=head1 NAME

GeodesicProj -- perform projections based on geodesics

=head1 SYNOPSIS

B<GeodesicProj> ( B<-z> | B<-c> | B<-g> ) I<lat0> I<lon0> [ B<-r> ]
[ B<-e> I<a> I<f> ] [ B<-w> ] [ B<-p> I<prec> ]
[ B<--comment-delimiter> I<commentdelim> ]
[ B<--version> | B<-h> | B<--help> ]
[ B<--input-file> I<infile> | B<--input-string> I<instring> ]
[ B<--line-separator> I<linesep> ]
[ B<--output-file> I<outfile> ]

=head1 DESCRIPTION

Perform projections based on geodesics.  Convert geodetic coordinates to
either azimuthal equidistant, Cassini-Soldner, or gnomonic coordinates.
The center of the projection (I<lat0>, I<lon0>) is specified by either
the B<-c> option (for Cassini-Soldner), the B<-z> option (for azimuthal
equidistant), or the B<-g> option (for gnomonic).  At least one of these
options must be given (the last one given is used).

Geodetic coordinates are provided on standard input as a set of lines
containing (blank separated) I<latitude> and I<longitude> (decimal
degrees or degrees, minutes, seconds); for details on the allowed
formats for latitude and longitude, see the C<GEOGRAPHIC COORDINATES>
section of GeoConvert(1).  For each set of geodetic coordinates, the
corresponding projected coordinates I<x>, I<y> (meters) are printed on
standard output together with the azimuth I<azi> (degrees) and
reciprocal scale I<rk>.  For Cassini-Soldner, I<azi> is the bearing of
the easting direction and the scale in the easting direction is 1 and
the scale in the northing direction is 1/I<rk>.  For azimuthal
equidistant and gnomonic, I<azi> is the bearing of the radial direction
and the scale in the azimuthal direction is 1/I<rk>.  For azimuthal
equidistant and gnomonic, the scales in the radial direction are 1 and
1/I<rk>^2, respectively.

=head1 OPTIONS

=over

=item B<-z> I<lat0> I<lon0>

use the azimuthal equidistant projection centered at latitude = I<lat0>,
longitude = I<lon0>.  The B<-w> flag can be used to swap the default
order of the 2 coordinates, provided that it appears before B<-z>.

=item B<-c> I<lat0> I<lon0>

use the Cassini-Soldner projection centered at latitude = I<lat0>,
longitude = I<lon0>.  The B<-w> flag can be used to swap the default
order of the 2 coordinates, provided that it appears before B<-c>.

=item B<-g> I<lat0> I<lon0>

use the ellipsoidal gnomonic projection centered at latitude = I<lat0>,
longitude = I<lon0>.  The B<-w> flag can be used to swap the default
order of the 2 coordinates, provided that it appears before B<-g>.

=item B<-r>

perform the reverse projection.  I<x> and I<y> are given on standard
input and each line of standard output gives I<latitude>, I<longitude>,
I<azi>, and I<rk>.

=item B<-e> I<a> I<f>

specify the ellipsoid via the equatorial radius, I<a> and
the flattening, I<f>.  Setting I<f> = 0 results in a sphere.  Specify
I<f> E<lt> 0 for a prolate ellipsoid.  A simple fraction, e.g., 1/297,
is allowed for I<f>.  By default, the WGS84 ellipsoid is used, I<a> =
6378137 m, I<f> = 1/298.257223563.

=item B<-w>

toggle the longitude first flag (it starts off); if the flag is on, then
on input and output, longitude precedes latitude (except that, on input,
this can be overridden by a hemisphere designator, I<N>, I<S>, I<E>,
I<W>).

=item B<-p> I<prec>

set the output precision to I<prec> (default 6).  I<prec> is the number
of digits after the decimal point for lengths (in meters).  For
latitudes, longitudes, and azimuths (in degrees), the number of digits
after the decimal point is I<prec> + 5.  For the scale, the number of
digits after the decimal point is I<prec> + 6.

=item B<--comment-delimiter> I<commentdelim>

set the comment delimiter to I<commentdelim> (e.g., "#" or "//").  If
set, the input lines will be scanned for this delimiter and, if found,
the delimiter and the rest of the line will be removed prior to
processing and subsequently appended to the output line (separated by a
space).

=item B<--version>

print version and exit.

=item B<-h>

print usage and exit.

=item B<--help>

print full documentation and exit.

=item B<--input-file> I<infile>

read input from the file I<infile> instead of from standard input; a file
name of "-" stands for standard input.

=item B<--input-string> I<instring>

read input from the string I<instring> instead of from standard input.
All occurrences of the line separator character (default is a semicolon)
in I<instring> are converted to newlines before the reading begins.

=item B<--line-separator> I<linesep>

set the line separator character to I<linesep>.  By default this is a
semicolon.

=item B<--output-file> I<outfile>

write output to the file I<outfile> instead of to standard output; a
file name of "-" stands for standard output.

=back

=head1 EXAMPLES

   echo 48.648 -2.007 | GeodesicProj -c 48.836 2.337
   => -319919 -11791 86.7 0.999
   echo -319919 -11791 | GeodesicProj -c 48.836 2.337 -r
   => 48.648 -2.007 86.7 0.999

=head1 ERRORS

An illegal line of input will print an error message to standard output
beginning with C<ERROR:> and causes B<GeodesicProj> to return an exit
code of 1.  However, an error does not cause B<GeodesicProj> to
terminate; following lines will be converted.

=head1 SEE ALSO

The ellipsoidal gnomonic projection is derived in Section 8 of
C. F. F. Karney, I<Algorithms for geodesics>, J. Geodesy 87, 43-55 (2013); DOI
L<https://doi.org/10.1007/s00190-012-0578-z>;
addenda: L<https://geographiclib.sourceforge.io/geod-addenda.html>.

=head1 AUTHOR

B<GeodesicProj> was written by Charles Karney.

=head1 HISTORY

B<GeodesicProj> was added to GeographicLib,
L<https://geographiclib.sourceforge.io>, in 2009-08.
Prior to version 1.9 it was called EquidistantTest.
