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## Copyright (C) 2008-2022 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{lato},@var{lono}] = } reckon(@var{lat},@var{lon},@var{range},@var{azimuth})
## @deftypefnx {Function File} {[@var{lato},@var{lono}] = } reckon(@var{lat},@var{lon},@var{range},@var{azimuth},@var{units})
## Compute the coordinates of the end-point of a displacement on a
## sphere. @var{lat},@var{lon} are the coordinates of the starting point, @var{range}
## is the covered distance of the displacements along a great circle and
## @var{azimuth} is the direction of the displacement relative to the North.
## The units of all input and output parameters can be either 'degrees' (default)
## or 'radians'.
##
## This function can also be used to define a spherical coordinate system
## with rotated poles.
##
## @seealso{geodeticfwd, vincentyDirect}
## @end deftypefn
## Author: Alexander Barth <barth.alexander@gmail.com>
function [lato,lono] = reckon(varargin);
units = "degrees";
[reg,prop] = parseparams(varargin);
## Input checking
if length(reg) != 4
print_usage ();
endif
sz = [1 1];
for i=1:4
if !isscalar(reg{i})
sz = size(reg{i});
break;
endif
endfor
for i=1:4
if isscalar(reg{i})
reg{i} = repmat(reg{i},sz);
elseif !isequal(size(reg{i}),sz)
print_usage();
endif
endfor
if length(prop) == 1
units = prop{1};
elseif length(prop) > 1
error("reckon: wrong number of type of arguments");
end
lat = reg{1};
lon = reg{2};
range = reg{3};
azimuth = reg{4};
if strcmp(units,"degrees")
d = pi/180;
elseif strcmp(units,"radians")
d = 1;
else
error(["reckon: unknown units: " units]);
endif
## convert to radians
lat = lat*d;
lon = lon*d;
range = range*d;
azimuth = azimuth*d;
lato = pi/2 - acos(sin(lat).*cos(range) + cos(lat).*sin(range).*cos(azimuth));
cos_gamma = (cos(range) - sin(lato).*sin(lat))./(cos(lato).*cos(lat));
sin_gamma = sin(azimuth).*sin(range)./cos(lato);
gamma = atan2(sin_gamma,cos_gamma);
lono = lon + gamma;
## bring the lono in the interval [-pi pi[
lono = mod(lono+pi,2*pi)-pi;
## convert to degrees
lono = lono/d;
lato = lato/d;
endfunction
%!test
%! [lato,lono] = reckon(30,-80,20,40);
%! assert(lato,44.16661401448592,1e-10)
%! assert(lono,-62.15251496909770,1e-10)
%!test
%! [lato,lono] = reckon(-30,80,[5 10],[40 45]);
%! assert(lato,[-26.12155703039504 -22.70996703614572],1e-10)
%! assert(lono,[83.57732793979254 87.64920016442251],1e-10)
%!test
%! [lato,lono] = reckon([-30 31],[80 81],[5 10],[40 45]);
%! assert(lato,[-26.12155703039504 37.76782079033356],1e-10)
%! assert(lono,[83.57732793979254 89.93590456974810],1e-10)
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