1 | /*
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2 | * Import from fr.geo.convert package, a geographic coordinates converter.
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3 | * (https://www.i3s.unice.fr/~johan/gps/)
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4 | * License: GPL. For details, see LICENSE file.
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5 | * Copyright (C) 2002 Johan Montagnat (johan@creatis.insa-lyon.fr)
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6 | */
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7 |
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8 | package org.openstreetmap.josm.data.projection;
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9 |
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10 | import org.openstreetmap.josm.data.coor.LatLon;
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11 |
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12 | /**
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13 | * the reference ellipsoids
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14 | */
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15 | public final class Ellipsoid {
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16 | /**
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17 | * Clarke 1880 IGN (French national geographic institute)
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18 | */
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19 | public static final Ellipsoid clarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0);
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20 | /**
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21 | * Hayford's ellipsoid 1909 (ED50 system)
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22 | * Proj.4 code: intl
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23 | */
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24 | public static final Ellipsoid hayford = Ellipsoid.create_a_rf(6378388.0, 297.0);
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25 | /**
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26 | * GRS67 ellipsoid
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27 | */
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28 | public static final Ellipsoid GRS67 = Ellipsoid.create_a_rf(6378160.0, 298.247167472);
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29 | /**
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30 | * GRS80 ellipsoid
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31 | */
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32 | public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101);
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33 |
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34 | /**
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35 | * WGS84 ellipsoid
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36 | */
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37 | public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563);
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38 |
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39 | /**
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40 | * Bessel 1841 ellipsoid
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41 | */
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42 | public static final Ellipsoid Bessel1841 = Ellipsoid.create_a_rf(6377397.155, 299.1528128);
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43 |
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44 | /**
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45 | * half long axis
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46 | */
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47 | public final double a;
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48 | /**
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49 | * half short axis
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50 | */
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51 | public final double b;
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52 | /**
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53 | * first eccentricity
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54 | */
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55 | public final double e;
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56 | /**
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57 | * first eccentricity squared
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58 | */
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59 | public final double e2;
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60 |
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61 | /**
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62 | * square of the second eccentricity
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63 | */
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64 | public final double eb2;
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65 |
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66 | /**
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67 | * private constructur - use one of the create_* methods
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68 | *
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69 | * @param a semimajor radius of the ellipsoid axis
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70 | * @param b semiminor radius of the ellipsoid axis
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71 | * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a)))
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72 | * @param e2 first eccentricity squared
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73 | * @param eb2 square of the second eccentricity
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74 | */
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75 | private Ellipsoid(double a, double b, double e, double e2, double eb2) {
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76 | this.a = a;
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77 | this.b = b;
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78 | this.e = e;
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79 | this.e2 = e2;
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80 | this.eb2 = eb2;
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81 | }
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82 |
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83 | /**
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84 | * create a new ellipsoid
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85 | *
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86 | * @param a semimajor radius of the ellipsoid axis (in meters)
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87 | * @param b semiminor radius of the ellipsoid axis (in meters)
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88 | */
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89 | public static Ellipsoid create_a_b(double a, double b) {
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90 | double e2 = (a*a - b*b) / (a*a);
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91 | double e = Math.sqrt(e2);
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92 | double eb2 = e2 / (1.0 - e2);
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93 | return new Ellipsoid(a, b, e, e2, eb2);
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94 | }
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95 |
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96 | /**
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97 | * create a new ellipsoid
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98 | *
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99 | * @param a semimajor radius of the ellipsoid axis (in meters)
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100 | * @param es first eccentricity squared
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101 | */
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102 | public static Ellipsoid create_a_es(double a, double es) {
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103 | double b = a * Math.sqrt(1.0 - es);
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104 | double e = Math.sqrt(es);
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105 | double eb2 = es / (1.0 - es);
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106 | return new Ellipsoid(a, b, e, es, eb2);
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107 | }
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108 |
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109 | /**
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110 | * create a new ellipsoid
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111 | *
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112 | * @param a semimajor radius of the ellipsoid axis (in meters)
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113 | * @param f flattening ( = (a - b) / a)
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114 | */
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115 | public static Ellipsoid create_a_f(double a, double f) {
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116 | double b = a * (1.0 - f);
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117 | double e2 = f * (2 - f);
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118 | double e = Math.sqrt(e2);
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119 | double eb2 = e2 / (1.0 - e2);
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120 | return new Ellipsoid(a, b, e, e2, eb2);
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121 | }
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122 |
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123 | /**
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124 | * create a new ellipsoid
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125 | *
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126 | * @param a semimajor radius of the ellipsoid axis (in meters)
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127 | * @param rf inverse flattening
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128 | */
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129 | public static Ellipsoid create_a_rf(double a, double rf) {
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130 | return create_a_f(a, 1.0 / rf);
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131 | }
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132 |
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133 | @Override
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134 | public String toString() {
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135 | return "Ellipsoid{a="+a+", b="+b+"}";
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136 | }
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137 |
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138 | /**
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139 | * Returns the <i>radius of curvature in the prime vertical</i>
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140 | * for this reference ellipsoid at the specified latitude.
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141 | *
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142 | * @param phi The local latitude (radians).
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143 | * @return The radius of curvature in the prime vertical (meters).
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144 | */
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145 | public double verticalRadiusOfCurvature(final double phi) {
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146 | return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi))));
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147 | }
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148 |
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149 | private static double sqr(final double x) {
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150 | return x * x;
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151 | }
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152 |
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153 | /**
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154 | * Returns the meridional arc, the true meridional distance on the
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155 | * ellipsoid from the equator to the specified latitude, in meters.
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156 | *
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157 | * @param phi The local latitude (in radians).
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158 | * @return The meridional arc (in meters).
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159 | */
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160 | public double meridionalArc(final double phi) {
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161 | final double sin2Phi = Math.sin(2.0 * phi);
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162 | final double sin4Phi = Math.sin(4.0 * phi);
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163 | final double sin6Phi = Math.sin(6.0 * phi);
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164 | final double sin8Phi = Math.sin(8.0 * phi);
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165 | // TODO . calculate 'f'
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166 | //double f = 1.0 / 298.257222101; // GRS80
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167 | double f = 1.0 / 298.257223563; // WGS84
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168 | final double n = f / (2.0 - f);
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169 | final double n2 = n * n;
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170 | final double n3 = n2 * n;
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171 | final double n4 = n3 * n;
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172 | final double n5 = n4 * n;
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173 | final double n1n2 = n - n2;
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174 | final double n2n3 = n2 - n3;
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175 | final double n3n4 = n3 - n4;
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176 | final double n4n5 = n4 - n5;
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177 | final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5));
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178 | final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5);
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179 | final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5));
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180 | final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5);
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181 | final double ep = (315.0 / 512.0) * a * (n4n5);
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182 | return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi;
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183 | }
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184 |
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185 | /**
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186 | * Returns the <i>radius of curvature in the meridian</i>
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187 | * for this reference ellipsoid at the specified latitude.
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188 | *
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189 | * @param phi The local latitude (in radians).
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190 | * @return The radius of curvature in the meridian (in meters).
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191 | */
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192 | public double meridionalRadiusOfCurvature(final double phi) {
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193 | return verticalRadiusOfCurvature(phi)
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194 | / (1.0 + eb2 * sqr(Math.cos(phi)));
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195 | }
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196 |
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197 | /**
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198 | * Returns isometric latitude of phi on given first eccentricity (e)
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199 | * @param phi The local latitude (radians).
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200 | * @return isometric latitude of phi on first eccentricity (e)
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201 | */
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202 | public double latitudeIsometric(double phi, double e) {
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203 | double v1 = 1-e*Math.sin(phi);
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204 | double v2 = 1+e*Math.sin(phi);
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205 | return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
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206 | }
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207 |
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208 | /**
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209 | * Returns isometric latitude of phi on first eccentricity (e)
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210 | * @param phi The local latitude (radians).
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211 | * @return isometric latitude of phi on first eccentricity (e)
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212 | */
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213 | public double latitudeIsometric(double phi) {
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214 | double v1 = 1-e*Math.sin(phi);
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215 | double v2 = 1+e*Math.sin(phi);
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216 | return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
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217 | }
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218 |
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219 | /*
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220 | * Returns geographic latitude of isometric latitude of first eccentricity (e)
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221 | * and epsilon precision
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222 | */
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223 | public double latitude(double latIso, double e, double epsilon) {
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224 | double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2;
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225 | double lati = lat0;
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226 | double lati1 = 1.0; // random value to start the iterative processus
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227 | while(Math.abs(lati1-lati)>=epsilon) {
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228 | lati = lati1;
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229 | double v1 = 1+e*Math.sin(lati);
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230 | double v2 = 1-e*Math.sin(lati);
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231 | lati1 = 2*Math.atan(Math.pow(v1/v2,e/2)*Math.exp(latIso))-Math.PI/2;
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232 | }
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233 | return lati1;
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234 | }
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235 |
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236 | /**
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237 | * convert cartesian coordinates to ellipsoidal coordinates
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238 | *
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239 | * @param xyz the coordinates in meters (X, Y, Z)
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240 | * @return The corresponding latitude and longitude in degrees
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241 | */
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242 | public LatLon cart2LatLon(double[] xyz) {
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243 | return cart2LatLon(xyz, 1e-11);
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244 | }
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245 |
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246 | public LatLon cart2LatLon(double[] xyz, double epsilon) {
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247 | double norm = Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]);
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248 | double lg = 2.0 * Math.atan(xyz[1] / (xyz[0] + norm));
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249 | double lt = Math.atan(xyz[2] / (norm * (1.0 - (a * e2 / Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1] + xyz[2] * xyz[2])))));
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250 | double delta = 1.0;
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251 | while (delta > epsilon) {
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252 | double s2 = Math.sin(lt);
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253 | s2 *= s2;
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254 | double l = Math.atan((xyz[2] / norm)
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255 | / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2)))));
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256 | delta = Math.abs(l - lt);
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257 | lt = l;
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258 | }
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259 | return new LatLon(Math.toDegrees(lt), Math.toDegrees(lg));
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260 | }
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261 |
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262 | /**
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263 | * convert ellipsoidal coordinates to cartesian coordinates
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264 | *
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265 | * @param coord The Latitude and longitude in degrees
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266 | * @return the corresponding (X, Y Z) cartesian coordinates in meters.
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267 | */
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268 | public double[] latLon2Cart(LatLon coord) {
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269 | double phi = Math.toRadians(coord.lat());
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270 | double lambda = Math.toRadians(coord.lon());
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271 |
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272 | double Rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2));
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273 | double[] xyz = new double[3];
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274 | xyz[0] = Rn * Math.cos(phi) * Math.cos(lambda);
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275 | xyz[1] = Rn * Math.cos(phi) * Math.sin(lambda);
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276 | xyz[2] = Rn * (1 - e2) * Math.sin(phi);
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277 |
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278 | return xyz;
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279 | }
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280 | }
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