157 lines
5.0 KiB
Plaintext
157 lines
5.0 KiB
Plaintext
=head1 NAME
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TransverseMercatorProj -- perform transverse Mercator projection
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=head1 SYNOPSIS
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B<TransverseMercatorProj> [ B<-s> | B<-t> ]
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[ B<-l> I<lon0> ] [ B<-k> I<k0> ] [ B<-r> ]
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[ B<-e> I<a> I<f> ]
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[ B<--comment-delimiter> I<commentdelim> ]
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[ B<--version> | B<-h> | B<--help> ]
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[ B<--input-file> I<infile> | B<--input-string> I<instring> ]
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[ B<--line-separator> I<linesep> ]
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[ B<--output-file> I<outfile> ]
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=head1 DESCRIPTION
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Perform the transverse Mercator projections. Convert geodetic
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coordinates to transverse Mercator coordinates. The central meridian is
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given by I<lon0>. The longitude of origin is the equator. The scale on
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the central meridian is I<k0>. By default an implementation of the
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exact transverse Mercator projection is used.
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Geodetic coordinates are provided on standard input as a set of lines
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containing (blank separated) I<latitude> and I<longitude> (decimal
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degrees or degrees, minutes, seconds). For each set of geodetic
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coordinates, the corresponding projected easting, I<x>, and northing,
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I<y>, (meters) are printed on standard output together with the meridian
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convergence I<gamma> (degrees) and scale I<k>. The meridian convergence
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is the bearing of the I<y> axis measured clockwise from true north.
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=head1 OPTIONS
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=over
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=item B<-s>
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use the sixth-order Krueger series approximation to the transverse
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Mercator projection instead of the exact projection.
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=item B<-t>
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use the exact algorithm with the L</EXTENDED DOMAIN>.
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=item B<-l>
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specify the longitude of origin I<lon0> (degrees, default 0).
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=item B<-k>
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specify the scale I<k0> on the central meridian (default 0.9996).
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=item B<-r>
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perform the reverse projection. I<x> and I<y> are given on standard
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input and each line of standard output gives I<latitude>, I<longitude>,
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I<gamma>, and I<k>.
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=item B<-e>
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specify the ellipsoid via I<a> I<f>; the equatorial radius is I<a> and
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the flattening is I<f>. Setting I<f> = 0 results in a sphere. Specify
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I<f> E<lt> 0 for a prolate ellipsoid. A simple fraction, e.g., 1/297,
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is allowed for I<f>. (Also, if I<f> E<gt> 1, the flattening is set to
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1/I<f>.) By default, the WGS84 ellipsoid is used, I<a> = 6378137 m,
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I<f> = 1/298.257223563. If the exact algorithm is used, I<f> must be
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positive.
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=item B<--comment-delimiter>
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set the comment delimiter to I<commentdelim> (e.g., "#" or "//"). If
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set, the input lines will be scanned for this delimiter and, if found,
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the delimiter and the rest of the line will be removed prior to
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processing and subsequently appended to the output line (separated by a
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space).
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=item B<--version>
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print version and exit.
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=item B<-h>
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print usage and exit.
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=item B<--help>
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print full documentation and exit.
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=item B<--input-file>
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read input from the file I<infile> instead of from standard input; a file
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name of "-" stands for standard input.
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=item B<--input-string>
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read input from the string I<instring> instead of from standard input.
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All occurrences of the line separator character (default is a semicolon)
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in I<instring> are converted to newlines before the reading begins.
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=item B<--line-separator>
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set the line separator character to I<linesep>. By default this is a
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semicolon.
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=item B<--output-file>
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write output to the file I<outfile> instead of to standard output; a
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file name of "-" stands for standard output.
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=back
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=head1 EXTENDED DOMAIN
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The exact transverse Mercator projection has a I<branch point> on the
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equator at longitudes (relative to I<lon0>) of +/- (1 - I<e>) 90, where
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I<e> is the eccentricity of the ellipsoid. The standard convention for
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handling this branch point is to map positive (negative) latitudes into
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positive (negative) northings I<y>; i.e., a branch cut is placed on the
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equator. With the I<extended> domain, the northern sheet of the
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projection is extended into the south hemisphere by pushing the branch
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cut south from the branch points. See the reference below for details.
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=head1 EXAMPLES
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echo 0 90 | TransverseMercatorProj
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=> 25953592.84 9997964.94 90 18.40
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echo 260e5 100e5 | TransverseMercatorProj -r
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=> -0.02 90.00 90.01 18.48
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=head1 ERRORS
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An illegal line of input will print an error message to standard output
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beginning with C<ERROR:> and causes B<TransverseMercatorProj> to return an exit
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code of 1. However, an error does not cause B<TransverseMercatorProj> to
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terminate; following lines will be converted.
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=head1 AUTHOR
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B<TransverseMercatorProj> was written by Charles Karney.
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=head1 SEE ALSO
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The algorithms for the transverse Mercator projection are described in
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C. F. F. Karney, I<Transverse Mercator with an accuracy of a few
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nanometers>, J. Geodesy B<85>(8), 475-485 (Aug. 2011); DOI
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L<http://dx.doi.org/10.1007/s00190-011-0445-3>; preprint
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L<http://arxiv.org/abs/1002.1417>. The explanation of the extended
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domain of the projection with the B<-t> option is given in Section 5 of
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this paper.
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=head1 HISTORY
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B<TransverseMercatorProj> was added to GeographicLib,
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L<http://geographiclib.sf.net>, in 2009-01. Prior to version 1.9 it was
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called TransverseMercatorTest (and its interface was slightly
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different).
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