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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{phi} =} con2geo (@var{chi})
## @deftypefnx {} {@var{phi} =} con2geo (@var{chi}, @var{spheroid})
## @deftypefnx {} {@var{phi} =} con2geo (@var{chi}, @var{spheroid}, @var{angleUnit})
## Returns the geodetic latitude given latitude conformal @var{chi}
##
## Input
## @itemize
## @item
## @var{chi}: the conformal latitude(s). Scalar, vector or nD arrays are
## accepted.
##
## @item
## (optional) @var{spheroid}: referenceEllipsoid parameter struct: the default
## 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{phi}: the geodetic latitude(s), shape similar to @var{chi}.
## @end itemize
##
## Example
## @example
## con2geo(44.8077)
## ans = 45.000
## @end example
## @seealso{geo2auth, geo2con, geo2iso, geo2rect, rect2geo}
## @end deftypefn
function [phi] = con2geo (chi, spheroid ="", angleUnit = "degrees")
if (nargin < 1 || nargin > 3)
print_usage();
endif
if (! isnumeric (chi) || ! isreal (chi))
error ("con2geo: numeric input expected");
endif
E = sph_chk (spheroid);
if (! ischar (angleUnit))
error ("con2geo: character value expected for 'angleUnit'");
elseif (strncmpi (angleUnit, "degrees", min (length (angleUnit), 7)))
## Latitude must be within [-90 ... 90]
if (any (abs (chi) > 90))
error ("con2geo: azimuth value(s) out of acceptable range [-90, 90]")
endif
chi = deg2rad (chi);
elseif (strncmpi (angleUnit, "radians", min (length (angleUnit), 7)))
## Latitude must be within [-pi/2 ... pi/2]
if (any (abs (chi) > pi / 2))
error("con2geo: azimuth value(s) out of acceptable range (-pi/2, pi/2)")
endif
else
error ("con2geo: illegal input for 'angleUnit'");
endif
ecc = E.Eccentricity;
## From Snyder's "Map Projections-A Working Manual" [pg 15].
e2 = ecc ^ 2;
e4 = ecc ^ 4;
e6 = ecc ^ 6;
e8 = ecc ^ 8;
phi = chi + ...
((e2 / 2 + (5 /24) * e4 + e6 / 12 + (13 / 360) * e8) * sin (2 * chi)) + ...
((7/48 * e4 + (29 / 240) * e6 + (811 / 11520) * e8) * sin (4 * chi)) + ...
(((7 / 120) * e6 + (81 / 1120) * e8) * sin (6 * chi)) + ...
(((4279 / 161280) * e8) * sin (8 * chi));
if (strncmpi (angleUnit, "degrees", length (angleUnit)))
phi = rad2deg (phi);
endif
endfunction
%!test
%! chi = [0:15:90];
%! phi = con2geo (chi);
%! Z = degrees2dm (phi - chi);
%! check = [0
%! 5.7891134
%! 10.01261
%! 11.538913
%! 9.9734791
%! 5.7499818
%! 0];
%! assert (Z(:,2), check, 1e-6)
%!error <numeric> con2geo ("s")
%!error <numeric> con2geo (5i)
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