1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
## 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{xi} =} geo2auth (@var{phi})
## @deftypefnx {} {@var{xi} =} geo2auth (@var{phi}, @var{spheroid})
## @deftypefnx {} {@var{xi} =} geo2auth (@var{phi}, @var{spheroid}, @var{angleUnit})
## Returns the authalic 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 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{xi}: the authalic latitude
## @end itemize
##
## Example
## @example
## geo2auth(45)
## ans = 44.872
## @end example
## @seealso{geo2con, geo2iso, geo2rect}
## @end deftypefn
function [xi] = geo2auth (phi, spheroid ="", angleUnit = "degrees")
if (nargin < 1 || nargin > 3)
print_usage();
endif
if (! isnumeric (phi) || ! isreal (phi))
error ("geo2auth: 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 ("geo2auth: 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 ("geo2auth: 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 ("geo2auth: azimuth value(s) out of acceptable range (-pi/2, pi/2)");
endif
else
error ("geo2auth: illegal input for 'angleUnit'");
endif
ecc = E.Eccentricity;
em = 1 - ecc .^ 2;
sp = sin (phi);
q_p = 1 + ((em ./ ecc) .* atanh(ecc));
q = (em .* sp) ./ (1 - ecc .^ 2 .* sp .^2) + ...
((em ./ ecc) .* atanh(ecc .* sp));
xi = asin (q ./ q_p);
if (strncmpi (angleUnit, "degrees", length (angleUnit)))
xi = rad2deg (xi);
endif
endfunction
%!test
%! phi = [0:15:90];
%! xi = geo2auth (phi);
%! Z = degrees2dm(xi - phi);
%! check = [0; ...
%! -3.84258303680237; ...
%! -6.66017793242659; ...
%! -7.69782759396364; ...
%! -6.67286580689009; ...
%! -3.85527095139878; ...
%! 0];
%! assert (Z(:,2), check, 1e-6)
%!error <numeric> geo2auth ("s")
%!error <numeric> geo2auth (5i)
|
