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<!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>
