source: issm/oecreview/Archive/14312-15392/ISSM-15125-15126.diff

../trunk-jpl/src/m/lambert/lambert2xy.m

@@ -1 @@
-function [x,y] = lambert2xy(lat,lon,projection_center_lat,projection_center_lon)  
+function [x,y] = lambert2xy(lat,lon,sgn,projection_center_lat,projection_center_lon)  
 %LAMBERT2XY - converts lat long from Lambert Azimuthal to Polar Stereographic
 %
 %   Converts from geodetic latitude and longitude that are 
@@ -6 +6 @@
 %   Stereographic (X,Y) coordinates for the polar regions.
 %
 %   Usage:
-%      [x,y] = ll2xy(lat,lon)
-%      [x,y] = ll2xy(lat,lon,projection_center_lat,projection_center_lon)
+%      [x,y] = lambert2xy(lat,lon,sgn)
+%      [x,y] = lambert2xy(lat,lon,sgn,projection_center_lat,projection_center_lon)
 %
 %      - provide lat in [-90,90] and lon in [-180,180].
-%
-%      - default: North hemisphere [projection center lat = 90 lon=0]
-%                 South hemisphere [projection center lat = -90 lon=0]
 
+%      - sgn = +1 N hemisphere [default projection center lat = 90 lon=0]
+%              -1 S hemisphere [default projection center lat = -90 lon=0]
+
 %Get projection_center_lat and projection_center_lon 
-if nargin==4,
+if nargin==5,
         latitude0  = projection_center_lat;
         longitude0 = projection_center_lon;
-elseif nargin==2,
-        if lat>0,
+elseif nargin==3,
+        if sgn==1,
                 latitude0 = 90; longitude0 = 0;
                 disp('Info: creating coordinates in polar stereographic (Projection center lat: 90N lon: 0)');
-        elseif lat<0,
+        elseif sgn==-1,
                 latitude0 = -90; longitude0 = 0;
                 disp('Info: creating coordinates in polar stereographic (Projection center lat: 90S lon: 0)');
+        else
+                error('Sign should be either +1 or -1');
         end
 else
         help lambert2xy
@@ -57 +59 @@
 B =Rq*sqrt(2/(1+sin(b0)*sin(b)+(cos(b0)*cos(b)*cos(lam-lam0))));
 
 % Calculation of x and y
-if(lat==90)
-        rho=a*sqrt(qp-q);
-        x=rho*sin(lam-lam0);
-        y=-rho*cos(lam-lam0);
-elseif(lat==-90)
-        rho=a*sqrt(qp+q);
-        x=rho*sin(lam-lam0);
-        y=rho*cos(lam-lam0);
+if(abs(lat)==90)
+        x=0.0; 
+        y=0.0; 
 else
         x=(B*D)*(cos(b)*sin(lam-lam0));
         y=(B/D)*((cos(b0)*sin(b))-(sin(b0)*cos(b)*cos(lam-lam0)));
 end
+

../trunk-jpl/src/m/lambert/xy2lambert.m

@@ +1 @@
+function [lat,lon] = xy2lambert(x,y,sgn,projection_center_lat,projection_center_lon)  
+%XY2LAMBERT - converts xy to lat lon in Lambert Azimuthal
+%
+%   Converts from Ploar Stereographic (X,Y) coordinates to geodetic 
+%   lat lon that are in Lambert Azimuthal (equal area) projection.
+%
+%   Usage:
+%      [lat,lon] = xy2lambert(x,y,sgn)
+%      [lat,lon] = xy2lambert(x,y,sgn,projection_center_lat,projection_center_lon)
+%
+%      - provide lat in [-90,90] and lon in [-180,180].
+%
+%      - sgn = +1 N hemisphere [default projection center lat = 90 lon=0]
+%              -1 S hemisphere [default projection center lat = -90 lon=0]
+
+%Get projection_center_lat and projection_center_lon 
+if nargin==5,
+        latitude0  = projection_center_lat;
+        longitude0 = projection_center_lon;
+elseif nargin==3,
+        if sgn==1,
+                latitude0 = 90; longitude0 = 0;
+                disp('Info: creating coordinates in Lambert Azimuthal equal-area (Projection center lat: 90N lon: 0)');
+        elseif sgn==-1,
+                latitude0 = -90; longitude0 = 0;
+                disp('Info: creating coordinates in Lambert Azimuthal equal-area (Projection center lat: 90S lon: 0)');
+        else
+                error('Sign should be either +1 or -1');
+        end
+else
+        help xy2lambert
+        error('bad usage');
+end
+
+% Radius of the earth in meters 
+a = 6378137.0;
+% Eccentricity of the Hughes ellipsoid squared
+e = 0.081819191;
+
+% Projection center latitude and longitude in radians 
+phi0 = latitude0 * pi/180; 
+lam0 = longitude0 * pi/180; 
+
+% Some constants based on phi0 and lam0
+% (as in forward calculation)
+qp= (1-e^2)*((1/(1-e^2))-((1/(2*e))*log((1-e)/(1+e))));
+q0=(1-e^2)*((sin(phi0)/(1-e^2*sin(phi0)*sin(phi0)))-((1/(2*e))*log((1-e*sin(phi0))/(1+e*sin(phi0)))));
+Rq=a*sqrt(qp/2);
+b0=asin(q0/qp);
+D =a*(cos(phi0)/sqrt(1-e^2*sin(phi0)*sin(phi0)))/(Rq*cos(b0));
+
+% Some other (x,y) dependent parameters 
+rho=sqrt((x/D)^2+(D*y)^2);
+C=2*asin(rho/(2*Rq));
+b_prime=asin((cos(C)*sin(b0))+((D*y*sin(C)*cos(b0))/rho));
+
+% Calculation of lat and lon 
+dist=sqrt(x^2+y^2);
+if(dist<=0.1)
+        lat=sgn*90.0;
+        lon=0.0;
+else
+        lat_rad=b_prime+((e^2/3+31*e^4/180+517*e^6/5040)*sin(2*b_prime))+((23*e^4/360+251*e^6/3780)*sin(4*b_prime))+((761*e^6/45360)*sin(6*b_prime));
+        lon_rad=lam0+atan(x*sin(C)/(D*rho*cos(b0)*cos(C)-D^2*y*sin(b0)*sin(C)));
+        % in degrees 
+        lat=lat_rad*180/pi;
+        lon=lon_rad*180/pi;
+end
+