gps_utm.py

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#! /usr/bin/env python
# -*- coding: utf-8 -*-
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# Lat Long - UTM, UTM - Lat Long conversions
from math import pi, sin, cos, tan, sqrt

#LatLong- UTM conversion..h
#definitions for lat/long to UTM and UTM to lat/lng conversions
#include <string.h>

_deg2rad = pi / 180.0
_rad2deg = 180.0 / pi

_EquatorialRadius = 2
_eccentricitySquared = 3

_ellipsoid = [
#  id, Ellipsoid name, Equatorial Radius, square of eccentricity        
# first once is a placeholder only, To allow array indices to match id numbers
        [ -1, "Placeholder", 0, 0],
        [ 1, "Airy", 6377563, 0.00667054],
        [ 2, "Australian National", 6378160, 0.006694542],
        [ 3, "Bessel 1841", 6377397, 0.006674372],
        [ 4, "Bessel 1841 (Nambia] ", 6377484, 0.006674372],
        [ 5, "Clarke 1866", 6378206, 0.006768658],
        [ 6, "Clarke 1880", 6378249, 0.006803511],
        [ 7, "Everest", 6377276, 0.006637847],
        [ 8, "Fischer 1960 (Mercury] ", 6378166, 0.006693422],
        [ 9, "Fischer 1968", 6378150, 0.006693422],
        [ 10, "GRS 1967", 6378160, 0.006694605],
        [ 11, "GRS 1980", 6378137, 0.00669438],
        [ 12, "Helmert 1906", 6378200, 0.006693422],
        [ 13, "Hough", 6378270, 0.00672267],
        [ 14, "International", 6378388, 0.00672267],
        [ 15, "Krassovsky", 6378245, 0.006693422],
        [ 16, "Modified Airy", 6377340, 0.00667054],
        [ 17, "Modified Everest", 6377304, 0.006637847],
        [ 18, "Modified Fischer 1960", 6378155, 0.006693422],
        [ 19, "South American 1969", 6378160, 0.006694542],
        [ 20, "WGS 60", 6378165, 0.006693422],
        [ 21, "WGS 66", 6378145, 0.006694542],
        [ 22, "WGS-72", 6378135, 0.006694318],
        [ 23, "WGS-84", 6378137, 0.00669438]
]

#Reference ellipsoids derived from Peter H. Dana's website- 
#http://www.utexas.edu/depts/grg/gcraft/notes/datum/elist.html
#Department of Geography, University of Texas at Austin
#Internet: pdana@mail.utexas.edu
#3/22/95

#Source
#Defense Mapping Agency. 1987b. DMA Technical Report: Supplement to Department of Defense World Geodetic System
#1984 Technical Report. Part I and II. Washington, DC: Defense Mapping Agency

#def LLtoUTM(int ReferenceEllipsoid, const double Lat, const double Long, 
#                        double &UTMNorthing, double &UTMEasting, char* UTMZone)

def LLtoUTM(ReferenceEllipsoid, Lat, Long, zone = None):
    a = _ellipsoid[ReferenceEllipsoid][_EquatorialRadius]
    eccSquared = _ellipsoid[ReferenceEllipsoid][_eccentricitySquared]
    k0 = 0.9996

#Make sure the longitude is between -180.00 .. 179.9
    LongTemp = (Long+180)-int((Long+180)/360)*360-180 # -180.00 .. 179.9

    LatRad = Lat*_deg2rad
    LongRad = LongTemp*_deg2rad

    if zone is None:
        ZoneNumber = int((LongTemp + 180)/6) + 1
    else:
        ZoneNumber = zone
  
    if Lat >= 56.0 and Lat < 64.0 and LongTemp >= 3.0 and LongTemp < 12.0:
        ZoneNumber = 32

    # Special zones for Svalbard
    if Lat >= 72.0 and Lat < 84.0:
        if  LongTemp >= 0.0  and LongTemp <  9.0:ZoneNumber = 31
        elif LongTemp >= 9.0  and LongTemp < 21.0: ZoneNumber = 33
        elif LongTemp >= 21.0 and LongTemp < 33.0: ZoneNumber = 35
        elif LongTemp >= 33.0 and LongTemp < 42.0: ZoneNumber = 37

    LongOrigin = (ZoneNumber - 1)*6 - 180 + 3 #+3 puts origin in middle of zone
    LongOriginRad = LongOrigin * _deg2rad

    #compute the UTM Zone from the latitude and longitude
    UTMZone = "%d%c" % (ZoneNumber, _UTMLetterDesignator(Lat))

    eccPrimeSquared = (eccSquared)/(1-eccSquared)
    N = a/sqrt(1-eccSquared*sin(LatRad)*sin(LatRad))
    T = tan(LatRad)*tan(LatRad)
    C = eccPrimeSquared*cos(LatRad)*cos(LatRad)
    A = cos(LatRad)*(LongRad-LongOriginRad)

    M = a*((1
            - eccSquared/4
            - 3*eccSquared*eccSquared/64
            - 5*eccSquared*eccSquared*eccSquared/256)*LatRad 
           - (3*eccSquared/8
              + 3*eccSquared*eccSquared/32
              + 45*eccSquared*eccSquared*eccSquared/1024)*sin(2*LatRad)
           + (15*eccSquared*eccSquared/256 + 45*eccSquared*eccSquared*eccSquared/1024)*sin(4*LatRad) 
           - (35*eccSquared*eccSquared*eccSquared/3072)*sin(6*LatRad))
    
    UTMEasting = (k0*N*(A+(1-T+C)*A*A*A/6
                        + (5-18*T+T*T+72*C-58*eccPrimeSquared)*A*A*A*A*A/120)
                  + 500000.0)

    UTMNorthing = (k0*(M+N*tan(LatRad)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24
                                        + (61
                                           -58*T
                                           +T*T
                                           +600*C
                                           -330*eccPrimeSquared)*A*A*A*A*A*A/720)))

    if Lat < 0:
        UTMNorthing = UTMNorthing + 10000000.0; #10000000 meter offset for southern hemisphere
    return (UTMZone, UTMEasting, UTMNorthing)


def _UTMLetterDesignator(Lat):
    if 84 >= Lat >= 72: return 'X'
    elif 72 > Lat >= 64: return 'W'
    elif 64 > Lat >= 56: return 'V'
    elif 56 > Lat >= 48: return 'U'
    elif 48 > Lat >= 40: return 'T'
    elif 40 > Lat >= 32: return 'S'
    elif 32 > Lat >= 24: return 'R'
    elif 24 > Lat >= 16: return 'Q'
    elif 16 > Lat >= 8: return 'P'
    elif  8 > Lat >= 0: return 'N'
    elif  0 > Lat >= -8: return 'M'
    elif -8> Lat >= -16: return 'L'
    elif -16 > Lat >= -24: return 'K'
    elif -24 > Lat >= -32: return 'J'
    elif -32 > Lat >= -40: return 'H'
    elif -40 > Lat >= -48: return 'G'
    elif -48 > Lat >= -56: return 'F'
    elif -56 > Lat >= -64: return 'E'
    elif -64 > Lat >= -72: return 'D'
    elif -72 > Lat >= -80: return 'C'
    else: return 'Z'    # if the Latitude is outside the UTM limits

#void UTMtoLL(int ReferenceEllipsoid, const double UTMNorthing, const double UTMEasting, const char* UTMZone,
#                         double& Lat,  double& Long )

def UTMtoLL(ReferenceEllipsoid, northing, easting, zone):
    k0 = 0.9996
    a = _ellipsoid[ReferenceEllipsoid][_EquatorialRadius]
    eccSquared = _ellipsoid[ReferenceEllipsoid][_eccentricitySquared]
    e1 = (1-sqrt(1-eccSquared))/(1+sqrt(1-eccSquared))
    #NorthernHemisphere; //1 for northern hemispher, 0 for southern

    x = easting - 500000.0 #remove 500,000 meter offset for longitude
    y = northing

    ZoneLetter = zone[-1]
    ZoneNumber = int(zone[:-1])
    if ZoneLetter >= 'N':
        NorthernHemisphere = 1  # point is in northern hemisphere
    else:
        NorthernHemisphere = 0  # point is in southern hemisphere
        y -= 10000000.0         # remove 10,000,000 meter offset used for southern hemisphere

    LongOrigin = (ZoneNumber - 1)*6 - 180 + 3  # +3 puts origin in middle of zone

    eccPrimeSquared = (eccSquared)/(1-eccSquared)

    M = y / k0
    mu = M/(a*(1-eccSquared/4-3*eccSquared*eccSquared/64-5*eccSquared*eccSquared*eccSquared/256))

    phi1Rad = (mu + (3*e1/2-27*e1*e1*e1/32)*sin(2*mu) 
               + (21*e1*e1/16-55*e1*e1*e1*e1/32)*sin(4*mu)
               +(151*e1*e1*e1/96)*sin(6*mu))
    phi1 = phi1Rad*_rad2deg;

    N1 = a/sqrt(1-eccSquared*sin(phi1Rad)*sin(phi1Rad))
    T1 = tan(phi1Rad)*tan(phi1Rad)
    C1 = eccPrimeSquared*cos(phi1Rad)*cos(phi1Rad)
    R1 = a*(1-eccSquared)/pow(1-eccSquared*sin(phi1Rad)*sin(phi1Rad), 1.5)
    D = x/(N1*k0)

    Lat = phi1Rad - (N1*tan(phi1Rad)/R1)*(D*D/2-(5+3*T1+10*C1-4*C1*C1-9*eccPrimeSquared)*D*D*D*D/24
                                          +(61+90*T1+298*C1+45*T1*T1-252*eccPrimeSquared-3*C1*C1)*D*D*D*D*D*D/720)
    Lat = Lat * _rad2deg

    Long = (D-(1+2*T1+C1)*D*D*D/6+(5-2*C1+28*T1-3*C1*C1+8*eccPrimeSquared+24*T1*T1)
            *D*D*D*D*D/120)/cos(phi1Rad)
    Long = LongOrigin + Long * _rad2deg
    return (Lat, Long)

if __name__ == '__main__':
    (z, e, n) = LLtoUTM(23, 45.00, -75.00)
    print z, e, n
    print UTMtoLL(23, e, n, z)