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[x,y,utmzone] = wgs2utm(Lat,Lon,Zone)
Description:
Convert WGS84 coordinates (Latitude, Longitude) into UTM coordinates
(northing, easting) according to (optional) input UTM zone and
hemisphere.
Input:
Lat: WGS84 Latitude scalar, vector or array in decimal degrees.
Lon: WGS84 Longitude scalar, vector or array in decimal degrees.
utmzone (optional): UTM longitudinal zone. Scalar or same size as Lat
and Lon.
utmhemi (optional): UTM hemisphere as a single character, 'N' or 'S',
or array of 'N' or 'S' characters of same size as Lat and Lon.
Output:
x: UTM easting in meters.
y: UTM northing in meters.
utmzone: UTM longitudinal zone.
utmhemi: UTM hemisphere as array of 'N' or 'S' characters.
Author notes:
I downloaded and tried deg2utm.m from Rafael Palacios but found
differences of up to 1m with my reference converters in southern
hemisphere so I wrote my own code based on "Map Projections - A
Working Manual" by J.P. Snyder (1987). Quick quality control performed
only by comparing with LINZ converter
(www.linz.govt.nz/apps/coordinateconversions/) and Chuck Taylor's
(http://home.hiwaay.net/~taylorc/toolbox/geography/geoutm.html) on a
few test points, so use results with caution. Equations not suitable
for a latitude of +/- 90deg.
UPDATE: Following requests, this new version allows forcing UTM zone
in input.
Examples:
% set random latitude and longitude arrays
Lat= 90.*(2.*rand(3)-1)
Lon= 180.*(2.*rand(3)-1)
% let the function find appropriate UTM zone and hemisphere from data
[x1,y1,utmzone1,utmhemi1] = wgs2utm(Lat,Lon)
% forcing unique UTM zone and hemisphere for all data entries
% note: resulting easting and northing are way off the usual values
[x2,y2,utmzone2,utmhemi2] = wgs2utm(Lat,Lon,60,'S')
% forcing different UTM zone and hemisphere for each data entry
% note: resulting easting and northing are way off the usual values
utmzone = floor(59.*rand(3))+1
utmhemi = char(78 + 5.*round(rand(3)))
[x3,y3,utmzone3,utmhemi3] = wgs2utm(Lat,Lon,utmzone,utmhemi)
Author:
Alexandre Schimel
MetOcean Solutions Ltd
New Plymouth, New Zealand
Version 2:
February 2011
-------------------------------------------------------------------------0001 function [x,y,utmzone,utmhemi] = wgs2utm(Lat,Lon,utmzone,utmhemi) 0002 % ------------------------------------------------------------------------- 0003 % [x,y,utmzone] = wgs2utm(Lat,Lon,Zone) 0004 % 0005 % Description: 0006 % Convert WGS84 coordinates (Latitude, Longitude) into UTM coordinates 0007 % (northing, easting) according to (optional) input UTM zone and 0008 % hemisphere. 0009 % 0010 % Input: 0011 % Lat: WGS84 Latitude scalar, vector or array in decimal degrees. 0012 % Lon: WGS84 Longitude scalar, vector or array in decimal degrees. 0013 % utmzone (optional): UTM longitudinal zone. Scalar or same size as Lat 0014 % and Lon. 0015 % utmhemi (optional): UTM hemisphere as a single character, 'N' or 'S', 0016 % or array of 'N' or 'S' characters of same size as Lat and Lon. 0017 % 0018 % Output: 0019 % x: UTM easting in meters. 0020 % y: UTM northing in meters. 0021 % utmzone: UTM longitudinal zone. 0022 % utmhemi: UTM hemisphere as array of 'N' or 'S' characters. 0023 % 0024 % Author notes: 0025 % I downloaded and tried deg2utm.m from Rafael Palacios but found 0026 % differences of up to 1m with my reference converters in southern 0027 % hemisphere so I wrote my own code based on "Map Projections - A 0028 % Working Manual" by J.P. Snyder (1987). Quick quality control performed 0029 % only by comparing with LINZ converter 0030 % (www.linz.govt.nz/apps/coordinateconversions/) and Chuck Taylor's 0031 % (http://home.hiwaay.net/~taylorc/toolbox/geography/geoutm.html) on a 0032 % few test points, so use results with caution. Equations not suitable 0033 % for a latitude of +/- 90deg. 0034 % 0035 % UPDATE: Following requests, this new version allows forcing UTM zone 0036 % in input. 0037 % 0038 % Examples: 0039 % 0040 % % set random latitude and longitude arrays 0041 % Lat= 90.*(2.*rand(3)-1) 0042 % Lon= 180.*(2.*rand(3)-1) 0043 % 0044 % % let the function find appropriate UTM zone and hemisphere from data 0045 % [x1,y1,utmzone1,utmhemi1] = wgs2utm(Lat,Lon) 0046 % 0047 % % forcing unique UTM zone and hemisphere for all data entries 0048 % % note: resulting easting and northing are way off the usual values 0049 % [x2,y2,utmzone2,utmhemi2] = wgs2utm(Lat,Lon,60,'S') 0050 % 0051 % % forcing different UTM zone and hemisphere for each data entry 0052 % % note: resulting easting and northing are way off the usual values 0053 % utmzone = floor(59.*rand(3))+1 0054 % utmhemi = char(78 + 5.*round(rand(3))) 0055 % [x3,y3,utmzone3,utmhemi3] = wgs2utm(Lat,Lon,utmzone,utmhemi) 0056 % 0057 % Author: 0058 % Alexandre Schimel 0059 % MetOcean Solutions Ltd 0060 % New Plymouth, New Zealand 0061 % 0062 % Version 2: 0063 % February 2011 0064 %------------------------------------------------------------------------- 0065 0066 %% Argument checking 0067 if ~sum(double(nargin==[2,4])) 0068 error('Wrong number of input arguments');return 0069 end 0070 n1=size(Lat); 0071 n2=size(Lon); 0072 if (n1~=n2) 0073 error('Lat and Lon should have same size');return 0074 end 0075 if exist('utmzone','var') && exist('utmhemi','var') 0076 n3=size(utmzone); 0077 n4=size(utmhemi); 0078 if (sort(n3)~=sort(n4)) 0079 error('utmzone and utmhemi should have same size');return 0080 end 0081 if max(n3)~=1 && max(n3)~=max(n1) 0082 error('utmzone should have either same size as Lat and Long, or size=1');return 0083 end 0084 end 0085 0086 % expand utmzone and utmhemi if needed 0087 if exist('utmzone','var') && exist('utmhemi','var') 0088 n3=size(utmzone); 0089 n4=size(utmhemi); 0090 if n3==[1 1] 0091 utmzone = utmzone.*ones(size(Lat)); 0092 utmhemi = char(utmhemi.*ones(size(Lat))); 0093 end 0094 end 0095 0096 %% coordinates in radians 0097 lat = Lat.*pi./180; 0098 lon = Lon.*pi./180; 0099 0100 %% WGS84 parameters 0101 a = 6378137; %semi-major axis 0102 b = 6356752.314245; %semi-minor axis 0103 % b = 6356752.314140; %GRS80 value, originally used for WGS84 before refinements 0104 e = sqrt(1-(b./a).^2); % eccentricity 0105 0106 %% UTM parameters 0107 % lat0 = 0; % reference latitude, not used here 0108 if exist('utmzone','var') 0109 Lon0 = 6.*utmzone-183; % reference longitude in degrees 0110 else 0111 Lon0 = floor(Lon./6).*6+3; % reference longitude in degrees 0112 end 0113 lon0 = Lon0.*pi./180; % in radians 0114 k0 = 0.9996; % scale on central meridian 0115 0116 FE = 500000; % false easting 0117 if exist('utmhemi','var') 0118 FN = double(utmhemi=='S').*10000000; 0119 else 0120 FN = (Lat < 0).*10000000; % false northing 0121 end 0122 0123 %% Equations parameters 0124 eps = e.^2./(1-e.^2); % e prime square 0125 % N: radius of curvature of the earth perpendicular to meridian plane 0126 % Also, distance from point to polar axis 0127 N = a./sqrt(1-e.^2.*sin(lat).^2); 0128 T = tan(lat).^2; 0129 C = ((e.^2)./(1-e.^2)).*(cos(lat)).^2; 0130 A = (lon-lon0).*cos(lat); 0131 % M: true distance along the central meridian from the equator to lat 0132 M = a.*( ( 1 - e.^2./4 - 3.*e.^4./64 - 5.*e.^6./256 ) .* lat ... 0133 -( 3.*e.^2./8 + 3.*e.^4./32 + 45.*e.^6./1024 ) .* sin(2.*lat) ... 0134 +( 15.*e.^4./256 + 45.*e.^6./1024 ) .* sin(4.*lat) ... 0135 -(35.*e.^6./3072 ) .* sin(6.*lat) ); 0136 0137 %% easting 0138 x = FE + k0.*N.*( A ... 0139 + (1-T+C) .* A.^3./6 ... 0140 + (5-18.*T+T.^2+72.*C-58.*eps) .* A.^5./120 ); 0141 0142 %% northing 0143 % M(lat0) = 0 so not used in following formula 0144 y = FN + k0.*M + k0.*N.*tan(lat).*( A.^2./2 ... 0145 + (5-T+9.*C+4.*C.^2) .* A.^4./24 ... 0146 + (61-58.*T+T.^2+600.*C-330.*eps) .* A.^6./720 ); 0147 0148 %% UTM zone 0149 if exist('utmzone','var') && exist('utmhemi','var') 0150 utmzone = utmzone; 0151 utmhemi = utmhemi; 0152 else 0153 utmzone = floor(Lon0./6)+31; 0154 utmhemi = char( 83.* (Lat < 0) + 78.* (Lat >= 0) ); 0155 end