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
124
|
## 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} =} rect2geo (@var{mu})
## @deftypefnx {} {@var{phi} =} rect2geo (@var{mu}, @var{spheroid})
## @deftypefnx {} {@var{phi} =} rect2geo (@var{mu}, @var{spheroid}, @var{angleUnit})
## Returns the geodetic latitude given rectifying latitude @var{mu}
##
## Input
## @itemize
## @item
## @var{mu}: the rectifying latitude(s). Can be a scalar value, a vector or
## an nD array.
##
## @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 character will do). Default is 'degrees'.
## @end itemize
##
## Output
## @itemize
## @item
## @var{phi}: the geodetic latitude(s), same shape as @var{mu}.
## @end itemize
##
## Example
## @example
## rect2geo(44.856)
## ans = 45.000
## @end example
## @seealso{geo2auth, geo2con, geo2iso, geo2rect}
## @end deftypefn
function [phi] = rect2geo (mu, spheroid ="", angleUnit = "degrees")
if (nargin < 1 || nargin > 3)
print_usage();
endif
if (! isnumeric (mu) || ! isreal (mu))
error ("rect2geo: numeric input expected");
endif
if (isnumeric (spheroid))
spheroid = num2str (spheroid);
endif
E = sph_chk (spheroid);
if (! ischar (angleUnit))
error ("rect2geo: character value expected for 'angleUnit'");
elseif (strncmpi (angleUnit, "degrees", min (length (angleUnit), 7)))
## Latitude must be within [-90 ... 90]
if (any (abs (mu) > 90))
error ("rect2geo: azimuth value(s) out of acceptable range [-90, 90]")
endif
mu = deg2rad (mu);
elseif (strncmpi (angleUnit, "radians", min (length (angleUnit), 7)))
## Latitude must be within [-pi/2 ... pi/2]
if (any (abs (mu) > pi / 2))
error("rect2geo: azimuth value(s) out of acceptable range (-pi/2, pi/2)")
endif
else
error ("rect2geo: illegal input for 'angleUnit'");
endif
if (isfield (E, "ThirdFlattening") == 1)
n = E.ThirdFlattening;
else
ecc = E.Eccentricity;
## From Snyder's "Map Projections-A Working Manual" [pg 17].
ecc1 = (1 - ecc ^ 2) ^ ( 1 / 2);
n = (1 - ecc1) / (1 + ecc1);
endif
## From R.E. Deakin "A FRESH LOOK AT THE UTM PROJECTION" [pg 5]
n2 = n ^ 2;
n3 = n ^ 3;
n4 = n ^ 4;
phi = mu + ...
(((3 / 2) * n - (27 / 32) * n3) * sin (2 * mu)) + ...
(((21 / 16) * n2 - (55 / 32) * n4) * sin (4 * mu)) + ...
(((151 / 48) * n3) * sin (6 * mu)) + ...
(((1097 / 512) * n4) * sin (8 * mu));
if (strncmpi (angleUnit, "degrees", length (angleUnit)))
phi = rad2deg (phi);
endif
endfunction
%!test
%! mu = [0:15:90];
%! phi = rect2geo (mu);
%! Z = degrees2dm (phi - mu);
%! check = [0,
%! 4.3406136,
%! 7.5100085,
%! 8.6590367,
%! 7.4879718,
%! 4.3185768,
%! 0];
%! assert (Z(:,2), check, 1e-6)
%!error <numeric> rect2geo ("s")
%!error <numeric> rect2geo (5i)
|
