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<H2><A NAME="SECTION001356000000000000000">
5.5.6 Sinusoidal Projection (<B>-Ji</B> <B>-JI</B>)</A>
</H2>
<P>
<A NAME="9498"></A>
<A NAME="9499"></A>
<A NAME="9500"></A>
<P>
The sinusoidal projection is one of the oldest known
projections, is equal-area, and has been used since the
mid-16th century. It has also been called the
``Equal-area Mercator'' projection. The central meridian
is a straight line; all other meridians are sinusoidal
curves. Parallels are all equally spaced straight lines,
with scale being true along all parallels (and central
meridian). To use it, you need to select:
<P>
<DL>
<DD><P>
</DD>
<DT><STRONG><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img54.gif"
ALT="$\bullet$"></STRONG></DT>
<DD>The central meridian
<P>
</DD>
<DT><STRONG><IMG
WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img54.gif"
ALT="$\bullet$"></STRONG></DT>
<DD>Scale along equator in inch/degree or
1:xxxxx (<B>-Ji</B>), or map width (<B>-JI</B>)
<P>
</DD>
</DL>
<P>
A simple world map using the sinusoidal projection is therefore obtained by
<P>
<P>
<BR>
<P>
<BR CLEAR="ALL">
<HR>
<BR>
<PRE>
#!/bin/sh
# $Id: GMT_sinusoidal.sh,v 1.1 2001/03/21 04:10:21 pwessel Exp $
#
pscoast -R-180/180/-90/90 -JI0/4.5i -Bg30/g15 -Dc -A10000 -G128 -P > GMT_sinusoidal.ps
</PRE>
<P>
<BR>
<BR>
<P>
<BR CLEAR="ALL">
<HR>
<P></P>
<DIV ALIGN="CENTER"><A NAME="fig:GMT_sinusoidal"></A><A NAME="9629"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.32:</STRONG>
World map using the Sinusoidal projection</CAPTION>
<TR><TD><IMG
WIDTH="520" HEIGHT="261" BORDER="0"
SRC="img94.gif"
ALT="\begin{figure}\centering\epsfig{figure=eps/GMT_sinusoidal.eps}\end{figure}"></TD></TR>
</TABLE>
</DIV><P></P>
<P>
To reduce distortion of shape the interrupted sinusoidal
projection was introduced in 1927. Here, three symmetrical
segments are used to cover the entire world. Traditionally,
the interruptions are at 160<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$">W, 20<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$">W, and 60<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$">E.
To make the interrupted map we must call <A NAME="tex2html348"
HREF="../pscoast.html"><I><B>pscoast</B></I></A><A NAME="9637"></A> for
each segment and superpose the results. To produce an
interrupted world map (with the traditional boundaries
just mentioned) that is 5.04 inches wide we use the scale
5.04/360<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$"> = 0.014 and offset the subsequent plots
horizontally by their widths (140<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$"><IMG
WIDTH="8" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img95.gif"
ALT="$\cdot$">0.014 and 80<IMG
WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img61.gif"
ALT="$^{o}$">
<IMG
WIDTH="8" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img95.gif"
ALT="$\cdot$">0.014):
<P>
<A NAME="9626"></A>
<P>
<P>
<BR>
<P>
<BR CLEAR="ALL">
<HR>
<BR>
<PRE>
#!/bin/sh
# $Id: GMT_sinusoidal_int.sh,v 1.1 2001/03/21 04:10:21 pwessel Exp $
#
pscoast -R200/340/-90/90 -Ji270/0.014i -Bg30/g15 -A10000 -Dc -G0 -P -K -P > GMT_sinusoidal_int.ps
pscoast -R-20/60/-90/90 -Ji20/0.014i -Bg30/g15 -Dc -A10000 -G0 -X1.96i -O -K >> GMT_sinusoidal_int.ps
pscoast -R60/200/-90/90 -Ji130/0.014i -Bg30/g15 -Dc -A10000 -G0 -X1.12i -O >> GMT_sinusoidal_int.ps
</PRE>
<P>
<BR>
<BR>
<P>
<BR CLEAR="ALL">
<HR>
<P></P>
<DIV ALIGN="CENTER"><A NAME="fig:GMT_sinusoidal_int"></A><A NAME="9722"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.33:</STRONG>
World map using the Interrupted Sinusoidal projection</CAPTION>
<TR><TD><IMG
WIDTH="582" HEIGHT="291" BORDER="0"
SRC="img96.gif"
ALT="\begin{figure}\centering\epsfig{figure=eps/GMT_sinusoidal_int.eps}\end{figure}"></TD></TR>
</TABLE>
</DIV><P></P>
<P>
The usefulness of the interrupted sinusoidal projection is
basically limited to display of global, discontinuous data
distributions like hydrocarbon and mineral resources, etc.
<P>
<A NAME="9713"></A>
<A NAME="9714"></A>
<A NAME="9715"></A>
<P>
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<ADDRESS>
Paul Wessel
2001-04-18
</ADDRESS>
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