/usr/bin/Cart3Convert

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SYNOPSIS
       Cart3Convert [ -E | -G | -P | -C | -GX | -PX | -CX ] [ -r ] [ -3 | -D ]
       [ -R nrand ] [ --seed s ] [ -t a b c | -e b e2 k2 kp2 ] [ -d | -: ] [
       -w ] [ -p prec ] [ --comment-delimiter commentdelim ] [ --version | -h
       | --help ] [ --input-file infile | --input-string instring ] [
       --line-separator linesep ] [ --output-file outfile ]

DESCRIPTION
       Convert coordinates for a triaxial ellipsoid to geocentric coordinates.
       Geocentric coordinates have the origin at the center of the earth, with
       the X, Y, and Z axes aligned with the major, median, and minor
       semiaxes, a, b, and c.  By default, the conversion is to geocentric
       coordinates.  Specifying -r causes the reverse conversion to be
       performed.

       Seven latitude/longitude/heading coordinate systems are supported

       1.  Ellipsoidal coordinates, beta, omega, and alpha, signified by -En
           (the default)

       2.  Geodetic coordinates, phi, lambda, and zeta, signified by -G.

       3.  Parametric coordinates, phi', lambda', and zeta, signified by -P.

       4.  Geocentric coordinates, phi", lambda", and zeta, signified by -C.

       5.  Geodetic coordinates, phi*, lambda*, and zeta*, with the north pole
           lying on the X axis, signified by -GX.

       6.  Parametric coordinates, phi*', lambda*', and zeta*, with the north
           pole lying on the X axis, signified by -PX.

       7.  Geocentric coordinates, phi*", lambda*", and zeta*, with the north
           pole lying on the X axis, signified by -CX.

       In general, only ellipsoidal coordinates are orthogonal.  However for
       all coordinates, we define the heading as the direction measured
       clockwise from a line of constant longitude.  zeta is the same for the
       geodetic, parametric, and geocentric coordinate systems.

       Points away from the surface of the ellipsoid can be described by the
       orthogonal height h above from the ellipsoid and the position is given
       by phi, lambda (giving the closest point on the ellipsoid), and h.
       Alternatively, the confocal ellipsoid of minor radius c + H point can
       be found and the position of the point is then given by beta, omega for
       the confocal ellipsoid and H.

       By default, coordinates are provided on standard input as a set of
       lines containing (blank separated) latitude and longitude (decimal
       degrees or degrees, minutes and seconds).  The interpretation of the
       coordinates is governed by the -E, -G, -P, -C -GX, -PX, and -CX flags.
       For each set of coordinates, the corresponding cartesian coordinates X,
       Y, Z (meters) are printed on standard output.  If -r is provided, the
       reserve operation is undertaken reading X, Y, Z (which are assumed to
       denote a point on the ellipsoid) on standard input and printing the
       latitude and longitude.

       If the -3 flag is given (this cannot be combined with -D), an arbitrary
       point in three-dimensional space is specified either with beta omega H
       or with phi lambda h.

       If the -D flag is given (this cannot be combined with -3), the heading
       (direction) is included in the computation converting beta omega alpha
       or phi lambda zeta to X, Y, Z Vx, Vy, Vz where [vx, vy, vz] is a unit
       vector lying in the surface of the ellipsoid.

       If the -R flag is given, do not read any input; instead output random
       cartesian points lying on the surface of the ellipsoid.  If the -r flag
       is specified the cartesian points are converted into one of the
       triaxial coordinate systems.

OPTIONS
       -E  latitude and longitude is interpreted as ellipsoidal coordinates
           beta and omega.  This is the default.

       -G or -GX
           latitude and longitude is interpreted as geodetic coordinates phi
           and lambda.  The X added to the flags means that the north pole
           lies on the X axis.

       -P or -PX
           latitude and longitude is interpreted as parametric coordinates
           phi' and lambda'.  The X added to the flags means that the north
           pole lies on the X axis.

       -C or -CX
           latitude and longitude is interpreted as geocentric coordinates
           phi" and lambda".  The X added to the flags means that the north
           pole lies on the X axis.

       -r  perform the reverse projection from x, y, z to latitude, longitude.
           Unless -3 is given, it is assumed that the point lies on the
           surface of the ellipsoid.

       -3  include the height h or H in the calculation.  This cannot be
           combined with -D.

       -D  include the direction alpha or zeta in the calculation.  With the
           -r option, it is assumed that the vector [vx, vy, vz] is tangent to
           the surface of the ellipsoid.  This cannot be combined with -3.

       -R nrand
           output nrand random points on the surface of the ellipsoid as
           cartesian coordinates.  With -D add also a random cartesian
           direction tangent to the surface of the ellipsoid.  In this mode,
           nothing is read from standard input.  With the -r option the random
           points are converted into one of the triaxial coordinate systems
           (and the direction is converted to a heading if -D is given).

       --seed s
           set the random number seed to s when using -R.  s = 0 (the default)
           causes a random seed to be used.

       -t a b c
           specify the ellipsoid via its major semiaxis a, median semiaxis b,
           and minor semixis c.  By default, we have a = 6378172 m, b =
           6378102 m, c = 6356752 m, an approximate triaxial model of the
           earth.  (With this model omg = 0deg, corresponds to lon =
           -14.93deg.

       -e b e2 k2 kp2
           specify the ellipsoid via the median semiaxis, b and the shape
           parameters e2 = (a^2 - c^2)/b^2, k2 = (b^2 - c^2)/(a^2 - c^2), and
           kp2 = (a^2 - b^2)/(a^2 - c^2).  Simple fractions are allowed for
           e2, k2, and kp2.  Internally, the supplied values of k2 and kp2 are
           normalized so that k2 + kp2 = 1.

       -d  output angles as degrees, minutes, seconds instead of decimal
           degrees.

       -:  like -d, except use : as a separator instead of the d, ', and "
           delimiters.

       -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, N, S,
           E, W).

       -p prec
           set the output precision to prec (default 3).  For distances, prec
           is the number of digits after the decimal point for ellipsoids
           which are approximately the same size as the Earth; for other
           ellipsoids the precision is adjusted to retain the same relative
           precision.  For latitudes and longitudes (in degrees), the number
           of digits after the decimal point is prec + 5.  For cartesian
           directions, the precision is prec + 7.

       --comment-delimiter commentdelim
           set the comment delimiter to 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).

       --version
           print version and exit.

       -h  print usage and exit.

       --help
           print full documentation and exit.

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

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

       --line-separator linesep
           set the line separator character to linesep.  By default this is a
           semicolon.

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

EXAMPLES
          echo 1 2 3 | Cart3Convert -t 3 2 1 -3 -p 0 -r
          => 58.69140 75.11263 2.5860649
          echo 58.69140 75.11263 2.5860649 | Cart3Convert -t 3 2 1 -3 -p 0
          => 1.0000001 2.0000003 2.9999999

ERRORS
       An illegal line of input will print an error message to standard output
       beginning with "ERROR:" and causes Cart3Convert to return an exit code
       of 1.  However, an error does not cause Cart3Convert to terminate;
       following lines will be converted.

AUTHOR
       Cart3Convert was written by Charles Karney.

SEE ALSO
       Geod3Solve(1).

       The algorithms are described in Appendices A and B of C. F. F. Karney,
       Jacobi's solution for geodesics on a triaxial ellipsoid, Technical
       Report, SRI International, Nov. 2025,
       <https://arxiv.org/abs/2511.01621>.

       The Wikipedia page, Geodesics on an ellipsoid,
       <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid>.

HISTORY