Sophie

Sophie

distrib > Fedora > 13 > i386 > by-pkgid > 5764c67416561ab82b35afcf9c650e17 > files > 871

GMT-doc-4.5.2-1.fc13.noarch.rpm

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">

<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
original version by:  Nikos Drakos, CBLU, University of Leeds
* revised and updated by:  Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
  Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>3.2.2 Gridding with Splines in Tension</TITLE>
<META NAME="description" CONTENT="3.2.2 Gridding with Splines in Tension">
<META NAME="keywords" CONTENT="GMT_Tutorial">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">

<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">

<LINK REL="STYLESHEET" HREF="GMT_Tutorial.css">

<LINK REL="next" HREF="node47.html">
<LINK REL="previous" HREF="node44.html">
<LINK REL="up" HREF="node43.html">
<LINK REL="next" HREF="node47.html">
</HEAD>

<BODY  bgcolor="#ffffff">
<!--Navigation Panel-->
<A NAME="tex2html1047"
  HREF="node47.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
<A NAME="tex2html1041"
  HREF="node43.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
<A NAME="tex2html1035"
  HREF="node45.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
<A NAME="tex2html1043"
  HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> 
<A NAME="tex2html1045"
  HREF="node63.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> 
<BR>
<B> Next:</B> <A NAME="tex2html1048"
  HREF="node47.html">3.2.3 Preprocessing</A>
<B> Up:</B> <A NAME="tex2html1042"
  HREF="node43.html">3.2 Gridding of arbitrarily</A>
<B> Previous:</B> <A NAME="tex2html1036"
  HREF="node45.html">3.2.1.1 Exercises</A>
 &nbsp; <B>  <A NAME="tex2html1044"
  HREF="node1.html">Contents</A></B> 
 &nbsp; <B>  <A NAME="tex2html1046"
  HREF="node63.html">Index</A></B> 
<BR>
<BR>
<!--End of Navigation Panel-->

<H2><A NAME="SECTION00522000000000000000">
3.2.2 Gridding with Splines in Tension</A>
</H2>

<P>
As an alternative, we may use a global procedure to grid our data.
This approach, implemented in the program <A NAME="tex2html188"
  HREF="../man/surface.html"><I><B>surface</B></I></A><A NAME="2391"></A>, represents
an improvement over standard minimum curvature algorithms by allowing
users to introduce some tension into the surface.
Physically, we are trying to force a thin elastic plate to go through
all our data points; the values of this surface at the grid points
become the gridded data.  Mathematically, we want to find the function
<IMG
 WIDTH="43" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img36.png"
 ALT="$z(x, y)$"> that satisfies the following constraints: 
<BR><A NAME="1199"></A>

<P>
<!-- MATH
 $\begin{array}{ll}
z(x_k, y_k) = z_k,      &       \mbox{for all data $(x_k, y_k, z_k), k =1,n$} \\
(1-t)\nabla^4 z -  t \nabla^2 z = 0     &       \mbox{elsewhere}
\end{array}$
 -->
<IMG
 WIDTH="367" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="img37.png"
 ALT="\( \begin{array}{ll}
z(x_k, y_k) = z_k, &amp; \mbox{for all data $(x_k, y_k, z_k), k =1,n$} \\
(1-t)\nabla^4 z - t \nabla^2 z = 0 &amp; \mbox{elsewhere}
\end{array} \)"> 
<BR>
<P>
where <IMG
 WIDTH="9" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img38.png"
 ALT="$t$"> is the ``tension'', <!-- MATH
 $0 \leq t \leq 1$
 -->
<IMG
 WIDTH="64" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img39.png"
 ALT="$0 \leq t \leq 1$">.  Basically, as
<!-- MATH
 $t \rightarrow 0$
 -->
<IMG
 WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img40.png"
 ALT="$t \rightarrow 0$"> we obtain the minimum curvature solution, while as
<!-- MATH
 $t \rightarrow \infty$
 -->
<IMG
 WIDTH="44" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img41.png"
 ALT="$t \rightarrow \infty$"> we go towards a harmonic solution (which is linear
in cross-section).  The theory behind all this is quite involved
and we do not have the time to explain it all here, please see
<I>Smith and Wessel</I> [1990] for details.  Some of the most important
switches for this program are indicated in Table&nbsp;<A HREF="#tbl:surface">3.3</A><A NAME="tex2html184"
  HREF="footnode.html#foot1611"><SUP>3.1</SUP></A>.

<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1614"></A>
<TABLE>
<CAPTION><STRONG>Table 3.3:</STRONG>
Some of the options in <A NAME="tex2html185"
  HREF="../man/surface.html"><I><B>surface</B></I></A><A NAME="2400"></A>.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER"><TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=1><FONT SIZE="-1">
<I>Option</I></FONT></TD>
<TD ALIGN="CENTER" COLSPAN=1><FONT SIZE="-1"> <I>Purpose</I></FONT></TD>
</TR>
<TR><TH ALIGN="LEFT"><FONT SIZE="-1">   
<B>-A</B></FONT><FONT SIZE="-1"><I>aspect</I> </FONT></TH>
<TD ALIGN="LEFT"><FONT SIZE="-1"> Sets aspect ratio for anisotropic grids. </FONT></TD>
</TR>
<TR><TH ALIGN="LEFT"><FONT SIZE="-1">  
<B>-C</B></FONT><FONT SIZE="-1"><I>limit</I> </FONT></TH>
<TD ALIGN="LEFT"><FONT SIZE="-1"> Sets convergence limit.  Default is 1/1000 of data range. </FONT></TD>
</TR>
<TR><TH ALIGN="LEFT"><FONT SIZE="-1">  
<B>-T</B></FONT><FONT SIZE="-1"><I>tension</I> </FONT></TH>
<TD ALIGN="LEFT"><FONT SIZE="-1"> Sets the tension [Default is 0] </FONT></TD>
</TR>
</TABLE><FONT SIZE="-1">

<A NAME="tbl:surface"></A></FONT></DIV></TD></TR>
</TABLE>
</DIV><P></P>
<BR>

<P>
<HR>
<!--Navigation Panel-->
<A NAME="tex2html1047"
  HREF="node47.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> 
<A NAME="tex2html1041"
  HREF="node43.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> 
<A NAME="tex2html1035"
  HREF="node45.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> 
<A NAME="tex2html1043"
  HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> 
<A NAME="tex2html1045"
  HREF="node63.html">
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> 
<BR>
<B> Next:</B> <A NAME="tex2html1048"
  HREF="node47.html">3.2.3 Preprocessing</A>
<B> Up:</B> <A NAME="tex2html1042"
  HREF="node43.html">3.2 Gridding of arbitrarily</A>
<B> Previous:</B> <A NAME="tex2html1036"
  HREF="node45.html">3.2.1.1 Exercises</A>
 &nbsp; <B>  <A NAME="tex2html1044"
  HREF="node1.html">Contents</A></B> 
 &nbsp; <B>  <A NAME="tex2html1046"
  HREF="node63.html">Index</A></B> 
<!--End of Navigation Panel-->
<ADDRESS>
Paul Wessel
2010-01-14
</ADDRESS>
</BODY>
</HTML>

Perl :: Catalyst :: PostgreSQL :: RPM Valid HTML 4.01 Transitional