## Copyright (C) 2004-2020 Andrew Collier <abcollier@users.sourceforge.net>
## Copyright (C) 2006-2020 Alexander Barth <abarth93@users.sourceforge.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{az} = azimuth(@var{lat1},@var{lon1},@var{lat2},@var{lon2})
## @deftypefnx {Function File} {} @var{az} = azimuth(@var{lat1},@var{lon1},@var{lat2},@var{lon2},@var{units})
## @deftypefnx {Function File} {} @var{az} = azimuth(@var{pt1}, @var{pt2})
## @deftypefnx {Function File} {} @var{az} = azimuth(@var{pt1}, @var{pt2},@var{units})
##
## Calculates the great circle azimuth from a point 1 to a point 2.
## The latitude and longitude of these two points can either be given
## independently or as columns of the matrices @var{pt1} and @var{pt2} in
## the form [latitude longitude].
##
## The units for the input coordinates and output angles can be 
## "degrees" (the default) or "radians".
##
## @example
## >> azimuth([10,10], [10,40])
## ans = 87.336
## >> azimuth([0,10], [0,40])
## ans = 90
## >> azimuth(pi/4,0,pi/4,-pi/2,"radians")
## ans = 5.3279
## @end example
##
## @seealso{elevation,distance}
## @end deftypefn

## Author: Andrew Collier <abcollier@users.sourceforge.net>
## Adapted-by: Alexander Barth <abarth93@users.sourceforge.net>

## Uses "four-parts" formula.

function az = azimuth(varargin)
  ## default units are degrees

  units = "degrees";

  [reg,prop] = parseparams(varargin);

  if length(reg) == 2
    pt1 = reg{1};
    pt2 = reg{2};

    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("Wrong number of type of arguments");
  end
  
  if length(prop) == 1
    units = prop{1};

    if (~strcmp(units,"degrees") && ~strcmp(units,"radians"))
      error("Only degrees and radians are allowed as units");
    end
  elseif length(prop) > 1
    error("Wrong number of type of arguments");
  end

  if (strcmp(units,"degrees"))
    a = deg2rad(a);
    b = deg2rad(b);
    C = deg2rad(C);
  end

  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 (strcmp(units,"degrees"))
     az = rad2deg(az);
  end
endfunction

%!test
%! assert(azimuth([10,10], [10,40]), 87.336, 1e-3)
%! assert(azimuth([0,10], [0,40]),   90, 1e-3)
%! assert(azimuth(pi/4,0,pi/4,-pi/2,"radians"), 5.3279, 1e-4)
