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int usage(int retval, bool brief) {
if (brief)
( retval ? std::cerr : std::cout ) << "Usage:\n"
" Geod3Solve [ -i | -L bet1 omg1 alp1 ] [ -t a b c | -e b e2 k2 kp2 | -e2\n"
" b f ] [ -u ] [ -d | -: ] [ -w ] [ -f ] [ -p prec ] [\n"
" --comment-delimiter commentdelim ] [ --version | -h | --help ] [\n"
" --input-file infile | --input-string instring ] [ --line-separator\n"
" linesep ] [ --output-file outfile ]\n"
"\n"
"For full documentation type:\n"
" Geod3Solve --help\n"
"or visit:\n"
" https://geographiclib.sourceforge.io/C++/2.7/Geod3Solve.1.html\n";
else
( retval ? std::cerr : std::cout ) << "Man page:\n"
"\n"
"SYNOPSIS\n"
" Geod3Solve [ -i | -L bet1 omg1 alp1 ] [ -t a b c | -e b e2 k2 kp2 | -e2\n"
" b f ] [ -u ] [ -d | -: ] [ -w ] [ -f ] [ -p prec ] [\n"
" --comment-delimiter commentdelim ] [ --version | -h | --help ] [\n"
" --input-file infile | --input-string instring ] [ --line-separator\n"
" linesep ] [ --output-file outfile ]\n"
"\n"
"DESCRIPTION\n"
" The shortest path between two points on a triaxial ellipsoid at (bet1,\n"
" omg1) and (bet2, omg2) is called the geodesic. Its length is s12 and\n"
" the geodesic from point 1 to point 2 has forward azimuths alp1 and alp2\n"
" at the two end points. Here bet and omg denote the ellipsoidal\n"
" latitude, beta, and longitude, omega; alp is an abbreviation of alpha\n"
"\n"
" Geod3Solve operates in one of three modes:\n"
"\n"
" 1. By default, Geod3Solve accepts lines on the standard input\n"
" containing bet1 omg1 alp1 s12 and prints bet2 omg2 alp2 on standard\n"
" output. This is the direct geodesic calculation.\n"
"\n"
" 2. With the -i option, Geod3Solve performs the inverse geodesic\n"
" calculation. It reads lines containing bet1 omg1 bet2 omg2 and\n"
" prints the corresponding values of alp1 alp2 s12.\n"
"\n"
" 3. Command line arguments -L bet1 omg1 alp1 specify a geodesic line.\n"
" Geod3Solve then accepts a sequence of s12 values (one per line) on\n"
" standard input and prints bet2 omg2 alp2 for each. This generates\n"
" a sequence of points on a single geodesic.\n"
"\n"
"OPTIONS\n"
" -i perform an inverse geodesic calculation (see 2 above).\n"
"\n"
" -L bet1 omg1 alp1\n"
" line mode (see 3 above); generate a sequence of points along the\n"
" geodesic specified by bet1 omg1 alp1. The -w flag can be used to\n"
" swap the default order of the 2 geographic coordinates, provided\n"
" that it appears before -L.\n"
"\n"
" -t a b c\n"
" specify the ellipsoid via its major semiaxis a, median semiaxis b,\n"
" and minor semixis c. By default, we have a = 6378172 m, b =\n"
" 6378102 m, c = 6356752 m, an approximate triaxial model of the\n"
" earth. (With this model omg = 0deg, corresponds to lon =\n"
" -14.93deg.\n"
"\n"
" -e b e2 k2 kp2\n"
" specify the ellipsoid via the median semiaxis, b and the shape\n"
" parameters e2 = (a^2 - c^2)/b^2, k2 = (b^2 - c^2)/(a^2 - c^2), and\n"
" kp2 = (a^2 - b^2)/(a^2 - c^2). Simple fractions are allowed for\n"
" e2, k2, and kp2. Internally, the supplied values of k2 and kp2 are\n"
" normalized so that k2 + kp2 = 1.\n"
"\n"
" -e2 b f\n"
" specify a biaxial ellipsoid via its equatorial radius b and\n"
" flattening f. A simple fraction, is allowed for f. In this mode,\n"
" latitudes are interpreted as geodetic latitudes on both input and\n"
" output. If f is negative, bet and omg are swapped so that latitude\n"
" and longitude have their conventional interpretations (e.g.,\n"
" longitude measures the angle about the axis of symmetry).\n"
"\n"
" -u unroll the latitude and longitude. Normally, on output latitudes\n"
" and longitudes are reduced to lie in [-90deg,90deg] and\n"
" [-180deg,180deg) respectively. However with this option, the\n"
" returned longitude bet2 and omg2 are \"unrolled\" so that bet2 - bet1\n"
" and omg2 - omg1 indicates how often and in what sense the geodesic\n"
" has encircled the ellipsoid.\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 toggle the longitude first flag (it starts off); if the flag is on,\n"
" then on input and output, longitude precedes latitude (except that,\n"
" on input, this can be overridden by a hemisphere designator, N, S,\n"
" E, W).\n"
"\n"
" -f full output; each line of output consists of 7 quantities: bet1\n"
" omg1 alp1 bet2 omg2 alp2 s12.\n"
"\n"
" -p prec\n"
" set the output precision to prec (default 3). For distances, prec\n"
" is the number of digits after the decimal point for ellipsoids\n"
" which are approximately the same size as the Earth; for other\n"
" ellipsoids the precision is adjusted to retain the same relative\n"
" precision. For latitudes and longitudes (in degrees), the number\n"
" of digits after the decimal point is prec + 5. For cartesian\n"
" directions, the precision is prec + 7.\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"
" Geod3Solve measures all angles in degrees and all lengths (s12) in\n"
" meters. On input angles (latitude, longitude, azimuth) can be as\n"
" decimal degrees or degrees, minutes, seconds. For example, \"40d30\",\n"
" \"40d30'\", \"40:30\", \"40.5d\", and 40.5 are all equivalent. By default,\n"
" latitude precedes longitude for each point (the -w flag switches this\n"
" convention); however on input either may be given first by appending\n"
" (or prepending) N or S to the latitude and E or W to the longitude.\n"
" Azimuths are measured clockwise from north; however this may be\n"
" 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"
"ERRORS\n"
" An illegal line of input will print an error message to standard output\n"
" beginning with \"ERROR:\" and causes Geod3Solve to return an exit code of\n"
" 1. However, an error does not cause Geod3Solve to terminate; following\n"
" lines will be converted.\n"
"\n"
"EXAMPLES\n"
" Route from JFK Airport to Singapore Changi Airport on a triaxial\n"
" ellipsoid:\n"
"\n"
" echo 40:38:23N 073:46:44W-19.43W X 01:21:33N 103:59:22E-19.43W |\n"
" tr X '\\n' |\n"
" tools/Cart3Convert -G | tools/Cart3Convert -E -r | tr '\\n' ' ' |\n"
" tools/Geod3Solve -i -: -p 0\n"
" => 003:15:05.9 177:27:09.0 15339505\n"
"\n"
" The steps here are shift for longitude of major axis (-19.43d), convert\n"
" to geocentric for biaxial Earth, convert to ellipsoidal for triaxial\n"
" Earth, compute geodesic distance.\n"
"\n"
"SEE ALSO\n"
" Cart3Convert(1).\n"
"\n"
" The algorithms are described in C. F. F. Karney, Jacobi's solution for\n"
" geodesics on a triaxial ellipsoid, Technical Report, SRI International,\n"
" Nov. 2025, <https://arxiv.org/abs/2511.01621>.\n"
"\n"
" The Wikipedia page, Geodesics on an ellipsoid,\n"
" <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid>.\n"
"\n"
"AUTHOR\n"
" Geod3Solve was written by Charles Karney.\n"
"\n"
"HISTORY\n"
;
return retval;
}
|
