/******************************************************************************* NAME TRANSVERSE MERCATOR PURPOSE: Transforms input Easting and Northing to longitude and latitude for the Transverse Mercator projection. The Easting and Northing must be in meters. The longitude and latitude values will be returned in radians. PROGRAMMER DATE REASON ---------- ---- ------ D. Steinwand, EROS Nov, 1991 T. Mittan Mar, 1993 S. Nelson Feb, 1995 Divided tminv.c into two files, one for UTM (utminv.c) and one for TM (tminv.c). This was a necessary change to run inverse projection conversions for both UTM and TM in the same process. 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. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ #include #include "cproj.h" /* Variables common to all subroutines in this code file -----------------------------------------------------*/ static double r_major; /* major axis */ static double r_minor; /* minor axis */ static double scale_factor; /* scale factor */ static double lon_center; /* Center longitude (projection center) */ static double lat_origin; /* center latitude */ static double e0,e1,e2,e3; /* eccentricity constants */ static double e,es,esp; /* eccentricity constants */ static double ml0; /* small value m */ static double false_northing; /* y offset in meters */ static double false_easting; /* x offset in meters */ static long ind; /* sphere flag value */ /* Initialize the Transverse Mercator (TM) projection -------------------------------------------------------------*/ long tminvint(r_maj,r_min,scale_fact,center_lon,center_lat,false_east, false_north) double r_maj; /* major axis */ double r_min; /* minor axis */ double scale_fact; /* scale factor */ double center_lon; /* center longitude */ double center_lat; /* center latitude */ double false_east; /* x offset in meters */ double false_north; /* y offset in meters */ { double temp; /* temporary variable */ /* Place parameters in static storage for common use -------------------------------------------------*/ r_major = r_maj; r_minor = r_min; scale_factor = scale_fact; lon_center = center_lon; lat_origin = center_lat; false_northing = false_north; false_easting = false_east; temp = r_minor / r_major; es = 1.0 - SQUARE(temp); e = sqrt(es); e0 = e0fn(es); e1 = e1fn(es); e2 = e2fn(es); e3 = e3fn(es); ml0 = r_major * mlfn(e0, e1, e2, e3, lat_origin); esp = es / (1.0 - es); if (es < .00001) ind = 1; /* Report parameters to the user -----------------------------*/ ptitle("TRANSVERSE MERCATOR (TM)"); radius2(r_major, r_minor); genrpt(scale_factor,"Scale Factor at C. Meridian: "); cenlonmer(lon_center); origin(lat_origin); offsetp(false_easting,false_northing); return(OK); } /* Transverse Mercator inverse equations--mapping x,y to lat,long Note: The algorithm for UTM is exactly the same as TM and therefore if a change is implemented, also make the change to UTMINV.c --------------------------------------------------------------*/ long tminv(x, y, lon, lat) double x; /* (I) X projection coordinate */ double y; /* (I) Y projection coordinate */ double *lon; /* (O) Longitude */ double *lat; /* (O) Latitude */ { double con,phi; /* temporary angles */ double delta_phi; /* difference between longitudes */ long i; /* counter variable */ double sin_phi, cos_phi, tan_phi; /* sin cos and tangent values */ double c, cs, t, ts, n, r, d, ds; /* temporary variables */ double f, h, g, temp; /* temporary variables */ long max_iter = 6; /* maximun number of iterations */ /* fortran code for spherical form --------------------------------*/ if (ind != 0) { f = exp(x/(r_major * scale_factor)); g = .5 * (f - 1/f); temp = lat_origin + y/(r_major * scale_factor); h = cos(temp); con = sqrt((1.0 - h * h)/(1.0 + g * g)); *lat = asinz(con); if (temp < 0) *lat = -*lat; if ((g == 0) && (h == 0)) { *lon = lon_center; return(OK); } else { *lon = adjust_lon(atan2(g,h) + lon_center); return(OK); } } /* Inverse equations -----------------*/ x = x - false_easting; y = y - false_northing; con = (ml0 + y / scale_factor) / r_major; phi = con; for (i=0;;i++) { delta_phi = ((con + e1 * sin(2.0*phi) - e2 * sin(4.0*phi) + e3 * sin(6.0*phi)) / e0) - phi; /* delta_phi = ((con + e1 * sin(2.0*phi) - e2 * sin(4.0*phi)) / e0) - phi; */ phi += delta_phi; if (fabs(delta_phi) <= EPSLN) break; if (i >= max_iter) { p_error("Latitude failed to converge","TM-INVERSE"); return(95); } } if (fabs(phi) < HALF_PI) { sincos(phi, &sin_phi, &cos_phi); tan_phi = tan(phi); c = esp * SQUARE(cos_phi); cs = SQUARE(c); t = SQUARE(tan_phi); ts = SQUARE(t); con = 1.0 - es * SQUARE(sin_phi); n = r_major / sqrt(con); r = n * (1.0 - es) / con; d = x / (n * scale_factor); ds = SQUARE(d); *lat = phi - (n * tan_phi * ds / r) * (0.5 - ds / 24.0 * (5.0 + 3.0 * t + 10.0 * c - 4.0 * cs - 9.0 * esp - ds / 30.0 * (61.0 + 90.0 * t + 298.0 * c + 45.0 * ts - 252.0 * esp - 3.0 * cs))); *lon = adjust_lon(lon_center + (d * (1.0 - ds / 6.0 * (1.0 + 2.0 * t + c - ds / 20.0 * (5.0 - 2.0 * c + 28.0 * t - 3.0 * cs + 8.0 * esp + 24.0 * ts))) / cos_phi)); } else { *lat = HALF_PI * sign(y); *lon = lon_center; } return(OK); }