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5.1.3 Cartesian power projection
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<DIV ALIGN="CENTER"><A NAME="fig:GMT_pow"></A><A NAME="21201"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.5:</STRONG>
Exponential or power transformation of <IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.png"
 ALT="$x$">-coordinates.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER"><IMG
 WIDTH="391" HEIGHT="209" ALIGN="BOTTOM" BORDER="0"
 SRC="img100.png"
 ALT="\includegraphics{scripts/GMT_pow}"></DIV></TD></TR>
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This projection uses <!-- MATH
 $u' = a u^b + c$
 -->
<IMG
 WIDTH="82" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="img101.png"
 ALT="$u' = a u^b + c$"> and allows us to explore exponential relationships like <I>x<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img102.png"
 ALT="$^p$"></I> versus <I>y<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="img103.png"
 ALT="$^q$"></I>.
While <IMG
 WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img104.png"
 ALT="$p$"> and <IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img105.png"
 ALT="$q$"> can be any values, we will select <IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img106.png"
 ALT="$p
= 0.5$"> and <IMG
 WIDTH="39" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img107.png"
 ALT="$q = 1$"> which means we will plot <IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.png"
 ALT="$x$"> versus <IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.png"
 ALT="$\sqrt {x}$">.
We indicate this scaling by appending a <B>p</B> (lower case P) followed
by the desired exponent, in our case 0.5.  Since <IMG
 WIDTH="39" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img107.png"
 ALT="$q = 1$"> we do not
need to specify <B>p</B>1 since it is identical to the linear transformation.
Thus our command becomes

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<PRE>psxy -R0/100/0/10 -Jx0.3ip0.5/0.15i -Ba1p/a2f1WSne -Wthick -P -K sqrt.d &gt; GMT_pow.ps
psxy -R -J -Sc0.075i -Gwhite -W -O sqrt.d10 &gt;&gt; GMT_pow.ps
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<ADDRESS>
Paul Wessel
2010-07-14
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