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function [range,A12,A21]=dist(lat,long,argu1,argu2); |
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% DIST Computes distance and bearing between points on the earth |
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% using various reference spheroids. |
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% |
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% [RANGE,AF,AR]=DIST(LAT,LONG) computes the ranges RANGE between |
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% points specified in the LAT and LONG vectors (decimal degrees with |
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% positive indicating north/east). Forward and reverse bearings |
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% (degrees) are returned in AF, AR. |
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% |
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% [RANGE,GLAT,GLONG]=DIST(LAT,LONG,N) computes N-point geodesics |
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% between successive points. Each successive geodesic occupies |
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% it's own row (N>=2) |
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% |
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% [..]=DIST(...,'ellipsoid') uses the specified ellipsoid |
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% to get distances and bearing. Available ellipsoids are: |
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% |
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% 'clarke66' Clarke 1866 |
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% 'iau73' IAU 1973 |
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% 'wgs84' WGS 1984 |
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% 'sphere' Sphere of radius 6371.0 km |
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% |
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% The default is 'wgs84'. |
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% |
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% Ellipsoid formulas are recommended for distance d<2000 km, |
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% but can be used for longer distances. |
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|
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%Notes: RP (WHOI) 3/Dec/91 |
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% Mostly copied from BDC "dist.f" routine (copied from ....?), but |
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% then wildly modified to bring it in line with Matlab vectorization. |
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% |
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% RP (WHOI) 6/Dec/91 |
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% Feeping Creaturism! - added geodesic computations. This turned |
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% out to be pretty hairy since there were a lot of branch problems |
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% with asin, atan when computing geodesics subtending > 90 degrees |
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% that were ignored in the original code! |
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% RP (WHOI) 15/Jan/91 |
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% Fixed some bothersome special cases, like when computing geodesics |
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% and N=2, or LAT=0... |
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|
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%C GIVEN THE LATITUDES AND LONGITUDES (IN DEG.) IT ASSUMES THE IAU SPHERO |
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%C DEFINED IN THE NOTES ON PAGE 523 OF THE EXPLANATORY SUPPLEMENT TO THE |
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%C AMERICAN EPHEMERIS. |
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%C |
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%C THIS PROGRAM COMPUTES THE DISTANCE ALONG THE NORMAL |
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%C SECTION (IN M.) OF A SPECIFIED REFERENCE SPHEROID GIVEN |
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%C THE GEODETIC LATITUDES AND LONGITUDES OF THE END POINTS |
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%C *** IN DECIMAL DEGREES *** |
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%C |
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%C IT USES ROBBIN'S FORMULA, AS GIVEN BY BOMFORD, GEODESY, |
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%C FOURTH EDITION, P. 122. CORRECT TO ONE PART IN 10**8 |
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%C AT 1600 KM. ERRORS OF 20 M AT 5000 KM. |
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%C |
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%C CHECK: SMITHSONIAN METEOROLOGICAL TABLES, PP. 483 AND 484, |
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%C GIVES LENGTHS OF ONE DEGREE OF LATITUDE AND LONGITUDE |
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%C AS A FUNCTION OF LATITUDE. (SO DOES THE EPHEMERIS ABOVE) |
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%C |
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%C PETER WORCESTER, AS TOLD TO BRUCE CORNUELLE...1983 MAY 27 |
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%C |
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|
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spheroid='wgs84'; |
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geodes=0; |
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if (nargin >= 3), |
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if (isstr(argu1)), |
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spheroid=argu1; |
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else |
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geodes=1; |
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Ngeodes=argu1; |
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if (Ngeodes <2), error('Must have at least 2 points in a goedesic!');end; |
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if (nargin==4), spheroid=argu2; end; |
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end; |
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end; |
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|
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if (spheroid(1:3)=='sph'), |
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A = 6371000.0; |
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B = A; |
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E = sqrt(A*A-B*B)/A; |
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EPS= E*E/(1-E*E); |
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elseif (spheroid(1:3)=='cla'), |
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A = 6378206.4E0; |
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B = 6356583.8E0; |
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E= sqrt(A*A-B*B)/A; |
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EPS = E*E/(1.-E*E); |
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elseif(spheroid(1:3)=='iau'), |
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A = 6378160.e0; |
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B = 6356774.516E0; |
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E = sqrt(A*A-B*B)/A; |
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EPS = E*E/(1.-E*E); |
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elseif(spheroid(1:3)=='wgs'), |
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|
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%c on 9/11/88, Peter Worcester gave me the constants for the |
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%c WGS84 spheroid, and he gave A (semi-major axis), F = (A-B)/A |
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%c (flattening) (where B is the semi-minor axis), and E is the |
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%c eccentricity, E = ( (A**2 - B**2)**.5 )/ A |
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%c the numbers from peter are: A=6378137.; 1/F = 298.257223563 |
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%c E = 0.081819191 |
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A = 6378137.; |
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E = 0.081819191; |
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EPS= E*E/(1.-E*E); |
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|
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B = sqrt(A^2-(E*A)^2); % added by D Menemenlis, 4 nov 97 |
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|
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else |
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error('dist: Unknown spheroid specified!'); |
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end; |
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|
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|
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NN=max(size(lat)); |
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if (NN ~= max(size(long))), |
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error('dist: Lat, Long vectors of different sizes!'); |
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end |
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|
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if (NN==size(lat)), rowvec=0; % It is easier if things are column vectors, |
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else rowvec=1; end; % but we have to fix things before returning! |
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|
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lat=lat(:)*pi/180; % convert to radians |
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long=long(:)*pi/180; |
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|
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lat(lat==0)=eps*ones(sum(lat==0),1); % Fixes some nasty 0/0 cases in the |
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% geodesics stuff |
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|
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PHI1=lat(1:NN-1); % endpoints of each segment |
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XLAM1=long(1:NN-1); |
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PHI2=lat(2:NN); |
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XLAM2=long(2:NN); |
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|
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% wiggle lines of constant lat to prevent numerical probs. |
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if (any(PHI1==PHI2)), |
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for ii=1:NN-1, |
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if (PHI1(ii)==PHI2(ii)), PHI2(ii)=PHI2(ii)+ 1e-14; end; |
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end; |
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end; |
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% wiggle lines of constant long to prevent numerical probs. |
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if (any(XLAM1==XLAM2)), |
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for ii=1:NN-1, |
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if (XLAM1(ii)==XLAM2(ii)), XLAM2(ii)=XLAM2(ii)+ 1e-14; end; |
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end; |
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end; |
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|
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|
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|
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%C COMPUTE THE RADIUS OF CURVATURE IN THE PRIME VERTICAL FOR |
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%C EACH POINT |
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|
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xnu=A./sqrt(1.0-(E*sin(lat)).^2); |
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xnu1=xnu(1:NN-1); |
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xnu2=xnu(2:NN); |
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|
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%C*** COMPUTE THE AZIMUTHS. A12 (A21) IS THE AZIMUTH AT POINT 1 (2) |
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%C OF THE NORMAL SECTION CONTAINING THE POINT 2 (1) |
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|
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TPSI2=(1.-E*E)*tan(PHI2) + E*E*xnu1.*sin(PHI1)./(xnu2.*cos(PHI2)); |
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PSI2=atan(TPSI2); |
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|
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%C*** SOME FORM OF ANGLE DIFFERENCE COMPUTED HERE?? |
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|
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DPHI2=PHI2-PSI2; |
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DLAM=XLAM2-XLAM1; |
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CTA12=(cos(PHI1).*TPSI2 - sin(PHI1).*cos(DLAM))./sin(DLAM); |
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A12=atan((1.)./CTA12); |
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CTA21P=(sin(PSI2).*cos(DLAM) - cos(PSI2).*tan(PHI1))./sin(DLAM); |
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A21P=atan((1.)./CTA21P); |
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|
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%C GET THE QUADRANT RIGHT |
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DLAM2=(abs(DLAM)<pi).*DLAM + (DLAM>=pi).*(-2*pi+DLAM) + ... |
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(DLAM<=-pi).*(2*pi+DLAM); |
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A12=A12+(A12<-pi)*2*pi-(A12>=pi)*2*pi; |
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A12=A12+pi*sign(-A12).*( sign(A12) ~= sign(DLAM2) ); |
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A21P=A21P+(A21P<-pi)*2*pi-(A21P>=pi)*2*pi; |
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A21P=A21P+pi*sign(-A21P).*( sign(A21P) ~= sign(-DLAM2) ); |
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%%A12*180/pi |
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%%A21P*180/pi |
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|
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|
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SSIG=sin(DLAM).*cos(PSI2)./sin(A12); |
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% At this point we are OK if the angle < 90...but otherwise |
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% we get the wrong branch of asin! |
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% This fudge will correct every case on a sphere, and *almost* |
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% every case on an ellipsoid (wrong hnadling will be when |
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% angle is almost exactly 90 degrees) |
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dd2=[cos(long).*cos(lat) sin(long).*cos(lat) sin(lat)]; |
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dd2=sum((diff(dd2).*diff(dd2))')'; |
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if ( any(abs(dd2-2) < 2*((B-A)/A))^2 ), |
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disp('dist: Warning...point(s) too close to 90 degrees apart'); |
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end; |
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bigbrnch=dd2>2; |
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|
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SIG=asin(SSIG).*(bigbrnch==0) + (pi-asin(SSIG)).*bigbrnch; |
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|
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SSIGC=-sin(DLAM).*cos(PHI1)./sin(A21P); |
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SIGC=asin(SSIGC); |
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A21 = A21P - DPHI2.*sin(A21P).*tan(SIG/2.0); |
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|
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%C COMPUTE RANGE |
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|
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G2=EPS*(sin(PHI1)).^2; |
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G=sqrt(G2); |
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H2=EPS*(cos(PHI1).*cos(A12)).^2; |
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H=sqrt(H2); |
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TERM1=-SIG.*SIG.*H2.*(1.0-H2)/6.0; |
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TERM2=(SIG.^3).*G.*H.*(1.0-2.0*H2)/8.0; |
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TERM3=(SIG.^4).*(H2.*(4.0-7.0*H2)-3.0*G2.*(1.0-7.0*H2))/120.0; |
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TERM4=-(SIG.^5).*G.*H/48.0; |
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|
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range=xnu1.*SIG.*(1.0+TERM1+TERM2+TERM3+TERM4); |
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|
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|
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if (geodes), |
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|
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%c now calculate the locations along the ray path. (for extra accuracy, could |
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%c do it from start to halfway, then from end for the rest, switching from A12 |
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%c to A21... |
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%c started to use Rudoe's formula, page 117 in Bomford...(1980, fourth edition) |
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%c but then went to Clarke's best formula (pg 118) |
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|
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%RP I am doing this twice because this formula doesn't work when we go |
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%past 90 degrees! |
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Ngd1=round(Ngeodes/2); |
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|
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% First time...away from point 1 |
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if (Ngd1>1), |
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wns=ones(1,Ngd1); |
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CP1CA12 = (cos(PHI1).*cos(A12)).^2; |
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R2PRM = -EPS.*CP1CA12; |
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R3PRM = 3.0*EPS.*(1.0-R2PRM).*cos(PHI1).*sin(PHI1).*cos(A12); |
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C1 = R2PRM.*(1.0+R2PRM)/6.0*wns; |
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C2 = R3PRM.*(1.0+3.0*R2PRM)/24.0*wns; |
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R2PRM=R2PRM*wns; |
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R3PRM=R3PRM*wns; |
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|
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%c now have to loop over positions |
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RLRAT = (range./xnu1)*([0:Ngd1-1]/(Ngeodes-1)); |
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|
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THETA = RLRAT.*(1 - (RLRAT.^2).*(C1 - C2.*RLRAT)); |
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C3 = 1.0 - (R2PRM.*(THETA.^2))/2.0 - (R3PRM.*(THETA.^3))/6.0; |
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DSINPSI =(sin(PHI1)*wns).*cos(THETA) + ... |
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((cos(PHI1).*cos(A12))*wns).*sin(THETA); |
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%try to identify the branch...got to other branch if range> 1/4 circle |
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PSI = asin(DSINPSI); |
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|
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DCOSPSI = cos(PSI); |
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DSINDLA = (sin(A12)*wns).*sin(THETA)./DCOSPSI; |
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DTANPHI=(1.0+EPS)*(1.0 - (E^2)*C3.*(sin(PHI1)*wns)./DSINPSI).*tan(PSI); |
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%C compute output latitude (phi) and long (xla) in radians |
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%c I believe these are absolute, and don't need source coords added |
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PHI = atan(DTANPHI); |
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% fix branch cut stuff - |
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otherbrcnh= sign(DLAM2*wns) ~= sign([sign(DLAM2) diff(DSINDLA')'] ); |
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XLA = XLAM1*wns + asin(DSINDLA).*(otherbrcnh==0) + ... |
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(pi-asin(DSINDLA)).*(otherbrcnh); |
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else |
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PHI=PHI1; |
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XLA=XLAM1; |
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end; |
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|
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% Now we do the same thing, but in the reverse direction from the receiver! |
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if (Ngeodes-Ngd1>1), |
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wns=ones(1,Ngeodes-Ngd1); |
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CP2CA21 = (cos(PHI2).*cos(A21)).^2; |
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R2PRM = -EPS.*CP2CA21; |
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R3PRM = 3.0*EPS.*(1.0-R2PRM).*cos(PHI2).*sin(PHI2).*cos(A21); |
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C1 = R2PRM.*(1.0+R2PRM)/6.0*wns; |
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C2 = R3PRM.*(1.0+3.0*R2PRM)/24.0*wns; |
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R2PRM=R2PRM*wns; |
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R3PRM=R3PRM*wns; |
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|
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%c now have to loop over positions |
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RLRAT = (range./xnu2)*([0:Ngeodes-Ngd1-1]/(Ngeodes-1)); |
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|
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THETA = RLRAT.*(1 - (RLRAT.^2).*(C1 - C2.*RLRAT)); |
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C3 = 1.0 - (R2PRM.*(THETA.^2))/2.0 - (R3PRM.*(THETA.^3))/6.0; |
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DSINPSI =(sin(PHI2)*wns).*cos(THETA) + ... |
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((cos(PHI2).*cos(A21))*wns).*sin(THETA); |
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%try to identify the branch...got to other branch if range> 1/4 circle |
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PSI = asin(DSINPSI); |
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|
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DCOSPSI = cos(PSI); |
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DSINDLA = (sin(A21)*wns).*sin(THETA)./DCOSPSI; |
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DTANPHI=(1.0+EPS)*(1.0 - (E^2)*C3.*(sin(PHI2)*wns)./DSINPSI).*tan(PSI); |
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%C compute output latitude (phi) and long (xla) in radians |
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%c I believe these are absolute, and don't need source coords added |
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PHI = [PHI fliplr(atan(DTANPHI))]; |
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% fix branch cut stuff |
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otherbrcnh= sign(-DLAM2*wns) ~= sign( [sign(-DLAM2) diff(DSINDLA')'] ); |
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XLA = [XLA fliplr(XLAM2*wns + asin(DSINDLA).*(otherbrcnh==0) + ... |
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(pi-asin(DSINDLA)).*(otherbrcnh))]; |
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else |
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PHI = [PHI PHI2]; |
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XLA = [XLA XLAM2]; |
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end; |
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|
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%c convert to degrees |
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A12 = PHI*180/pi; |
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A21 = XLA*180/pi; |
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range=range*([0:Ngeodes-1]/(Ngeodes-1)); |
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|
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|
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else |
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|
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%C*** CONVERT TO DECIMAL DEGREES |
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A12=A12*180/pi; |
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A21=A21*180/pi; |
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if (rowvec), |
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range=range'; |
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A12=A12'; |
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A21=A21'; |
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end; |
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end; |
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|
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|
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|
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