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<H2><A NAME="SECTION001315000000000000000">
5.1.5 Linear Projection with Polar (<IMG
WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img2.gif"
ALT="$\theta , r$">)
Coordinates (<B>-Jp </B> <B>-JP</B>)</A>
</H2>
<A NAME="6148"></A>
<A NAME="6149"></A>
<A NAME="6170"></A>
<P>
<P></P>
<DIV ALIGN="CENTER"><A NAME="fig:GMT_polar"></A><A NAME="6179"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.5:</STRONG>
Polar (Cylindrical) transformation of
(<IMG
WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img2.gif"
ALT="$\theta , r$">) coordinates</CAPTION>
<TR><TD><IMG
WIDTH="404" HEIGHT="404" BORDER="0"
SRC="img62.gif"
ALT="\begin{figure}\centering\epsfig{figure=eps/GMT_polar.eps}\end{figure}"></TD></TR>
</TABLE>
</DIV><P></P>
<P>
In many applications the data is better described in polar or
cylindrical (<I><IMG
WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img63.gif"
ALT="$\theta$"></I>, <I>r</I>) coordinates rather than
the usual Cartesian coordinates (<I>x</I>, <I>y</I>). The
relationship between the Cartesian and polar coordinates are
described by <!-- MATH
$x = r \cdot \cos{\theta}, y = r \cdot \sin{\theta}$
-->
<IMG
WIDTH="154" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img64.gif"
ALT="$x = r \cdot \cos{\theta}, y = r \cdot \sin{\theta}$">.
The polar transformation is simply defined by providing
<BR>
<P>
<DL>
<DT><STRONG><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img54.gif"
ALT="$\bullet$"></STRONG></DT>
<DD>scale in inches/unit (<B>-Jp</B>) or full width of plot in inches (<B>-JP</B>)
</DD>
<DT><STRONG><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img54.gif"
ALT="$\bullet$"></STRONG></DT>
<DD>Optionally, insert <B>a</B> after <B>p<IMG
WIDTH="8" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$\vert$">P</B> to indicate CW azimuths rather than CCW directions
</DD>
<DT><STRONG><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img54.gif"
ALT="$\bullet$"></STRONG></DT>
<DD>Optionally, append /<IMG
WIDTH="43" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img65.gif"
ALT="$origin$"> in degrees to indicate an angular offset [0]
<P>
</DD>
</DL>
<P>
As an example of this projection we will create a gridded data set
in polar coordinates <!-- MATH
$z(\theta, r) = r^2 \cdot \cos{4\theta}$
-->
<IMG
WIDTH="124" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
SRC="img66.gif"
ALT="$z(\theta, r) = r^2 \cdot \cos{4\theta}$">
using <A NAME="tex2html302"
HREF="../grdmath.html"><I><B>grdmath</B></I></A><A NAME="6186"></A>, a RPN calculator that operates on or
creates grdfiles.
<P>
<P>
<BR>
<P>
<BR CLEAR="ALL">
<HR>
<BR>
<PRE>
#!/bin/sh
# $Id: GMT_polar.sh,v 1.1 2001/03/21 04:10:21 pwessel Exp $
#
grdmath -R0/360/2/4 -I6/0.1 X 4 MUL PI MUL 180 DIV COS Y 2 POW MUL = test.grd
grdcontour test.grd -JP3i -B30Ns -P -C2 -S4 > GMT_polar.ps
</PRE>
<P>
<BR>
<BR>
<P>
<BR CLEAR="ALL">
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<P>
We used <A NAME="tex2html303"
HREF="../grdcontour.html"><I><B>grdcontour</B></I></A><A NAME="6300"></A> to make a contour map of this data. Because
the data file only contains values with <!-- MATH
$2 \leq r \leq 4$
-->
<IMG
WIDTH="65" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img67.gif"
ALT="$2 \leq r \leq 4$">, a donut
shaped plot appears in Figure <A HREF="node40.html#fig:GMT_polar">5.5</A>. <A NAME="6293"></A>
<A NAME="6294"></A>
<A NAME="6297"></A>
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<ADDRESS>
Paul Wessel
2001-04-18
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