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## Copyright (C) 2004-2025 Andrew Collier <abcollier@users.sourceforge.net>
## Copyright (C) 2011-2025 Alexander Barth <abarth93@users.sourceforge.net>
## Copyright (C) 2019-2025 Philip Nienhuis <prnienhuis@users.sf.net>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} [@var{dist}, @var{az}] = distance(@var{pt1}, @var{pt2})
## @deftypefnx {Function File} {} [@var{dist}, @var{az}] = distance(@var{pt1}, @var{pt2},@var{units})
## @deftypefnx {Function File} {} [@var{dist}, @var{az}] = distance(@var{lat1}, @var{lon1}, @var{lat2}, @var{lon2})
## @deftypefnx {Function File} {} [@var{dist}, @var{az}] = distance(@var{lat1}, @var{lon1}, @var{lat2}, @var{lon2}, @var{units})
##
## Calculates the great circle distance @var{dist} between @var{pt1} and
## @var{pt2} and optionally the azimuth @var{az}.
##
## @var{pt1} and @var{pt2} are two-column matrices of the form
## [latitude longitude].
## The coordinates can also be given by the parameters @var{lat1}, @var{lon1},
## @var{lat2} and @var{lon2}.
## Units can be either "degrees" (the default) or "radians", just the first
## character(s) will do.
##
## @example
## >> distance ([37, -76], [37, -9])
## ans = 52.309
## >> distance ([37, -76], [67, -76])
## ans = 30.000
## >> distance (0, 0, 0, pi, "radians")
## ans = 3.1416
## @end example
##
## @seealso{azimuth, elevation, geodeticarc}
## @end deftypefn
## Author: Andrew Collier <abcollier@users.sourceforge.net>
## Adapted-by: Alexander Barth <abarth93@users.sourceforge.net>
## Uses "spherical cosine formula" for distances > 25-40 degrees,
## "haversine formula" for smaller distances.
function [dist, az] = distance (varargin)
## default units are degrees
units = "degrees";
luni = numel (units);
[reg, prop] = parseparams (varargin);
if (length (reg) == 2)
pt1 = reg{1};
pt2 = reg{2};
if (size (pt1, 2) < 2 || size (pt2, 2) < 2)
print_usage ();
endif
a = pt1(:, 1);
b = pt2(:, 1);
C = pt2(:, 2) - pt1(:, 2);
elseif (length (reg) == 4)
a = reg{1};
b = reg{3};
C = reg{4} - reg{2};
else
error ("distance: wrong number or type of arguments");
endif
if (length (prop) == 1)
units = prop{1};
luni = numel (units);
if (! strncmpi (units, "degrees", luni) && ! strncmpi (units, "radians", luni))
error ("distance: only degrees and radians are allowed as units");
endif
elseif (length(prop) > 1)
error ("distance: wrong number or type of arguments");
endif
if (strcmp (units, "degrees"))
a = deg2rad (a);
b = deg2rad (b);
C = deg2rad (C);
endif
id = abs (a - b) < 0.4 & abs (C) < 0.4;
## Plain spherical cosine formula
dist(! id) = acos (sin (b(! id)) .* sin (a(! id)) + ...
cos (b(! id)) .* cos (a(! id)) .* cos (C(! id)));
## Haversine formula for small distances
dist(id) = 2 * asin (sqrt ((sin ((b(id) - a(id)) / 2)) .^ 2 + ...
cos (b(id)) .* cos (a(id)) .* sin (C(id) / 2) .^ 2));
if (strncmpi (units, "degrees", luni))
dist = rad2deg (dist);
endif
if (nargout == 2)
az = atan2 (sin(C), cos (a) .* tan (b) - sin (a) .* cos (C));
## bring the angle in the interval [0..2*pi]
az = mod (az, 2 * pi);
## convert to degrees if desired
if (strncmpi (units, "degrees", luni))
az = rad2deg (az);
endif
endif
endfunction
%!test
%!error <Invalid>, distance (1, 2)
%!error <wrong number>, distance (1, 2, 3)
%!error <wrong number>, distance (1, 2, 3, 4, 5)
%!error <Invalid>, distance ([1, 2], 3)
%!error <Invalid>, distance (1, 2, "k")
%!error <wrong number>, distance (1, 2, 3, 4, 5, 6)
%!test
%! assert (distance ([37, -76], [37, -9]), 52.30942093, 1e-7)
%!test ## Very small distances, haversine formula
%! assert (distance (0, 0, 0, 1e-8), 1e-8, eps);
%!test ## Intermediate distance, check continuity around distance close to
%! ## cross-over point hav-cos at 0.4 radians (~ 22.89 - 22.93 degrees)
%! lat1 = 22.89 : 0.01 : 22.93;
%! lon1 = lat2 = lon2 = zeros (1, 5);
%! assert (distance (deg2rad (lat1), lon1, lat2, lon2, "rad"), deg2rad (lat1), 2*eps);
%!test ## Very large distance, spherical cosine formula. Sph.cos. degenerates
%! ## the least there
%! assert (distance (-90, 0, 89.999999, 0), 179.999999, 1e-6);
%!test
%! [d, az] = distance (0, 0, 0, pi, "radians");
%! assert (d, pi, 1e-7)
%! assert (az, pi / 2, 1e-7)
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