/
glEvalMesh.xml
626 lines (624 loc) · 25 KB
/
glEvalMesh.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="glEvalMesh">
<refmeta>
<refmetainfo>
<copyright>
<year>1991-2006</year>
<holder>Silicon Graphics, Inc.</holder>
</copyright>
</refmetainfo>
<refentrytitle>glEvalMesh</refentrytitle>
<manvolnum>3G</manvolnum>
</refmeta>
<refnamediv>
<refname>glEvalMesh</refname>
<refpurpose>compute a one- or two-dimensional grid of points or lines</refpurpose>
</refnamediv>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>glEvalMesh1</function></funcdef>
<paramdef>GLenum <parameter>mode</parameter></paramdef>
<paramdef>GLint <parameter>i1</parameter></paramdef>
<paramdef>GLint <parameter>i2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<!-- eqn: ignoring delim $$ -->
<refsect1 id="parameters"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>mode</parameter></term>
<listitem>
<para>
In <function>glEvalMesh1</function>, specifies whether to compute a one-dimensional mesh of points or lines.
Symbolic constants
<constant>GL_POINT</constant> and
<constant>GL_LINE</constant> are accepted.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>i1</parameter></term>
<term><parameter>i2</parameter></term>
<listitem>
<para>
Specify the first and last integer values for grid domain variable
<inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsynopsisdiv><title>C Specification</title>
<funcsynopsis>
<funcprototype>
<funcdef>void <function>glEvalMesh2</function></funcdef>
<paramdef>GLenum <parameter>mode</parameter></paramdef>
<paramdef>GLint <parameter>i1</parameter></paramdef>
<paramdef>GLint <parameter>i2</parameter></paramdef>
<paramdef>GLint <parameter>j1</parameter></paramdef>
<paramdef>GLint <parameter>j2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsect1 id="parameters2"><title>Parameters</title>
<variablelist>
<varlistentry>
<term><parameter>mode</parameter></term>
<listitem>
<para>
In <function>glEvalMesh2</function>, specifies whether to compute a two-dimensional mesh of points, lines,
or polygons.
Symbolic constants
<constant>GL_POINT</constant>,
<constant>GL_LINE</constant>, and
<constant>GL_FILL</constant> are accepted.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>i1</parameter></term>
<term><parameter>i2</parameter></term>
<listitem>
<para>
Specify the first and last integer values for grid domain variable
<inlineequation><mml:math><mml:mi mathvariant="italic">i</mml:mi></mml:math></inlineequation>.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term><parameter>j1</parameter></term>
<term><parameter>j2</parameter></term>
<listitem>
<para>
Specify the first and last integer values for grid domain variable
<inlineequation><mml:math><mml:mi mathvariant="italic">j</mml:mi></mml:math></inlineequation>.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsect1>
<refsect1 id="description"><title>Description</title>
<para>
<citerefentry><refentrytitle>glMapGrid</refentrytitle></citerefentry> and <function>glEvalMesh</function> are used in tandem to efficiently
generate and evaluate a series of evenly-spaced map domain values.
<function>glEvalMesh</function> steps through the integer domain of a one- or two-dimensional grid,
whose range is the domain of the evaluation maps specified by
<citerefentry><refentrytitle>glMap1</refentrytitle></citerefentry> and <citerefentry><refentrytitle>glMap2</refentrytitle></citerefentry>.
<parameter>mode</parameter> determines whether the resulting vertices are connected as
points,
lines,
or filled polygons.
</para>
<para>
In the one-dimensional case,
<function>glEvalMesh1</function>,
the mesh is generated as if the following code fragment were executed:
</para>
<para>
<programlisting>
glBegin( <parameter>type</parameter> );
for ( i = <parameter>i1</parameter>; i <= <parameter>i2</parameter>; i += 1 )
glEvalCoord1( <mml:math>
<!-- eqn: i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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> );
glEnd();
</programlisting>
where
</para>
<para>
<informalequation><mml:math>
<!-- eqn: DELTA u = (u sub 2 - u sub 1 ) / n:-->
<mml:mrow>
<mml:mrow>
<mml:mo>Δ</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.
<emphasis>type</emphasis> is <constant>GL_POINTS</constant> if <parameter>mode</parameter> is <constant>GL_POINT</constant>,
or <constant>GL_LINES</constant> if <parameter>mode</parameter> is <constant>GL_LINE</constant>.
</para>
<para>
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>·</mml:mo>
<mml:mrow>
<mml:mo>Δ</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>glEvalMesh2</function>, let
.cp
<informalequation><mml:math>
<!-- eqn: DELTA u = ( u sub 2 - u sub 1 ) / n:-->
<mml:mrow>
<mml:mrow>
<mml:mo>Δ</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>
<informalequation><mml:math>
<!-- eqn: DELTA v = ( v sub 2 - v sub 1 ) / m:-->
<mml:mrow>
<mml:mrow>
<mml:mo>Δ</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>
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, if
<parameter>mode</parameter> is <constant>GL_FILL</constant>, the <function>glEvalMesh2</function> command is equivalent
to:
</para>
<para>
<programlisting>
for ( j = <parameter>j1</parameter>; j < <parameter>j2</parameter>; j += 1 ) {
glBegin( GL_QUAD_STRIP );
for ( i = <parameter>i1</parameter>; i <= <parameter>i2</parameter>; i += 1 ) {
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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>·</mml:mo>
<mml:mo>Δ</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> );
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1, :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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 + 1) \cdot DELTA v + v sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>j</mml:mn>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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> );
}
glEnd();
}
</programlisting>
</para>
<para>
If <parameter>mode</parameter> is <constant>GL_LINE</constant>, then a call to <function>glEvalMesh2</function> is equivalent to:
</para>
<para>
<programlisting>
for ( j = <parameter>j1</parameter>; j <= <parameter>j2</parameter>; j += 1 ) {
glBegin( GL_LINE_STRIP );
for ( i = <parameter>i1</parameter>; i <= <parameter>i2</parameter>; i += 1 )
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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>
<!-- i \cdot DELTA v + v sub 1 :-->
<mml:mrow>
<mml:mn>j</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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> );
glEnd();
}
for ( i = <parameter>i1</parameter>; i <= <parameter>i2</parameter>; i += 1 ) {
glBegin( GL_LINE_STRIP );
for ( j = <parameter>j1</parameter>; j <= <parameter>j1</parameter>; j += 1 )
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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>
<!-- i \cdot DELTA v + v sub 1 :-->
<mml:mrow>
<mml:mn>j</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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> );
glEnd();
}
</programlisting>
</para>
<para>
And finally, if <parameter>mode</parameter> is <constant>GL_POINT</constant>, then a call to
<function>glEvalMesh2</function> is equivalent to:
</para>
<para>
<programlisting>
glBegin( GL_POINTS );
for ( j = <parameter>j1</parameter>; j <= <parameter>j2</parameter>; j += 1 )
for ( i = <parameter>i1</parameter>; i <= <parameter>i2</parameter>; i += 1 )
glEvalCoord2( <mml:math>
<!-- i \cdot DELTA u + u sub 1 :-->
<mml:mrow>
<mml:mrow>
<mml:mn>i</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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>
<!-- i \cdot DELTA v + v sub 1 :-->
<mml:mrow>
<mml:mn>j</mml:mn>
<mml:mo>·</mml:mo>
<mml:mo>Δ</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> );
glEnd();
</programlisting>
</para>
<para>
In all three cases, 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>·</mml:mo>
<mml:mrow>
<mml:mo>Δ</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>·</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="errors"><title>Errors</title>
<para>
<constant>GL_INVALID_ENUM</constant> is generated if <parameter>mode</parameter> is not an accepted value.
</para>
<para>
<constant>GL_INVALID_OPERATION</constant> is generated if <function>glEvalMesh</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_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>glBegin</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glEvalCoord</refentrytitle></citerefentry>,
<citerefentry><refentrytitle>glEvalPoint</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>