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<?xml version="1.0" encoding="ISO-8859-1"?>
<refentry version="5.0-subset Scilab" xml:id="interp3d" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns5="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:db="http://docbook.org/ns/docbook">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>interp3d</refname>
<refpurpose>funo de avaliao spline 3d</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Seqncia de Chamamento</title>
<synopsis>[fp[,dfpdx,dfpdy,dfpdz]]=interp3d(xp,yp,zp,tl,out_mode)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parmetros</title>
<variablelist>
<varlistentry>
<term>xp, yp, zp</term>
<listitem>
<para>vetores ou matrizes de reais de mesmo tamanho </para>
</listitem>
</varlistentry>
<varlistentry>
<term>tl</term>
<listitem>
<para>tlist do tipo "splin3d", definindo um tensor spline 3d
(chamado <literal>s</literal> a partir daqui) </para>
</listitem>
</varlistentry>
<varlistentry>
<term>out_mode</term>
<listitem>
<para>(opcional) string definindo a avaliao de
<literal>s</literal> fora do grid
([xmin,xmax]x[ymin,ymax]x[zmin,zmax]) </para>
</listitem>
</varlistentry>
<varlistentry>
<term>fp</term>
<listitem>
<para>vetor ou matriz de mesmo formato que <literal>xp</literal>,
<literal>yp</literal> e <literal>zp</literal>, avaliao elemento a
elemento de <literal>s</literal> onesses pontos. </para>
</listitem>
</varlistentry>
<varlistentry>
<term>dfpdx, dfpdy, dfpdz</term>
<listitem>
<para>vetores (ou matrizes) de mesmo formato que
<literal>xp</literal>, <literal>yp</literal> e
<literal>zp</literal>, avaliao elemento a elemento das primeiras
derivadas de <literal>s</literal> nesses pontos.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Descrio</title>
<para>Dada uma tlist <literal>tl</literal> definindo uma funo spline 3d
(ver <link linkend="splin3d">splin3d</link>) esta funo avalia
<emphasis>s</emphasis> (e <emphasis>ds/dx, ds/dy, ds/dz</emphasis> , se
necessrio) em <emphasis>(xp(i),yp(i),zp(i))</emphasis> :</para>
<programlisting role = ""><![CDATA[
zp(i) = s(xp(i),yp(i))
dzpdx(i) = ds/dx(xp(i),yp(i),zp(i))
dzpdy(i) = ds/dy(xp(i),yp(i),zp(i))
dzpdz(i) = ds/dz(xp(i),yp(i),zp(i))
]]></programlisting>
<para>O parmetro <literal>out_mode</literal>define a regra de avaliao
para extrapolao, i.e. para <emphasis>(xp(i),yp(i),zp(i)) fora de
[xmin,xmax]x[ymin,ymax]x[zmin,zmax]</emphasis>:</para>
<variablelist>
<varlistentry>
<term>"by_zero"</term>
<listitem>
<para>uma extrapolao por zero feita </para>
</listitem>
</varlistentry>
<varlistentry>
<term>"by_nan"</term>
<listitem>
<para>extrapolao por NaN ("no nmero") </para>
</listitem>
</varlistentry>
<varlistentry>
<term>"C0"</term>
<listitem>
<para>a extrapolao definida como segue :</para>
<programlisting role = ""><![CDATA[
s(x,y) = s(proj(x,y)) onde proj(x,y) o ponto mais prximo
em [x(1),x(nx)]x[y(1),y(ny)] de (x,y)
]]></programlisting>
</listitem>
</varlistentry>
<varlistentry>
<term>"periodic"</term>
<listitem>
<para> <literal>s</literal> estendido por periodicidade.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Exemplos </title>
<programlisting role="example"><![CDATA[
// veja exemplos na pgina da funo splin3d
]]></programlisting>
</refsection>
<refsection>
<title>Ver Tambm</title>
<simplelist type="inline">
<member><link linkend="splin3d">splin3d</link></member>
<member><link linkend="bsplin3val">bsplin3val</link></member>
</simplelist>
</refsection>
<refsection>
<title>Autores</title>
<simplelist type="vert">
<member>R.F. Boisvert, C. De Boor (cdigo da biblioteca FORTRAN CMLIB)
</member>
<member>B. Pincon (interface Scilab)</member>
</simplelist>
</refsection>
</refentry>
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