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Opentk/Source/Bind/Specifications/Docs/GL/glEvalPoint.xml

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE book PUBLIC "-//OASIS//DTD DocBook MathML Module V1.1b1//EN"
"http://www.oasis-open.org/docbook/xml/mathml/1.1CR1/dbmathml.dtd">
<refentry id="glEvalPoint">
<refmeta>
<refmetainfo>
<copyright>
<year>1991-2006</year>
<holder>Silicon Graphics, Inc.</holder>
</copyright>
</refmetainfo>
<refentrytitle>glEvalPoint</refentrytitle>
<manvolnum>3G</manvolnum>
</refmeta>
<refnamediv>
<refname>glEvalPoint</refname>
<refpurpose>generate and evaluate a single point in a mesh</refpurpose>
</refnamediv>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>glEvalPoint1</function></funcdef>
<paramdef>GLint <parameter>i</parameter></paramdef>
</funcprototype>
</funcsynopsis>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>glEvalPoint2</function></funcdef>
<paramdef>GLint <parameter>i</parameter></paramdef>
<paramdef>GLint <parameter>j</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<!-- eqn: ignoring delim $$ -->
<refsect1 id="parameters"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>i</parameter></term>
<listitem>
<para>
Specifies the integer value for grid domain variable
<inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>j</parameter></term>
<listitem>
<para>
Specifies the integer value for grid domain variable
<inlineequation><mml:math><mml:mi mathvariant="italic">j</mml:mi></mml:math></inlineequation>
(<function>glEvalPoint2</function> only).
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsect1 id="description"><title>Description</title>
<para>
<citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry> are used in tandem to efficiently
generate and evaluate a series of evenly spaced map domain values.
<function>glEvalPoint</function> can be used to evaluate a single grid point in the same gridspace
that is traversed by <citerefentry><refentrytitle>glEvalMesh</refentrytitle></citerefentry>.
Calling <function>glEvalPoint1</function> is equivalent to calling
<programlisting>
glEvalCoord1( <mml:math>
<!-- eqn: i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>&CenterDot;</mml:mo>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math> );
</programlisting>
where
<informalequation><mml:math>
<!-- eqn: DELTA u = ( u sub 2 - u sub 1 ) / n:-->
<mml:mrow>
<mml:mrow>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>-</mml:mo>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
<para>
and
<inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
<inlineequation><mml:math>
<!-- eqn: u sub 1:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:math></inlineequation>,
and
<inlineequation><mml:math>
<!-- eqn: u sub 2:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></inlineequation>
are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid1</refentrytitle></citerefentry> command.
The one absolute numeric requirement is that if
<inlineequation><mml:math>
<!-- eqn: i = n:-->
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:math></inlineequation>,
then the value computed from
<inlineequation><mml:math>
<!-- eqn: i cdot DELTA u + u sub 1:-->
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mo>&CenterDot;</mml:mo>
<mml:mrow>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math></inlineequation>
is exactly
<inlineequation><mml:math>
<!-- eqn: u sub 2:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></inlineequation>.
</para>
<para>
In the two-dimensional case, <function>glEvalPoint2</function>, let
</para>
<para>
<informalequation><mml:math>
<!-- eqn: DELTA u = ( u sub 2 - u sub 1 ) / n:-->
<mml:mrow>
<mml:mrow>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>-</mml:mo>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
<para>
<informalequation><mml:math>
<!-- eqn: DELTA v = ( v sub 2 - v sub 1 ) / m:-->
<mml:mrow>
<mml:mrow>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">v</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>-</mml:mo>
<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math></informalequation>
</para>
</para>
<para>
where
<inlineequation><mml:math><mml:mi mathvariant="italic">n</mml:mi></mml:math></inlineequation>,
<inlineequation><mml:math>
<!-- eqn: u sub 1:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:math></inlineequation>,
<inlineequation><mml:math>
<!-- eqn: u sub 2:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></inlineequation>,
<inlineequation><mml:math><mml:mi mathvariant="italic">m</mml:mi></mml:math></inlineequation>,
<inlineequation><mml:math>
<!-- eqn: v sub 1:-->
<mml:msub><mml:mi mathvariant="italic">v</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:math></inlineequation>,
and
<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>
are the arguments to the most recent <citerefentry><refentrytitle>glMapGrid2</refentrytitle></citerefentry> command.
Then the <function>glEvalPoint2</function> command is equivalent to calling
<programlisting>
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>&CenterDot;</mml:mo>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<!-- j \cdot DELTA v + v sub 1 :-->
<mml:mrow>
<mml:mn>j</mml:mn>
<mml:mo>&CenterDot;</mml:mo>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">v</mml:mi>
</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> );
</programlisting>
The only absolute numeric requirements are that if
<inlineequation><mml:math>
<!-- eqn: i = n:-->
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:math></inlineequation>,
then the value computed from
<inlineequation><mml:math>
<!-- eqn: i cdot DELTA u + u sub 1:-->
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mo>&CenterDot;</mml:mo>
<mml:mrow>
<mml:mo>&Delta;</mml:mo>
<mml:mi mathvariant="italic">u</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math></inlineequation>
is exactly
<inlineequation><mml:math>
<!-- eqn: u sub 2:-->
<mml:msub><mml:mi mathvariant="italic">u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:math></inlineequation>,
and if
<inlineequation><mml:math>
<!-- eqn: j = m:-->
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi mathvariant="italic">m</mml:mi>
</mml:mrow>
</mml:math></inlineequation>,
then the value computed from
<inlineequation><mml:math>
<!-- eqn: j cdot DELTA v + v sub 1:-->
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mo>&CenterDot;</mml:mo>
<mml:mrow>
<mml:mo>&Delta;</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>
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