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sominv.c
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sominv.c
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/*******************************************************************************
NAME SPACE OBLIQUE MERCATOR (SOM)
PURPOSE: The first method to Transform input Easting and Northing to
longitude and latitude for the SOM projection. The
Easting and Northing must be in meters. The longitude
and latitude values will be returned in radians.
PROGRAM HISTORY
PROGRAMMER DATE
---------- ----
D. Steinwand July, 1992
T. Mittan Mar, 1993
ALGORITHM REFERENCES
1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
State Government Printing Office, Washington D.C., 1987.
2. "Software Documentation for GCTP General Cartographic Transformation
Package", U.S. Geological Survey National Mapping Division, May 1982.
*******************************************************************************/
#include "cproj.h"
#define LANDSAT_RATIO 0.5201613
static double lon_center,a,b,a2,a4,c1,c3,q,t,u,w,xj,p21,sa,ca,es,s,start;
static double false_easting;
static double false_northing;
static void som_series(double *fb, double *fa2, double *fa4, double *fc1,
double *fc3,double *dlam);
long sominvint(r_major,r_minor,satnum,path,alf_in,lon,false_east,false_north,
time, start1,flag)
double r_major; /* major axis */
double r_minor; /* minor axis */
long satnum; /* Landsat satellite number (1,2,3,4,5) */
long path; /* Landsat path number */
double alf_in;
double lon;
double false_east; /* x offset in meters */
double false_north; /* y offset in meters */
double time;
long start1;
long flag;
{
long i;
double alf,e2c,e2s,one_es;
double dlam,fb,fa2,fa4,fc1,fc3,suma2,suma4,sumc1,sumc3,sumb;
/* Place parameters in static storage for common use
-------------------------------------------------*/
false_easting = false_east;
false_northing = false_north;
a = r_major;
b = r_minor;
es = 1.0 - SQUARE(r_minor/r_major);
if (flag != 0)
{
alf = alf_in;
lon_center = lon;
p21 = time/1440.0;
start = start1;
}
else
{
if (satnum < 4)
{
alf = 99.092 * D2R;
p21=103.2669323/1440.0;
lon_center = (128.87 - (360.0/251.0 * path)) * D2R;
}
else
{
alf = 98.2 * D2R;
p21=98.8841202/1440.0;
lon_center = (129.30 - (360.0/233.0 * path)) * D2R;
/*
lon_center = (129.30557714 - (360.0/233.0 * path)) * D2R;
*/
}
start=0.0;
}
/* Report parameters to the user (to device set up prior to this call)
-------------------------------------------------------------------*/
ptitle("SPACE OBLIQUE MERCATOR");
radius2(a,b);
genrpt_long(path, "Path Number: ");
genrpt_long(satnum, "Satellite Number: ");
genrpt(alf*R2D, "Inclination of Orbit: ");
genrpt(lon_center*R2D, "Longitude of Ascending Orbit: ");
offsetp(false_easting,false_northing);
genrpt(LANDSAT_RATIO, "Landsat Ratio: ");
ca=cos(alf);
if (fabs(ca)<1.e-9) ca=1.e-9;
sa=sin(alf);
e2c=es*ca*ca;
e2s=es*sa*sa;
w=(1.0-e2c)/(1.0-es);
w=w*w-1.0;
one_es=1.0-es;
q = e2s / one_es;
t = (e2s*(2.0-es)) / (one_es*one_es);
u= e2c / one_es;
xj = one_es*one_es*one_es;
dlam=0.0;
som_series(&fb,&fa2,&fa4,&fc1,&fc3,&dlam);
suma2=fa2;
suma4=fa4;
sumb=fb;
sumc1=fc1;
sumc3=fc3;
for(i=9;i<=81;i+=18)
{
dlam=i;
som_series(&fb,&fa2,&fa4,&fc1,&fc3,&dlam);
suma2=suma2+4.0*fa2;
suma4=suma4+4.0*fa4;
sumb=sumb+4.0*fb;
sumc1=sumc1+4.0*fc1;
sumc3=sumc3+4.0*fc3;
}
for(i=18; i<=72; i+=18)
{
dlam=i;
som_series(&fb,&fa2,&fa4,&fc1,&fc3,&dlam);
suma2=suma2+2.0*fa2;
suma4=suma4+2.0*fa4;
sumb=sumb+2.0*fb;
sumc1=sumc1+2.0*fc1;
sumc3=sumc3+2.0*fc3;
}
dlam=90.0;
som_series(&fb,&fa2,&fa4,&fc1,&fc3,&dlam);
suma2=suma2+fa2;
suma4=suma4+fa4;
sumb=sumb+fb;
sumc1=sumc1+fc1;
sumc3=sumc3+fc3;
a2=suma2/30.0;
a4=suma4/60.0;
b=sumb/30.0;
c1=sumc1/15.0;
c3=sumc3/45.0;
return(OK);
}
long sominv(y, x, lon, lat)
double x; /* (I) X projection coordinate */
double y; /* (I) Y projection coordinate */
double *lon; /* (O) Longitude */
double *lat; /* (O) Latitude */
{
double tlon,conv,sav,sd,sdsq,blon,dif,st,defac,actan,tlat,dd,bigk,bigk2,xlamt;
double sl,scl,dlat,dlon,temp;
long inumb;
/* Inverse equations. Begin inverse computation with approximation for tlon.
Solve for transformed long.
---------------------------*/
temp=y; y=x - false_easting; x= temp - false_northing;
tlon= x/(a*b);
conv=1.e-9;
for(inumb=0;inumb<50;inumb++)
{
sav=tlon;
sd=sin(tlon);
sdsq=sd*sd;
s=p21*sa*cos(tlon)*sqrt((1.0+t*sdsq)/((1.0+w*sdsq)*(1.0+q*sdsq)));
blon=(x/a)+(y/a)*s/xj-a2*sin(2.0*tlon)-a4*sin(4.0*tlon)-(s/xj)*(c1*
sin(tlon)+c3*sin(3.0*tlon));
tlon=blon/b;
dif=tlon-sav;
if(fabs(dif)<conv)break;
}
if(inumb>=50)
{
p_error("50 iterations without convergence","som-inverse");
return(214);
}
/* Compute transformed lat.
------------------------*/
st=sin(tlon);
defac=exp(sqrt(1.0+s*s/xj/xj)*(y/a-c1*st-c3*sin(3.0*tlon)));
actan=atan(defac);
tlat=2.0*(actan-(PI/4.0));
/* Compute geodetic longitude
--------------------------*/
dd=st*st;
if(fabs(cos(tlon))<1.e-7) tlon=tlon-1.e-7;
bigk=sin(tlat);
bigk2=bigk*bigk;
xlamt=atan(((1.0-bigk2/(1.0-es))*tan(tlon)*ca-bigk*sa*sqrt((1.0+q*dd)
*(1.0-bigk2)-bigk2*u)/cos(tlon))/(1.0-bigk2*(1.0+u)));
/* Correct inverse quadrant
------------------------*/
if(xlamt>=0.0) sl=1.0;
if(xlamt<0.0) sl= -1.0;
if(cos(tlon)>=0.0) scl=1.0;
if(cos(tlon)<0.0) scl= -1.0;
xlamt=xlamt-((PI/2.0)*(1.0-scl)*sl);
dlon=xlamt-p21*tlon;
/* Compute geodetic latitude
-------------------------*/
if(fabs(sa)<1.e-7)dlat=asin(bigk/sqrt((1.0-es)*(1.0-es)+es*bigk2));
if(fabs(sa)>=1.e-7)dlat=atan((tan(tlon)*cos(xlamt)-ca*sin(xlamt))/((1.0-es)*sa));
*lon = adjust_lon(dlon+lon_center);
*lat = dlat;
return(OK);
}
/* Series to calculate a,b,c coefficients to convert from transform
latitude,longitude to Space Oblique Mercator (SOM) rectangular coordinates
Mathematical analysis by John Snyder 6/82
--------------------------------------------------------------------------*/
static void som_series(fb,fa2,fa4,fc1,fc3,dlam)
double *fb,*fa2,*fa4,*fc1,*fc3,*dlam;
{
double sd,sdsq,h,sq,fc;
*dlam= *dlam*0.0174532925; /* Convert dlam to radians */
sd=sin(*dlam);
sdsq=sd*sd;
s=p21*sa*cos(*dlam)*sqrt((1.0+t*sdsq)/((1.0+w*sdsq)*(1.0+q*sdsq)));
h=sqrt((1.0+q*sdsq)/(1.0+w*sdsq))*(((1.0+w*sdsq)/((1.0+q*sdsq)*(1.0+
q*sdsq)))-p21*ca);
sq=sqrt(xj*xj+s*s);
*fb=(h*xj-s*s)/sq;
*fa2= *fb*cos(2.0* *dlam);
*fa4= *fb*cos(4.0* *dlam);
fc=s*(h+xj)/sq;
*fc1=fc*cos(*dlam);
*fc3=fc*cos(3.0* *dlam);
}