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Commit 219bf8fc authored by Pierre Cazenave's avatar Pierre Cazenave

Add utilities to convert from UTM to lat/long and vice versa

parent 11c87795
function [x,y,utmzone] = deg2utm(Lat,Lon)
% -------------------------------------------------------------------------
% [x,y,utmzone] = deg2utm(Lat,Lon)
%
% Description: Function to convert lat/lon vectors into UTM coordinates (WGS84).
% Some code has been extracted from UTM.m function by Gabriel Ruiz Martinez.
%
% Inputs:
% Lat: Latitude vector. Degrees. +ddd.ddddd WGS84
% Lon: Longitude vector. Degrees. +ddd.ddddd WGS84
%
% Outputs:
% x, y , utmzone. See example
%
% Example 1:
% Lat=[40.3154333; 46.283900; 37.577833; 28.645650; 38.855550; 25.061783];
% Lon=[-3.4857166; 7.8012333; -119.95525; -17.759533; -94.7990166; 121.640266];
% [x,y,utmzone] = deg2utm(Lat,Lon);
% fprintf('%7.0f ',x)
% 458731 407653 239027 230253 343898 362850
% fprintf('%7.0f ',y)
% 4462881 5126290 4163083 3171843 4302285 2772478
% utmzone =
% 30 T
% 32 T
% 11 S
% 28 R
% 15 S
% 51 R
%
% Example 2: If you have Lat/Lon coordinates in Degrees, Minutes and Seconds
% LatDMS=[40 18 55.56; 46 17 2.04];
% LonDMS=[-3 29 8.58; 7 48 4.44];
% Lat=dms2deg(mat2dms(LatDMS)); %convert into degrees
% Lon=dms2deg(mat2dms(LonDMS)); %convert into degrees
% [x,y,utmzone] = deg2utm(Lat,Lon)
%
% Author:
% Rafael Palacios
% Universidad Pontificia Comillas
% Madrid, Spain
% Version: Apr/06, Jun/06, Aug/06, Aug/06
% Aug/06: fixed a problem (found by Rodolphe Dewarrat) related to southern
% hemisphere coordinates.
% Aug/06: corrected m-Lint warnings
%-------------------------------------------------------------------------
% Argument checking
%
error(nargchk(2, 2, nargin)); %2 arguments required
n1=length(Lat);
n2=length(Lon);
if (n1~=n2)
error('Lat and Lon vectors should have the same length');
end
% Memory pre-allocation
%
x=zeros(n1,1);
y=zeros(n1,1);
utmzone(n1,:)='60 X';
% Main Loop
%
for i=1:n1
la=Lat(i);
lo=Lon(i);
sa = 6378137.000000 ; sb = 6356752.314245;
%e = ( ( ( sa ^ 2 ) - ( sb ^ 2 ) ) ^ 0.5 ) / sa;
e2 = ( ( ( sa ^ 2 ) - ( sb ^ 2 ) ) ^ 0.5 ) / sb;
e2cuadrada = e2 ^ 2;
c = ( sa ^ 2 ) / sb;
%alpha = ( sa - sb ) / sa; %f
%ablandamiento = 1 / alpha; % 1/f
lat = la * ( pi / 180 );
lon = lo * ( pi / 180 );
Huso = fix( ( lo / 6 ) + 31);
S = ( ( Huso * 6 ) - 183 );
deltaS = lon - ( S * ( pi / 180 ) );
if (la<-72), Letra='C';
elseif (la<-64), Letra='D';
elseif (la<-56), Letra='E';
elseif (la<-48), Letra='F';
elseif (la<-40), Letra='G';
elseif (la<-32), Letra='H';
elseif (la<-24), Letra='J';
elseif (la<-16), Letra='K';
elseif (la<-8), Letra='L';
elseif (la<0), Letra='M';
elseif (la<8), Letra='N';
elseif (la<16), Letra='P';
elseif (la<24), Letra='Q';
elseif (la<32), Letra='R';
elseif (la<40), Letra='S';
elseif (la<48), Letra='T';
elseif (la<56), Letra='U';
elseif (la<64), Letra='V';
elseif (la<72), Letra='W';
else Letra='X';
end
a = cos(lat) * sin(deltaS);
epsilon = 0.5 * log( ( 1 + a) / ( 1 - a ) );
nu = atan( tan(lat) / cos(deltaS) ) - lat;
v = ( c / ( ( 1 + ( e2cuadrada * ( cos(lat) ) ^ 2 ) ) ) ^ 0.5 ) * 0.9996;
ta = ( e2cuadrada / 2 ) * epsilon ^ 2 * ( cos(lat) ) ^ 2;
a1 = sin( 2 * lat );
a2 = a1 * ( cos(lat) ) ^ 2;
j2 = lat + ( a1 / 2 );
j4 = ( ( 3 * j2 ) + a2 ) / 4;
j6 = ( ( 5 * j4 ) + ( a2 * ( cos(lat) ) ^ 2) ) / 3;
alfa = ( 3 / 4 ) * e2cuadrada;
beta = ( 5 / 3 ) * alfa ^ 2;
gama = ( 35 / 27 ) * alfa ^ 3;
Bm = 0.9996 * c * ( lat - alfa * j2 + beta * j4 - gama * j6 );
xx = epsilon * v * ( 1 + ( ta / 3 ) ) + 500000;
yy = nu * v * ( 1 + ta ) + Bm;
if (yy<0)
yy=9999999+yy;
end
x(i)=xx;
y(i)=yy;
utmzone(i,:)=sprintf('%02d %c',Huso,Letra);
end
function [Lat,Lon] = utm2deg(xx,yy,utmzone)
% -------------------------------------------------------------------------
% [Lat,Lon] = utm2deg(x,y,utmzone)
%
% Description: Function to convert vectors of UTM coordinates into Lat/Lon vectors (WGS84).
% Some code has been extracted from UTMIP.m function by Gabriel Ruiz Martinez.
%
% Inputs:
% x, y , utmzone.
%
% Outputs:
% Lat: Latitude vector. Degrees. +ddd.ddddd WGS84
% Lon: Longitude vector. Degrees. +ddd.ddddd WGS84
%
% Example 1:
% x=[ 458731; 407653; 239027; 230253; 343898; 362850];
% y=[4462881; 5126290; 4163083; 3171843; 4302285; 2772478];
% utmzone=['30 T'; '32 T'; '11 S'; '28 R'; '15 S'; '51 R'];
% [Lat, Lon]=utm2deg(x,y,utmzone);
% fprintf('%11.6f ',lat)
% 40.315430 46.283902 37.577834 28.645647 38.855552 25.061780
% fprintf('%11.6f ',lon)
% -3.485713 7.801235 -119.955246 -17.759537 -94.799019 121.640266
%
% Example 2: If you need Lat/Lon coordinates in Degrees, Minutes and Seconds
% [Lat, Lon]=utm2deg(x,y,utmzone);
% LatDMS=dms2mat(deg2dms(Lat))
%LatDMS =
% 40.00 18.00 55.55
% 46.00 17.00 2.01
% 37.00 34.00 40.17
% 28.00 38.00 44.33
% 38.00 51.00 19.96
% 25.00 3.00 42.41
% LonDMS=dms2mat(deg2dms(Lon))
%LonDMS =
% -3.00 29.00 8.61
% 7.00 48.00 4.40
% -119.00 57.00 18.93
% -17.00 45.00 34.33
% -94.00 47.00 56.47
% 121.00 38.00 24.96
%
% Author:
% Rafael Palacios
% Universidad Pontificia Comillas
% Madrid, Spain
% Version: Apr/06, Jun/06, Aug/06
% Aug/06: corrected m-Lint warnings
%-------------------------------------------------------------------------
% Argument checking
%
error(nargchk(3, 3, nargin)); %3 arguments required
n1=length(xx);
n2=length(yy);
n3=size(utmzone,1);
if (n1~=n2 || n1~=n3)
error('x,y and utmzone vectors should have the same number or rows');
end
c=size(utmzone,2);
if (c~=4)
error('utmzone should be a vector of strings like "30 T"');
end
% Memory pre-allocation
%
Lat=zeros(n1,1);
Lon=zeros(n1,1);
% Main Loop
%
for i=1:n1
if (utmzone(i,4)>'X' || utmzone(i,4)<'C')
fprintf('utm2deg: Warning utmzone should be a vector of strings like "30 T", not "30 t"\n');
end
if (utmzone(i,4)>'M')
hemis='N'; % Northern hemisphere
else
hemis='S';
end
x=xx(i);
y=yy(i);
zone=str2double(utmzone(i,1:2));
sa = 6378137.000000 ; sb = 6356752.314245;
% e = ( ( ( sa ^ 2 ) - ( sb ^ 2 ) ) ^ 0.5 ) / sa;
e2 = ( ( ( sa ^ 2 ) - ( sb ^ 2 ) ) ^ 0.5 ) / sb;
e2cuadrada = e2 ^ 2;
c = ( sa ^ 2 ) / sb;
% alpha = ( sa - sb ) / sa; %f
% ablandamiento = 1 / alpha; % 1/f
X = x - 500000;
if hemis == 'S' || hemis == 's'
Y = y - 10000000;
else
Y = y;
end
S = ( ( zone * 6 ) - 183 );
lat = Y / ( 6366197.724 * 0.9996 );
v = ( c / ( ( 1 + ( e2cuadrada * ( cos(lat) ) ^ 2 ) ) ) ^ 0.5 ) * 0.9996;
a = X / v;
a1 = sin( 2 * lat );
a2 = a1 * ( cos(lat) ) ^ 2;
j2 = lat + ( a1 / 2 );
j4 = ( ( 3 * j2 ) + a2 ) / 4;
j6 = ( ( 5 * j4 ) + ( a2 * ( cos(lat) ) ^ 2) ) / 3;
alfa = ( 3 / 4 ) * e2cuadrada;
beta = ( 5 / 3 ) * alfa ^ 2;
gama = ( 35 / 27 ) * alfa ^ 3;
Bm = 0.9996 * c * ( lat - alfa * j2 + beta * j4 - gama * j6 );
b = ( Y - Bm ) / v;
Epsi = ( ( e2cuadrada * a^ 2 ) / 2 ) * ( cos(lat) )^ 2;
Eps = a * ( 1 - ( Epsi / 3 ) );
nab = ( b * ( 1 - Epsi ) ) + lat;
senoheps = ( exp(Eps) - exp(-Eps) ) / 2;
Delt = atan(senoheps / (cos(nab) ) );
TaO = atan(cos(Delt) * tan(nab));
longitude = (Delt *(180 / pi ) ) + S;
latitude = ( lat + ( 1 + e2cuadrada* (cos(lat)^ 2) - ( 3 / 2 ) * e2cuadrada * sin(lat) * cos(lat) * ( TaO - lat ) ) * ( TaO - lat ) ) * ...
(180 / pi);
Lat(i)=latitude;
Lon(i)=longitude;
end
\ No newline at end of file
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