| 1 | """Implementation of Redfearn's formula to compute UTM projections from latitude and longitude |
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| 2 | |
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| 3 | """ |
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| 4 | |
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| 5 | def degminsec2decimal_degrees(dd,mm,ss): |
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| 6 | assert abs(mm) == mm |
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| 7 | assert abs(ss) == ss |
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| 8 | |
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| 9 | if dd < 0: |
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| 10 | sign = -1 |
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| 11 | else: |
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| 12 | sign = 1 |
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| 13 | |
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| 14 | return sign * (abs(dd) + mm/60. + ss/3600.) |
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| 15 | |
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| 16 | def decimal_degrees2degminsec(dec): |
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| 17 | |
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| 18 | if dec < 0: |
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| 19 | sign = -1 |
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| 20 | else: |
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| 21 | sign = 1 |
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| 22 | |
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| 23 | dec = abs(dec) |
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| 24 | dd = int(dec) |
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| 25 | f = dec-dd |
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| 26 | |
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| 27 | mm = int(f*60) |
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| 28 | ss = (f*60-mm)*60 |
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| 29 | |
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| 30 | return sign*dd, mm, ss |
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| 31 | |
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| 32 | def redfearn(lat, lon, false_easting=None, false_northing=None): |
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| 33 | """Compute UTM projection using Redfearn's formula |
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| 34 | |
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| 35 | lat, lon is latitude and longitude in decimal degrees |
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| 36 | |
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| 37 | If false easting and northing are specified they will override |
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| 38 | the standard |
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| 39 | """ |
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| 40 | |
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| 41 | |
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| 42 | from math import pi, sqrt, sin, cos, tan |
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| 43 | |
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| 44 | |
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| 45 | |
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| 46 | #GDA Specifications |
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| 47 | a = 6378137.0 #Semi major axis |
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| 48 | inverse_flattening = 298.257222101 #1/f |
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| 49 | K0 = 0.9996 #Central scale factor |
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| 50 | zone_width = 6 #Degrees |
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| 51 | |
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| 52 | longitude_of_central_meridian_zone0 = -183 |
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| 53 | longitude_of_western_edge_zone0 = -186 |
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| 54 | |
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| 55 | if false_easting is None: |
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| 56 | false_easting = 500000 |
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| 57 | |
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| 58 | if false_northing is None: |
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| 59 | if lat < 0: |
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| 60 | false_northing = 10000000 #Southern hemisphere |
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| 61 | else: |
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| 62 | false_northing = 0 #Northern hemisphere) |
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| 63 | |
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| 64 | |
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| 65 | #Derived constants |
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| 66 | f = 1.0/inverse_flattening |
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| 67 | b = a*(1-f) #Semi minor axis |
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| 68 | |
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| 69 | e2 = 2*f - f*f# = f*(2-f) = (a^2-b^2/a^2 #Eccentricity |
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| 70 | e = sqrt(e2) |
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| 71 | e2_ = e2/(1-e2) # = (a^2-b^2)/b^2 #Second eccentricity |
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| 72 | e_ = sqrt(e2_) |
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| 73 | e4 = e2*e2 |
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| 74 | e6 = e2*e4 |
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| 75 | |
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| 76 | #Foot point latitude |
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| 77 | n = (a-b)/(a+b) #Same as e2 - why ? |
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| 78 | n2 = n*n |
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| 79 | n3 = n*n2 |
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| 80 | n4 = n2*n2 |
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| 81 | |
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| 82 | G = a*(1-n)*(1-n2)*(1+9*n2/4+225*n4/64)*pi/180 |
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| 83 | |
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| 84 | |
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| 85 | phi = lat*pi/180 #Convert latitude to radians |
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| 86 | |
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| 87 | sinphi = sin(phi) |
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| 88 | sin2phi = sin(2*phi) |
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| 89 | sin4phi = sin(4*phi) |
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| 90 | sin6phi = sin(6*phi) |
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| 91 | |
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| 92 | cosphi = cos(phi) |
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| 93 | cosphi2 = cosphi*cosphi |
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| 94 | cosphi3 = cosphi*cosphi2 |
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| 95 | cosphi4 = cosphi2*cosphi2 |
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| 96 | cosphi5 = cosphi*cosphi4 |
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| 97 | cosphi6 = cosphi2*cosphi4 |
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| 98 | cosphi7 = cosphi*cosphi6 |
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| 99 | cosphi8 = cosphi4*cosphi4 |
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| 100 | |
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| 101 | t = tan(phi) |
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| 102 | t2 = t*t |
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| 103 | t4 = t2*t2 |
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| 104 | t6 = t2*t4 |
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| 105 | |
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| 106 | #Radius of Curvature |
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| 107 | rho = a*(1-e2)/(1-e2*sinphi*sinphi)**1.5 |
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| 108 | nu = a/(1-e2*sinphi*sinphi)**0.5 |
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| 109 | psi = nu/rho |
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| 110 | psi2 = psi*psi |
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| 111 | psi3 = psi*psi2 |
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| 112 | psi4 = psi2*psi2 |
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| 113 | |
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| 114 | |
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| 115 | |
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| 116 | #Meridian distance |
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| 117 | |
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| 118 | A0 = 1 - e2/4 - 3*e4/64 - 5*e6/256 |
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| 119 | A2 = 3.0/8*(e2+e4/4+15*e6/128) |
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| 120 | A4 = 15.0/256*(e4+3*e6/4) |
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| 121 | A6 = 35*e6/3072 |
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| 122 | |
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| 123 | term1 = a*A0*phi |
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| 124 | term2 = -a*A2*sin2phi |
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| 125 | term3 = a*A4*sin4phi |
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| 126 | term4 = -a*A6*sin6phi |
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| 127 | |
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| 128 | m = term1 + term2 + term3 + term4 #OK |
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| 129 | |
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| 130 | #Zone |
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| 131 | zone = int((lon - longitude_of_western_edge_zone0)/zone_width) |
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| 132 | central_meridian = zone*zone_width+longitude_of_central_meridian_zone0 |
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| 133 | |
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| 134 | omega = (lon-central_meridian)*pi/180 #Relative longitude (radians) |
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| 135 | omega2 = omega*omega |
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| 136 | omega3 = omega*omega2 |
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| 137 | omega4 = omega2*omega2 |
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| 138 | omega5 = omega*omega4 |
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| 139 | omega6 = omega3*omega3 |
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| 140 | omega7 = omega*omega6 |
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| 141 | omega8 = omega4*omega4 |
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| 142 | |
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| 143 | |
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| 144 | #Northing |
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| 145 | term1 = nu*sinphi*cosphi*omega2/2 |
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| 146 | term2 = nu*sinphi*cosphi3*(4*psi2+psi-t2)*omega4/24 |
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| 147 | term3 = nu*sinphi*cosphi5*\ |
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| 148 | (8*psi4*(11-24*t2)-28*psi3*(1-6*t2)+\ |
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| 149 | psi2*(1-32*t2)-psi*2*t2+t4-t2)*omega6/720 |
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| 150 | term4 = nu*sinphi*cosphi7*(1385-3111*t2+543*t4-t6)*omega8/40320 |
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| 151 | northing = false_northing + K0*(m + term1 + term2 + term3 + term4) |
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| 152 | |
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| 153 | #Easting |
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| 154 | term1 = nu*omega*cosphi |
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| 155 | term2 = nu*cosphi3*(psi-t2)*omega3/6 |
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| 156 | term3 = nu*cosphi5*(4*psi3*(1-6*t2)+psi2*(1+8*t2)-2*psi*t2+t4)*omega5/120 |
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| 157 | term4 = nu*cosphi7*(61-479*t2+179*t4-t6)*omega7/5040 |
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| 158 | easting = false_easting + K0*(term1 + term2 + term3 + term4) |
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| 159 | |
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| 160 | return zone, easting, northing |
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