathvariant="italic">n</mml:mi>
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</mml:mrow>
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</mml:math></inlineequation>,
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then the value computed from
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<inlineequation><mml:math>
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<!-- eqn: i cdot DELTA u + u sub 1:-->
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<mml:mrow>
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<mml:mrow>
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<mml:mi mathvariant="italic">i</mml:mi>
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<mml:mo>·</mml:mo>
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<mml:mrow>
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<mml:mo>Δ</mml:mo>
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<mml:mi mathvariant="italic">u</mml:mi>
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</mml:mrow>
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</mml:mrow>
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<mml:mo>+</mml:mo>
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>1</mml:mn>
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</mml:msub>
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</mml:mrow>
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</mml:math></inlineequation>
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is exactly
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<inlineequation><mml:math>
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<!-- eqn: u sub 2:-->
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<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
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<mml:mn>2</mml:mn>
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</mml:msub>
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</mml:math></inlineequation>,
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and if
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<inlineequation><mml:math>
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<!-- eqn: j = m:-->
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<mml:mrow>
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<mml:mi mathvariant="italic">j</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:math></inlineequation>,
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then the value computed from
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<inlineequation><mml:math>
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||
|
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<!-- eqn: j cdot DELTA v + v sub 1:-->
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<mml:mrow>
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<mml:mrow>
|
||
|
|
<mml:mi mathvariant="italic">j</mml:mi>
|
||
|
|
<mml:mo>·</mml:mo>
|
||
|
|
<mml:mrow>
|
||
|
|
<mml:mo>Δ</mml:mo>
|
||
|
|
<mml:mi mathvariant="italic">v</mml:mi>
|
||
|
|
</mml:mrow>
|
||
|
|
</mml:mrow>
|
||
|
|
<mml:mo>+</mml:mo>
|
||
|
|
<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
|
||
|
|
<mml:mn>1</mml:mn>
|
||
|
|
</mml:msub>
|
||
|
|
</mml:mrow>
|
||
|
|
</mml:math></inlineequation>
|
||
|
|
is exactly
|
||
|
|
<inlineequation><mml:math>
|
||
|
|
<!-- eqn: v sub 2:-->
|
||
|
|
<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
|
||
|
|
<mml:mn>2</mml:mn>
|
||
|
|
</mml:msub>
|
||
|
|
</mml:math></inlineequation>.
|
||
|
|
</para>
|
||
|
|
</refsect1>
|
||
|
|
<refsect1 id="associatedgets"><title>Associated Gets</title>
|
||
|
|
<para>
|
||
|
|
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_DOMAIN</constant>
|
||
|
|
</para>
|
||
|
|
<para>
|
||
|
|
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_DOMAIN</constant>
|
||
|
|
</para>
|
||
|
|
<para>
|
||
|
|
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP1_GRID_SEGMENTS</constant>
|
||
|
|
</para>
|
||
|
|
<para>
|
||
|
|
<citerefentry><refentrytitle>glGet</refentrytitle></citerefentry> with argument <constant>GL_MAP2_GRID_SEGMENTS</constant>
|
||
|
|
</para>
|
||
|
|
</refsect1>
|
||
|
|
<refsect1 id="seealso"><title>See Also</title>
|
||
|
|
<para>
|
||
|
|
<citerefentry><refentrytitle>glEvalCoord</refentrytitle></citerefentry>,
|
||
|
|
<citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry>,
|
||
|
|
<citerefentry><refentrytitle>glMap1</refentrytitle></citerefentry>,
|
||
|
|
<citerefentry><refentrytitle>glMap2</refentrytitle></citerefentry>,
|
||
|
|
<citerefentry><refentrytitle>glMapGrid</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>
|