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int usage(int retval, bool brief) {
if (brief)
( retval ? std::cerr : std::cout ) << "Usage:\n"
" RhumbSolve [ -i | -L lat1 lon1 azi12 ] [ -e a f ] [ -u ] [ -d | -: ] [\n"
" -w ] [ -p prec ] [ -E ] [ --comment-delimiter commentdelim ] [\n"
" --version | -h | --help ] [ --input-file infile | --input-string\n"
" instring ] [ --line-separator linesep ] [ --output-file outfile ]\n"
"\n"
"For full documentation type:\n"
" RhumbSolve --help\n"
"or visit:\n"
" https://geographiclib.sourceforge.io/C++/2.6/RhumbSolve.1.html\n";
else
( retval ? std::cerr : std::cout ) << "Man page:\n"
"\n"
"SYNOPSIS\n"
" RhumbSolve [ -i | -L lat1 lon1 azi12 ] [ -e a f ] [ -u ] [ -d | -: ] [\n"
" -w ] [ -p prec ] [ -E ] [ --comment-delimiter commentdelim ] [\n"
" --version | -h | --help ] [ --input-file infile | --input-string\n"
" instring ] [ --line-separator linesep ] [ --output-file outfile ]\n"
"\n"
"DESCRIPTION\n"
" The path with constant heading between two points on the ellipsoid at\n"
" (lat1, lon1) and (lat2, lon2) is called the rhumb line or loxodrome.\n"
" Its length is s12 and the rhumb line has a forward azimuth azi12 along\n"
" its length. The quantity S12 is the area between the rhumb line from\n"
" point 1 to point 2 and the equator; i.e., it is the area, measured\n"
" counter-clockwise, of the geodesic quadrilateral with corners\n"
" (lat1,lon1), (0,lon1), (0,lon2), and (lat2,lon2). The longitude\n"
" becomes indeterminate when a rhumb line passes through a pole, and\n"
" RhumbSolve reports NaNs for the longitude and the area in this case.\n"
"\n"
" NOTE: the rhumb line is not the shortest path between two points; that\n"
" is the geodesic and it is calculated by GeodSolve(1).\n"
"\n"
" RhumbSolve operates in one of three modes:\n"
"\n"
" 1. By default, RhumbSolve accepts lines on the standard input\n"
" containing lat1 lon1 azi12 s12 and prints lat2 lon2 S12 on standard\n"
" output. This is the direct calculation.\n"
"\n"
" 2. With the -i option, RhumbSolve performs the inverse calculation.\n"
" It reads lines containing lat1 lon1 lat2 lon2 and prints the values\n"
" of azi12 s12 S12 for the corresponding shortest rhumb lines.\n"
"\n"
" 3. Command line arguments -L lat1 lon1 azi12 specify a rhumb line.\n"
" RhumbSolve then accepts a sequence of s12 values (one per line) on\n"
" standard input and prints lat2 lon2 S12 for each. This generates a\n"
" sequence of points on a rhumb line.\n"
"\n"
"OPTIONS\n"
" -i perform an inverse calculation (see 2 above).\n"
"\n"
" -L lat1 lon1 azi12\n"
" line mode (see 3 above); generate a sequence of points along the\n"
" rhumb line specified by lat1 lon1 azi12. The -w flag can be used\n"
" to swap the default order of the 2 geographic coordinates, provided\n"
" that it appears before -L.\n"
"\n"
" -e a f\n"
" specify the ellipsoid via the equatorial radius, a and the\n"
" flattening, f. Setting f = 0 results in a sphere. Specify f < 0\n"
" for a prolate ellipsoid. A simple fraction, e.g., 1/297, is\n"
" allowed for f. By default, the WGS84 ellipsoid is used, a =\n"
" 6378137 m, f = 1/298.257223563.\n"
"\n"
" -u unroll the longitude. Normally, on output longitudes are reduced\n"
" to lie in [-180deg,180deg). However with this option, the returned\n"
" longitude lon2 is \"unrolled\" so that lon2 - lon1 indicates how\n"
" often and in what sense the geodesic has encircled the earth.\n"
"\n"
" -d output angles as degrees, minutes, seconds instead of decimal\n"
" degrees.\n"
"\n"
" -: like -d, except use : as a separator instead of the d, ', and \"\n"
" delimiters.\n"
"\n"
" -w on input and output, longitude precedes latitude (except that on\n"
" input this can be overridden by a hemisphere designator, N, S, E,\n"
" W).\n"
"\n"
" -p prec\n"
" set the output precision to prec (default 3); prec is the precision\n"
" relative to 1 m. See \"PRECISION\".\n"
"\n"
" -E By default, the rhumb line calculations are carried out using\n"
" series expansions valid for |f| < 0.01. If -E is supplied, exact\n"
" equations for the rhumb line are used and the area integral is\n"
" computed with an accurate fit based on this exact equations; these\n"
" are valid for arbitrary eccentricities.\n"
"\n"
" --comment-delimiter commentdelim\n"
" set the comment delimiter to commentdelim (e.g., \"#\" or \"//\"). If\n"
" set, the input lines will be scanned for this delimiter and, if\n"
" found, the delimiter and the rest of the line will be removed prior\n"
" to processing and subsequently appended to the output line\n"
" (separated by a space).\n"
"\n"
" --version\n"
" print version and exit.\n"
"\n"
" -h print usage and exit.\n"
"\n"
" --help\n"
" print full documentation and exit.\n"
"\n"
" --input-file infile\n"
" read input from the file infile instead of from standard input; a\n"
" file name of \"-\" stands for standard input.\n"
"\n"
" --input-string instring\n"
" read input from the string instring instead of from standard input.\n"
" All occurrences of the line separator character (default is a\n"
" semicolon) in instring are converted to newlines before the reading\n"
" begins.\n"
"\n"
" --line-separator linesep\n"
" set the line separator character to linesep. By default this is a\n"
" semicolon.\n"
"\n"
" --output-file outfile\n"
" write output to the file outfile instead of to standard output; a\n"
" file name of \"-\" stands for standard output.\n"
"\n"
"INPUT\n"
" RhumbSolve measures all angles in degrees, all lengths (s12) in meters,\n"
" and all areas (S12) in meters^2. On input angles (latitude, longitude,\n"
" azimuth, arc length) can be as decimal degrees or degrees, minutes,\n"
" seconds. For example, \"40d30\", \"40d30'\", \"40:30\", \"40.5d\", and 40.5\n"
" are all equivalent. By default, latitude precedes longitude for each\n"
" point (the -w flag switches this convention); however on input either\n"
" may be given first by appending (or prepending) N or S to the latitude\n"
" and E or W to the longitude. Azimuths are measured clockwise from\n"
" north; however this may be overridden with E or W.\n"
"\n"
" For details on the allowed formats for angles, see the \"GEOGRAPHIC\n"
" COORDINATES\" section of GeoConvert(1).\n"
"\n"
"PRECISION\n"
" prec gives precision of the output with prec = 0 giving 1 m precision,\n"
" prec = 3 giving 1 mm precision, etc. prec is the number of digits\n"
" after the decimal point for lengths. For decimal degrees, the number\n"
" of digits after the decimal point is prec + 5. For DMS (degree,\n"
" minute, seconds) output, the number of digits after the decimal point\n"
" in the seconds component is prec + 1. The minimum value of prec is 0\n"
" and the maximum is 10.\n"
"\n"
"ERRORS\n"
" An illegal line of input will print an error message to standard output\n"
" beginning with \"ERROR:\" and causes RhumbSolve to return an exit code of\n"
" 1. However, an error does not cause RhumbSolve to terminate; following\n"
" lines will be converted.\n"
"\n"
"ACCURACY\n"
" The algorithm used by RhumbSolve uses either series expansions or (if\n"
" -E is specified) exact formulas for computing the rhumb line and the\n"
" area. These series are formulas are accurate for |f| < 0.01 and the\n"
" exact formulas apply for any value of the flattening. The computation\n"
" of rhumb lines and the area involves the ratio of differences and, for\n"
" nearly east- or west-going rhumb lines, this might result in a large\n"
" loss of accuracy. However, this problem is avoided by the use of\n"
" divided differences. For the WGS84 ellipsoid, the error is about 10\n"
" nanometers using either method.\n"
"\n"
"EXAMPLES\n"
" Route from JFK Airport to Singapore Changi Airport:\n"
"\n"
" echo 40:38:23N 073:46:44W 01:21:33N 103:59:22E |\n"
" RhumbSolve -i -: -p 0\n"
"\n"
" 103:34:58.2 18523563 45921660958919\n"
"\n"
" N.B. This is not the route typically taken by aircraft because it's\n"
" considerably longer than the geodesic given by GeodSolve(1).\n"
"\n"
" Waypoints on the route at intervals of 2000km:\n"
"\n"
" for ((i = 0; i <= 20; i += 2)); do echo ${i}000000;done |\n"
" RhumbSolve -L 40:38:23N 073:46:44W 103:34:58.2 -: -p 0\n"
"\n"
" 40:38:23.0N 073:46:44.0W 0\n"
" 36:24:30.3N 051:28:26.4W 9817078307821\n"
" 32:10:26.8N 030:20:57.3W 18224745682005\n"
" 27:56:13.2N 010:10:54.2W 25358020327741\n"
" 23:41:50.1N 009:12:45.5E 31321269267102\n"
" 19:27:18.7N 027:59:22.1E 36195163180159\n"
" 15:12:40.2N 046:17:01.1E 40041499143669\n"
" 10:57:55.9N 064:12:52.8E 42906570007050\n"
" 06:43:07.3N 081:53:28.8E 44823504180200\n"
" 02:28:16.2N 099:24:54.5E 45813843358737\n"
" 01:46:36.0S 116:52:59.7E 45888525219677\n"
"\n"
"SEE ALSO\n"
" GeoConvert(1), GeodSolve(1).\n"
"\n"
" An online version of this utility is availbable at\n"
" <https://geographiclib.sourceforge.io/cgi-bin/RhumbSolve>.\n"
"\n"
" An online version of this utility is availbable at\n"
" <https://geographiclib.sourceforge.io/cgi-bin/RhumbSolve>.\n"
"\n"
" This solution for rhumb line is described in C. F. F. Karney, The area\n"
" of rhumb polygons, Stud. Geophys. Geod. 68(3--4), 99--120 (2024); DOI\n"
" <https://doi.org/10.1007/s11200-024-0709-z>.\n"
"\n"
" The Wikipedia page, Rhumb line,\n"
" <https://en.wikipedia.org/wiki/Rhumb_line>.\n"
"\n"
"AUTHOR\n"
" RhumbSolve was written by Charles Karney.\n"
"\n"
"HISTORY\n"
" RhumbSolve was added to GeographicLib,\n"
;
return retval;
}
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