1 | """point.py - Represents a generic point on a sphere as a Python object. |
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2 | |
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3 | See documentation of class Point for details. |
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4 | Ole Nielsen, ANU 2002 |
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5 | """ |
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6 | |
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7 | |
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8 | from math import cos, sin, pi |
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9 | |
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10 | def acos(c): |
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11 | """acos - Safe inverse cosine |
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12 | |
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13 | Input argument c is shrunk to admissible interval |
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14 | to avoid case where a small rounding error causes |
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15 | a math domain error. |
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16 | """ |
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17 | from math import acos |
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18 | |
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19 | if c > 1: c=1 |
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20 | if c < -1: c=-1 |
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21 | |
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22 | return acos(c) |
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23 | |
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24 | |
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25 | |
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26 | |
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27 | class Point: |
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28 | """Definition of a generic point on the sphere. |
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29 | |
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30 | Defines a point in terms of latitude and longitude |
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31 | and computes distances to other points on the sphere. |
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32 | |
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33 | Initialise as |
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34 | Point(lat, lon), where lat and lon are in decimal degrees (dd.dddd) |
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35 | |
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36 | |
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37 | Public Methods: |
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38 | distance_to(P) |
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39 | bearing_to(P) |
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40 | dist(P) |
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41 | |
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42 | Author: Ole Nielsen, ANU 2002 |
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43 | """ |
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44 | |
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45 | # class constants |
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46 | R = 6372000 # Approximate radius of Earth (m) |
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47 | degrees2radians = pi/180.0 |
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48 | |
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49 | |
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50 | def __init__(self, latitude, longitude): |
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51 | |
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52 | assert(latitude >= -90 and latitude <= 90.0) |
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53 | assert(longitude >= -180 and longitude <= 180.0) |
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54 | |
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55 | self.latitude = float(latitude) |
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56 | self.longitude = float(longitude) |
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57 | |
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58 | lat = latitude * self.degrees2radians # Converted to radians |
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59 | lon = longitude * self.degrees2radians # Converted to radians |
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60 | self.coslat = cos(lat) |
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61 | self.coslon = cos(lon) |
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62 | self.sinlat = sin(lat) |
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63 | self.sinlon = sin(lon) |
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64 | |
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65 | def BearingTo(self,P): |
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66 | """ Bearing (in degrees) to point P""" |
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67 | AZ = self.AZ(P) |
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68 | return int(round(AZ/self.degrees2radians)) |
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69 | |
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70 | |
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71 | def DistanceTo(self,P): |
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72 | """ Distance to point P""" |
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73 | GCA = self.GCA(P) |
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74 | return self.R*GCA |
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75 | |
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76 | |
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77 | def Dist(self,P): |
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78 | """ Very cheap and rough approximation to distance""" |
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79 | return max(abs(self.latitude-P.latitude),abs(self.longitude-P.longitude)) |
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80 | |
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81 | |
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82 | #-------------------------------------------------------------------------- |
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83 | |
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84 | def __repr__(self): |
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85 | d = 2 |
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86 | lat = round(self.latitude,d) |
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87 | lon = round(self.longitude,d) |
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88 | return ' (' + str(lat)+ ', '+ str(lon)+')' |
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89 | |
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90 | |
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91 | def GCA(self,P): |
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92 | """ Compute the Creat Circle Angle (GCA) between current point and P. |
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93 | """ |
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94 | |
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95 | alpha = P.coslon*self.coslon + P.sinlon*self.sinlon |
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96 | # The original formula is alpha = cos(self.lon - P.lon) |
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97 | # but rewriting lets us make us of precomputed trigonometric values. |
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98 | |
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99 | x = alpha*self.coslat*P.coslat + self.sinlat*P.sinlat |
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100 | return acos(x) |
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101 | |
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102 | |
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103 | def AZ(self,P): |
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104 | """ Compute Azimuth bearing (AZ) from current point to P""" |
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105 | |
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106 | # Compute cosine(AZ), where AZ is the azimuth angle |
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107 | GCA = self.GCA(P) |
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108 | c = P.sinlat - self.sinlat*cos(GCA) |
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109 | c = c/self.coslat/sin(GCA) |
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110 | |
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111 | AZ = acos(c) |
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112 | |
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113 | # Reverse direction if bearing is westward, i.e. sin(self.lon - P.lon) > 0 |
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114 | # Without this correction the bearing due west, say, will be 90 degrees |
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115 | # because the formulas work in the positive direction which is east. |
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116 | # |
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117 | # Precomputed trigonometric values are used to rewrite the formula: |
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118 | |
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119 | if self.sinlon*P.coslon - self.coslon*P.sinlon > 0: AZ = 2*pi - AZ |
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120 | |
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121 | return AZ |
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122 | |
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123 | |
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124 | |
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125 | #----------------------------------------------------------------------- |
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126 | |
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127 | if __name__ == "__main__": |
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128 | pass |
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