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## Copyright (C) 2022 The Octave Project Developers
##
## 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 {} {@var{chi} =} geo2con (@var{phi})
## @deftypefnx {} {@var{chi} =} geo2con (@var{phi}, @var{spheroid})
## @deftypefnx {} {@var{chi} =} geo2con (@var{phi}, @var{spheroid}, @var{angleUnit})
## Returns the conformal latitude given geodetic latitude @var{phi}
##
## Input
## @itemize
## @item
## @var{phi}: the geodetic latitude
## @end itemize
##
## @itemize
## @item
## (optional) @var{spheroid}: referenceEllipsoid name, EPSG number, or
## parameter struct: the deualt is wgs84.
##
## @item
## (optional) @var{angleUnit}: string for angular units ('degrees' or 'radians',
## case-insensitive, just the first charachter will do). Default is 'degrees'.
## @end itemize
##
## Output
## @itemize
## @item
## @var{chi}: the conformal latitude
## @end itemize
##
## Example
## @example
## geo2con(45)
## ans = 44.808
## @end example
## @seealso{geo2auth, geo2iso, geo2rect}
## @end deftypefn
function [chi] = geo2con (phi, spheroid ="", angleUnit = "degrees")
if (nargin < 1 || nargin > 3)
print_usage();
endif
if (! isnumeric (phi) || ! isreal (phi))
error ("geo2con: numeric input expected");
endif
if (isempty (spheroid))
E = referenceEllipsoid ("wgs84");
else
if (isnumeric (spheroid))
spheroid = num2str (spheroid);
endif
E = sph_chk (spheroid);
endif
if (! ischar (angleUnit))
error ("geo2con: character value expected for 'angleUnit'");
elseif (strncmpi (angleUnit, "degrees", min (length (angleUnit), 7)))
## Latitude must be within [-90 ... 90]
if (any (abs (phi) > 90))
error ("geo2con: azimuth value(s) out of acceptable range [-90, 90]")
endif
phi = deg2rad (phi);
elseif (strncmpi (angleUnit, "radians", min (length (angleUnit), 7)))
## Latitude must be within [-pi/2 ... pi/2]
if (any (abs (phi) > pi / 2))
error("geo2con: azimuth value(s) out of acceptable range (-pi/2, pi/2)")
endif
else
error ("geo2con: illegal input for 'angleUnit'");
endif
ecc = E.Eccentricity;
chi = atan (sinh (asinh (tan (phi)) - ecc .* atanh (ecc .* sin (phi))));
if (strncmpi (angleUnit, "degrees", length (angleUnit)))
chi = rad2deg (chi);
endif
endfunction
%!test
%! phi = [0:15:90];
%! chi = geo2con (phi);
%! Z = degrees2dm(chi - phi);
%! check = [0; ...
%! -5.755543956550260; ...
%! -9.979077451140980; ...
%! -11.53895663467140; ...
%! -10.00703049899710; ...
%! -5.783497189944170; ...
%! 0];
%! assert (Z(:,2), check, 1e-6)
%!error <numeric> geo2con ("s")
%!error <numeric> geo2con (5i)
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