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<H1><A NAME="SECTION001400000000000000000"></A>
<A NAME="ch:6"></A>
<BR>
6. <A NAME="tex2html1330"
  HREF="http://gmt.soest.hawaii.edu"><B>GMT</B></A> Map Projections
</H1>

<P>
<A NAME="tex2html1332"
  HREF="http://gmt.soest.hawaii.edu"><B>GMT</B></A> implements more than 30 different projections.  They all project the input coordinates
longitude and latitude to positions on a map.  In general, <IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img120.png"
 ALT="$x' = f(x,y,z)$"> and <IMG
 WIDTH="87" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img121.png"
 ALT="$y' = g(x,y,z)$">, where
<IMG
 WIDTH="10" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.png"
 ALT="$z$"> is implicitly given as the radial vector length to the <IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img86.png"
 ALT="$(x,y)$"> point on the chosen ellipsoid.  The functions <IMG
 WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img93.png"
 ALT="$f$"> and <IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img122.png"
 ALT="$g$"> can be
quite nasty and we will refrain from presenting details in this document.  The interested read is referred to
<I>Snyder</I> [1987]<A NAME="tex2html1331"
  HREF="footnode.html#foot22161"><SUP>6.1</SUP></A>.
We will mostly be using the <A NAME="tex2html1333"
  HREF="../man/pscoast.html"><I><B>pscoast</B></I></A><A NAME="23114"></A> command to demonstrate each of the projections.
<A NAME="tex2html1334"
  HREF="http://gmt.soest.hawaii.edu"><B>GMT</B></A> map projections are grouped into four categories depending on the
nature of the projection.  The groups are

<P>

<OL>
<LI>Conic map projections
</LI>
<LI>Azimuthal map projections
</LI>
<LI>Cylindrical map projections
</LI>
<LI>Miscellaneous projections
</LI>
</OL>

<P>
Because <IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.png"
 ALT="$x$"> and <IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img32.png"
 ALT="$y$"> are coupled we can only specify one plot-dimensional scale, typically
a map <I>scale</I> (for lower-case map projection code) or a map <I>width</I> (for upper-case
map projection code).  However, in some cases it would be more
practical to specify map <I>height</I> instead of <I>width</I>, while in other situations it would be nice
to set either the <I>shortest</I> or <I>longest</I> map dimension.  Users may select
these alternatives by appending a character code to their map dimension.  To specify map <I>height</I>,
append <B>h</B> to the given dimension; to select the minimum map dimension, append <B>-</B>, whereas you may
append <B>+</B> to select the maximum map dimension.  Without the modifier the map width is
selected by default.

<P>
In <A NAME="tex2html1335"
  HREF="http://gmt.soest.hawaii.edu"><B>GMT</B></A> version 4.3.0 we noticed we ran out of the alphabet for 1-letter (and sometimes 2-letter) projection codes. To allow more flexibility, and to make it easier to remember the codes, we implemented the option to use the abbreviations used by the <I>Proj4</I><A NAME="23124"></A> mapping package. Since some of the <A NAME="tex2html1336"
  HREF="http://gmt.soest.hawaii.edu"><B>GMT</B></A> projections are not in <I>Proj4</I><A NAME="23130"></A>, we invented some of our own as well. For a full list of both the old 1- and 2-letter codes, as well as the <I>Proj4</I><A NAME="23133"></A>-equivalents see the quick reference cards in Section&nbsp;<A HREF="node32.html#sec:purpose">3.2</A>. For example, <B>-JM15c</B> and <B>-JMerc/15c</B> have the same meaning.

<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>

<UL>
<LI><A NAME="tex2html3863"
  HREF="node88.html">6.1 Conic projections</A>
<UL>
<LI><A NAME="tex2html3864"
  HREF="node89.html">6.1.1 Albers conic equal-area projection (<B>-Jb</B> <B>-JB</B>)</A>
<LI><A NAME="tex2html3865"
  HREF="node90.html">6.1.2 Equidistant conic projection (<B>-Jd</B> <B>-JD</B>)</A>
<LI><A NAME="tex2html3866"
  HREF="node91.html">6.1.3 Lambert conic conformal projection (<B>-Jl</B> <B>-JL</B>)</A>
<LI><A NAME="tex2html3867"
  HREF="node92.html">6.1.4 (American) polyconic projection (<B>-Jpoly</B> <B>-JPoly</B></A>
</UL>
<BR>
<LI><A NAME="tex2html3868"
  HREF="node93.html">6.2 Azimuthal projections</A>
<UL>
<LI><A NAME="tex2html3869"
  HREF="node94.html">6.2.1 Lambert Azimuthal Equal-Area (<B>-Ja</B> <B>-JA</B>)</A>
<UL>
<LI><A NAME="tex2html3870"
  HREF="node95.html">6.2.1.1 Rectangular map</A>
<LI><A NAME="tex2html3871"
  HREF="node96.html">6.2.1.2 Hemisphere map</A>
</UL>
<LI><A NAME="tex2html3872"
  HREF="node97.html">6.2.2 Stereographic Equal-Angle projection (<B>-Js</B> <B>-JS</B>)</A>
<UL>
<LI><A NAME="tex2html3873"
  HREF="node98.html">6.2.2.1 Polar Stereographic Map</A>
<LI><A NAME="tex2html3874"
  HREF="node99.html">6.2.2.2 Rectangular stereographic map</A>
<LI><A NAME="tex2html3875"
  HREF="node100.html">6.2.2.3 General stereographic map</A>
</UL>
<LI><A NAME="tex2html3876"
  HREF="node101.html">6.2.3 Perspective projection (<B>-Jg</B> <B>-JG</B>)</A>
<LI><A NAME="tex2html3877"
  HREF="node102.html">6.2.4 Orthographic projection (<B>-Jg</B> <B>-JG</B>)</A>
<LI><A NAME="tex2html3878"
  HREF="node103.html">6.2.5 Azimuthal Equidistant projection (<B>-Je</B> <B>-JE</B>)</A>
<LI><A NAME="tex2html3879"
  HREF="node104.html">6.2.6 Gnomonic projection (<B>-Jf</B> <B>-JF</B>)</A>
</UL>
<BR>
<LI><A NAME="tex2html3880"
  HREF="node105.html">6.3 Cylindrical projections</A>
<UL>
<LI><A NAME="tex2html3881"
  HREF="node106.html">6.3.1 Mercator projection (<B>-Jm</B> <B>-JM</B>)</A>
<LI><A NAME="tex2html3882"
  HREF="node107.html">6.3.2 Transverse Mercator projection (<B>-Jt</B> <B>-JT</B>)</A>
<LI><A NAME="tex2html3883"
  HREF="node108.html">6.3.3 Universal Transverse Mercator (UTM) projection (<B>-Ju</B> <B>-JU</B>)</A>
<LI><A NAME="tex2html3884"
  HREF="node109.html">6.3.4 Oblique Mercator projection (<B>-Jo</B> <B>-JO</B>)</A>
<LI><A NAME="tex2html3885"
  HREF="node110.html">6.3.5 Cassini cylindrical projection (<B>-Jc</B> <B>-JC</B>)</A>
<LI><A NAME="tex2html3886"
  HREF="node111.html">6.3.6 Cylindrical equidistant projection (<B>-Jq</B> <B>-JQ</B>)</A>
<LI><A NAME="tex2html3887"
  HREF="node112.html">6.3.7 Cylindrical equal-area projections (<B>-Jy</B> <B>-JY</B>)</A>
<LI><A NAME="tex2html3888"
  HREF="node113.html">6.3.8 Miller Cylindrical projection (<B>-Jj</B> <B>-JJ</B>)</A>
<LI><A NAME="tex2html3889"
  HREF="node114.html">6.3.9 Cylindrical stereographic projections (<B>-Jcyl_stere</B> <B>-JCyl_stere</B>)</A>
</UL>
<BR>
<LI><A NAME="tex2html3890"
  HREF="node115.html">6.4 Miscellaneous projections</A>
<UL>
<LI><A NAME="tex2html3891"
  HREF="node116.html">6.4.1 Hammer projection (<B>-Jh</B> <B>-JH</B>)</A>
<LI><A NAME="tex2html3892"
  HREF="node117.html">6.4.2 Mollweide projection (<B>-Jw</B> <B>-JW</B>)</A>
<LI><A NAME="tex2html3893"
  HREF="node118.html">6.4.3 Winkel Tripel projection (<B>-Jr</B> <B>-JR</B>)</A>
<LI><A NAME="tex2html3894"
  HREF="node119.html">6.4.4 Robinson projection (<B>-Jn</B> <B>-JN</B>)</A>
<LI><A NAME="tex2html3895"
  HREF="node120.html">6.4.5 Eckert IV and VI projection (<B>-Jk</B> <B>-JK</B>)</A>
<LI><A NAME="tex2html3896"
  HREF="node121.html">6.4.6 Sinusoidal projection (<B>-Ji</B> <B>-JI</B>)</A>
<LI><A NAME="tex2html3897"
  HREF="node122.html">6.4.7 Van der Grinten projection (<B>-Jv</B> <B>-JV</B>)</A>
</UL></UL>
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<ADDRESS>
Paul Wessel
2011-02-27
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