1 | """Implementation of Redfearn's formula to compute UTM projections from latitude and longitude |
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2 | |
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3 | Based in part on spreadsheet |
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4 | www.icsm.gov.au/gda/gdatm/redfearn.xls |
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5 | downloaded from INTERGOVERNMENTAL COMMITTEE ON SURVEYING & MAPPING (ICSM) |
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6 | http://www.icsm.gov.au/icsm/ |
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7 | |
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8 | """ |
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9 | from anuga.coordinate_transforms.geo_reference import Geo_reference, DEFAULT_ZONE |
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10 | from Numeric import array |
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11 | |
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12 | def degminsec2decimal_degrees(dd,mm,ss): |
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13 | assert abs(mm) == mm |
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14 | assert abs(ss) == ss |
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15 | |
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16 | if dd < 0: |
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17 | sign = -1 |
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18 | else: |
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19 | sign = 1 |
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20 | |
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21 | return sign * (abs(dd) + mm/60. + ss/3600.) |
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22 | |
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23 | def decimal_degrees2degminsec(dec): |
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24 | |
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25 | if dec < 0: |
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26 | sign = -1 |
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27 | else: |
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28 | sign = 1 |
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29 | |
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30 | dec = abs(dec) |
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31 | dd = int(dec) |
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32 | f = dec-dd |
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33 | |
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34 | mm = int(f*60) |
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35 | ss = (f*60-mm)*60 |
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36 | |
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37 | return sign*dd, mm, ss |
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38 | |
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39 | def redfearn(lat, lon, false_easting=None, false_northing=None): |
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40 | """Compute UTM projection using Redfearn's formula |
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41 | |
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42 | lat, lon is latitude and longitude in decimal degrees |
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43 | |
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44 | If false easting and northing are specified they will override |
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45 | the standard |
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46 | """ |
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47 | |
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48 | |
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49 | from math import pi, sqrt, sin, cos, tan |
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50 | |
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51 | |
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52 | |
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53 | #GDA Specifications |
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54 | a = 6378137.0 #Semi major axis |
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55 | inverse_flattening = 298.257222101 #1/f |
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56 | K0 = 0.9996 #Central scale factor |
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57 | zone_width = 6 #Degrees |
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58 | |
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59 | longitude_of_central_meridian_zone0 = -183 |
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60 | longitude_of_western_edge_zone0 = -186 |
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61 | |
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62 | if false_easting is None: |
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63 | false_easting = 500000 |
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64 | |
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65 | if false_northing is None: |
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66 | if lat < 0: |
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67 | false_northing = 10000000 #Southern hemisphere |
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68 | else: |
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69 | false_northing = 0 #Northern hemisphere) |
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70 | |
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71 | |
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72 | #Derived constants |
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73 | f = 1.0/inverse_flattening |
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74 | b = a*(1-f) #Semi minor axis |
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75 | |
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76 | e2 = 2*f - f*f# = f*(2-f) = (a^2-b^2/a^2 #Eccentricity |
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77 | e = sqrt(e2) |
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78 | e2_ = e2/(1-e2) # = (a^2-b^2)/b^2 #Second eccentricity |
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79 | e_ = sqrt(e2_) |
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80 | e4 = e2*e2 |
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81 | e6 = e2*e4 |
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82 | |
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83 | #Foot point latitude |
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84 | n = (a-b)/(a+b) #Same as e2 - why ? |
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85 | n2 = n*n |
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86 | n3 = n*n2 |
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87 | n4 = n2*n2 |
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88 | |
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89 | G = a*(1-n)*(1-n2)*(1+9*n2/4+225*n4/64)*pi/180 |
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90 | |
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91 | |
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92 | phi = lat*pi/180 #Convert latitude to radians |
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93 | |
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94 | sinphi = sin(phi) |
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95 | sin2phi = sin(2*phi) |
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96 | sin4phi = sin(4*phi) |
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97 | sin6phi = sin(6*phi) |
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98 | |
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99 | cosphi = cos(phi) |
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100 | cosphi2 = cosphi*cosphi |
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101 | cosphi3 = cosphi*cosphi2 |
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102 | cosphi4 = cosphi2*cosphi2 |
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103 | cosphi5 = cosphi*cosphi4 |
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104 | cosphi6 = cosphi2*cosphi4 |
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105 | cosphi7 = cosphi*cosphi6 |
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106 | cosphi8 = cosphi4*cosphi4 |
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107 | |
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108 | t = tan(phi) |
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109 | t2 = t*t |
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110 | t4 = t2*t2 |
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111 | t6 = t2*t4 |
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112 | |
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113 | #Radius of Curvature |
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114 | rho = a*(1-e2)/(1-e2*sinphi*sinphi)**1.5 |
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115 | nu = a/(1-e2*sinphi*sinphi)**0.5 |
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116 | psi = nu/rho |
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117 | psi2 = psi*psi |
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118 | psi3 = psi*psi2 |
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119 | psi4 = psi2*psi2 |
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120 | |
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121 | |
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122 | |
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123 | #Meridian distance |
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124 | |
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125 | A0 = 1 - e2/4 - 3*e4/64 - 5*e6/256 |
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126 | A2 = 3.0/8*(e2+e4/4+15*e6/128) |
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127 | A4 = 15.0/256*(e4+3*e6/4) |
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128 | A6 = 35*e6/3072 |
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129 | |
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130 | term1 = a*A0*phi |
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131 | term2 = -a*A2*sin2phi |
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132 | term3 = a*A4*sin4phi |
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133 | term4 = -a*A6*sin6phi |
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134 | |
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135 | m = term1 + term2 + term3 + term4 #OK |
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136 | |
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137 | #Zone |
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138 | zone = int((lon - longitude_of_western_edge_zone0)/zone_width) |
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139 | central_meridian = zone*zone_width+longitude_of_central_meridian_zone0 |
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140 | |
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141 | omega = (lon-central_meridian)*pi/180 #Relative longitude (radians) |
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142 | omega2 = omega*omega |
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143 | omega3 = omega*omega2 |
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144 | omega4 = omega2*omega2 |
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145 | omega5 = omega*omega4 |
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146 | omega6 = omega3*omega3 |
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147 | omega7 = omega*omega6 |
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148 | omega8 = omega4*omega4 |
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149 | |
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150 | |
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151 | #Northing |
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152 | term1 = nu*sinphi*cosphi*omega2/2 |
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153 | term2 = nu*sinphi*cosphi3*(4*psi2+psi-t2)*omega4/24 |
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154 | term3 = nu*sinphi*cosphi5*\ |
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155 | (8*psi4*(11-24*t2)-28*psi3*(1-6*t2)+\ |
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156 | psi2*(1-32*t2)-psi*2*t2+t4-t2)*omega6/720 |
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157 | term4 = nu*sinphi*cosphi7*(1385-3111*t2+543*t4-t6)*omega8/40320 |
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158 | northing = false_northing + K0*(m + term1 + term2 + term3 + term4) |
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159 | |
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160 | #Easting |
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161 | term1 = nu*omega*cosphi |
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162 | term2 = nu*cosphi3*(psi-t2)*omega3/6 |
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163 | term3 = nu*cosphi5*(4*psi3*(1-6*t2)+psi2*(1+8*t2)-2*psi*t2+t4)*omega5/120 |
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164 | term4 = nu*cosphi7*(61-479*t2+179*t4-t6)*omega7/5040 |
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165 | easting = false_easting + K0*(term1 + term2 + term3 + term4) |
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166 | |
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167 | return zone, easting, northing |
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168 | |
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169 | |
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170 | |
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171 | def convert_from_latlon_to_utm(points=None, |
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172 | latitudes=None, |
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173 | longitudes=None, |
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174 | false_easting=None, |
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175 | false_northing=None): |
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176 | """Convert latitude and longitude data to UTM as a list of coordinates. |
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177 | |
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178 | |
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179 | Input |
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180 | |
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181 | points: list of points given in decimal degrees (latitude, longitude) or |
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182 | latitudes: list of latitudes and |
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183 | longitudes: list of longitudes |
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184 | false_easting (optional) |
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185 | false_northing (optional) |
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186 | |
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187 | Output |
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188 | |
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189 | points: List of converted points |
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190 | zone: Common UTM zone for converted points |
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191 | |
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192 | |
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193 | Notes |
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194 | |
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195 | Assume the false_easting and false_northing are the same for each list. |
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196 | If points end up in different UTM zones, an ANUGAerror is thrown. |
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197 | """ |
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198 | |
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199 | old_geo = Geo_reference() |
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200 | utm_points = [] |
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201 | if points == None: |
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202 | assert len(latitudes) == len(longitudes) |
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203 | points = map(None, latitudes, longitudes) |
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204 | |
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205 | for point in points: |
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206 | |
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207 | zone, easting, northing = redfearn(float(point[0]), |
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208 | float(point[1]), |
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209 | false_easting=false_easting, |
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210 | false_northing=false_northing) |
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211 | new_geo = Geo_reference(zone) |
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212 | old_geo.reconcile_zones(new_geo) |
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213 | utm_points.append([easting, northing]) |
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214 | |
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215 | return utm_points, old_geo.get_zone() |
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