/usr/bin/IntersectTool

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SYNOPSIS
       IntersectTool [ -c | -n | -i | -o | [ -R maxdist ] [ -e a f] [ -E ] [
       -w ] [ -p prec ] [ --comment-delimiter commentdelim ] [ --version | -h
       | --help ] [ --input-file infile | --input-string instring ] [
       --line-separator linesep ] [ --output-file outfile ]

DESCRIPTION
       IntersectTool finds the intersection of two geodesics X and Y.  The
       geodesics may either be specified as a location and an azimuth, latX
       lonX aziX, or as the shortest geodesic segment between two locations,
       latX1 lonX1 and latX2 lonX2.  The intersection is then specified as the
       displacements, x and y, along the geodesics X and Y from the starting
       points to the intersection.  In the case of the intersection of
       geodesic segments, the starting point is first point specified for X or
       Y.

       Usually this tool returns the closest intersection defined as the one
       that minimizes the "L1" distance, |x| + |y|.  However, it is possible
       to specify an "origin" x0 and y0 when determining closeness so that the
       intersection which minimizes |x - x0| + |y - y0| is returned.

       In the case of intersecting segments the origin is taken to be the
       midpoints of the segments; x0 is half the distance from X1 to X2.  In
       addition a flag is returned specifying whether the intersection is
       "within" the segments.

       The tool also returns a "coincidence indicator" c.  This is typically
       0.  However if the geodesics lie on top of one another at the point of
       intersection, then c is set to 1, if they are parallel, and -1, if they
       are antiparallel.

       IntersectTool operates in one of three modes:

       1.  With the -c option (the default), IntersectTool accepts lines on
           the standard input containing latX lonX aziX latY lonY aziY,
           specifying two geodesic lines X and Y, and prints the location of
           the closest intersection x y c on standard output.

       2.  With the -n option, IntersectTool accepts lines on the standard
           input containing latX lonX aziX aziY aziY, specifying a point where
           two geodesic lines X and Y intersect, and prints the location of
           the next closest intersection x y c on standard output.

       3.  With the -i option, IntersectTool accepts lines on the standard
           input containing latX1 lonX1 latX2 lonX2 latY1 lonY1 latY2 lonY2,
           specifying two geodesic segments X1-X2 and Y1-Y2, and prints x y c
           k on standard output.  Here k is a flag in [-4,4] specifying
           whether the intersection is within the segments (0) or not
           (non-zero).  x and y give the distances from X1 and Y1
           respectively.  k is set to 3 kx + ky where kx = -1 if x < 0, 0 if 0
           <= x <= sx, 1 if sx < x, and similarly for ky; sx is the length of
           the segment X1-X2.

       4.  With the -o option, IntersectTool accepts lines on the standard
           input containing latX lonX aziX latY lonY aziY x0 y0, specifying
           two geodesic lines X and Y and two offsets, and prints x y c on
           standard output where [x, y] is the intersection closest to [x0,
           y0].

OPTIONS
       -c  find the closest intersection (see 1 above).

       -n  find the intersection closest to a given intersection (see 2
           above).

       -i  find the intersection of two geodesic segments (see 3 above).

       -o  find the closest intersection with an offset.

       -R maxdist
           modifies the four modes to return all the intersections within an
           L1 distance, maxdist, of the relevant origin: [0, 0] for -c and -n,
           the midpoints of the segments for -i, and [x0, y0] for -o.  For
           each intersection, x y c z is printed on standard output.  Here z
           is the L1 distance of the intersection from the origin and the
           intersections are sorted by the distances.  A line "nan nan 0 nan"
           is added after the intersections, so that the output can be
           associated with the correct lines of the input.  The number of
           intersections scales as (maxdist/(pi a))^2.

       -C  check the intersections.  For each computed intersection, print on
           standard error a line latX lonX latY lonY sXY giving the computed
           positions of the intersections points on X and Y and the distance
           between them.  If -w is specified, the longitude is given before
           the latitude.

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

       -E  use "exact" algorithms (based on elliptic integrals) for the
           geodesic calculations.  These are more accurate than the (default)
           series expansions for |f| > 0.02.

       -w  on input, 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); prec is the precision
           relative to 1 m.  See "PRECISION".

       --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.

INPUT
       IntersectTool measures all angles in degrees and all lengths in meters.
       On input angles (latitude, longitude, azimuth) can be as decimal
       degrees or degrees, minutes, seconds.  For example, "40d30", "40d30'",
       "40:30", "40.5d", and 40.5 are all equivalent.  By default, latitude
       precedes longitude for each point (the -w flag switches this
       convention); however either may be given first by appending (or
       prepending) N or S to the latitude and E or W to the longitude.
       Azimuths are measured clockwise from north; however this may be
       overridden with E or W.

       For details on the allowed formats for angles, see the "GEOGRAPHIC
       COORDINATES" section of GeoConvert(1).

PRECISION
       prec gives precision of the output with prec = 0 giving 1 m precision,
       prec = 3 giving 1 mm precision, etc.  prec is the number of digits
       after the decimal point for lengths.  The latitude and longitude
       printed to standard error with the -C option are given in decimal
       degrees with prec + 5 digits after the decimal point.  The minimum
       value of prec is 0 and the maximum is 10.

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

ACCURACY
       This tool will give nearly full double precision accuracy for |f| <
       0.02.  If the -E option is given, full accuracy is achieved for -1/4 <
       f < 1/5.  The tool had not been tested outside this range.

EXAMPLES
       A vessel leaves Plymouth 50N 4W on a geodesic path with initial heading
       147.7W.  When will it first cross the equator?

          echo 50N 4W 147.7W 0 0 90 | IntersectTool -c -p 0 -C

          6058049 -3311253 0
          0.00000 -29.74549 -0.00000 -29.74549 0

       Answer: after 6058km at longitude 29.7W.  When will it cross the date
       line, longitude 180E?  Here we need to use -R because there a closer
       intersection on the prime meridian:

          echo 50N 4W 147.7W 0 180 0 | IntersectTool -c -p 0 -C -R 2.6e7

          -494582 14052230 0 14546812
          53.69260 0.00000 53.69260 0.00000 0
          19529110 -5932344 0 25461454
          -53.51867 180.00000 -53.51867 180.00000 0
          nan nan 0 nan
          nan nan nan nan nan

       We want the second result: after 19529 km at latitude 53.5S.

SEE ALSO
       GeoConvert(1), GeodSolve(1).

       This solution for intersections is described in C. F. F. Karney,
       Geodesic intersections, J. Surveying Eng. 150(3), 04024005:1-9 (2024),
       DOI: <https://doi.org/10.1061/JSUED2.SUENG-1483>; preprint
       <https://arxiv.org/abs/2308.00495>.  It is based on the work of S.
       Baseldga and J. C. Martinez-Llario, Intersection and point-to-line
       solutions for geodesics on the ellipsoid, Stud. Geophys. Geod. 62,
       353-363 (2018); DOI: <https://doi.org/10.1007/s11200-017-1020-z>;

AUTHOR
       IntersectTool was written by Charles Karney.

HISTORY