svn-gvsig-desktop / branches / libProjection_v2_0_prep / libraries / libProjection / src / org / cresques / cts / GeoCalc.java @ 27135
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1 | 27135 | cmartinez | /*
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2 | * Cresques Mapping Suite. Graphic Library for constructing mapping applications.
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3 | *
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4 | * Copyright (C) 2004-5.
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5 | *
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6 | * This program is free software; you can redistribute it and/or
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7 | * modify it under the terms of the GNU General Public License
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8 | * as published by the Free Software Foundation; either version 2
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9 | * of the License, or (at your option) any later version.
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10 | *
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11 | * This program is distributed in the hope that it will be useful,
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12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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14 | * GNU General Public License for more details.
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15 | *
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16 | * You should have received a copy of the GNU General Public License
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17 | * along with this program; if not, write to the Free Software
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18 | * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,USA.
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19 | *
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20 | * For more information, contact:
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21 | *
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22 | * cresques@gmail.com
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23 | */
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24 | package org.cresques.cts; |
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25 | |||
26 | import java.awt.geom.Point2D; |
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27 | |||
28 | |||
29 | /**
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30 | * Operaciones relacionadas con las proyecciones y sistemas
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31 | * de coordenadas.
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32 | *
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33 | * cmartinez: Esta clase no deber?a formar parte de una API, pero
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34 | * se deja hasta que se aborde el refactoring de libProjection.
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35 | *
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36 | * @author Luis W. Sevilla (sevilla_lui@gva.es)
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37 | */
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38 | public class GeoCalc { |
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39 | IProjection proj; |
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40 | |||
41 | /**
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42 | *
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43 | * @param proj
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44 | */
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45 | public GeoCalc(IProjection proj) {
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46 | this.proj = proj;
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47 | } |
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48 | |||
49 | /* (non-Javadoc)
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50 | * @see org.cresques.impl.cts.GeoCalc#distanceGeo(java.awt.geom.Point2D, java.awt.geom.Point2D)
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51 | */
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52 | public double distanceGeo(Point2D pt1, Point2D pt2) { |
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53 | double R2 = Math.pow(proj.getDatum().getESemiMajorAxis(), 2); |
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54 | double dLat = Math.toRadians(pt2.getY() - pt1.getY()); |
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55 | double dLong = Math.toRadians(pt2.getX() - pt1.getX()); |
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56 | |||
57 | double alfa = Math.toRadians(pt1.getY()); |
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58 | double alfa2 = Math.toRadians(pt2.getY()); |
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59 | |||
60 | if (Math.abs(alfa2) < Math.abs(alfa)) { |
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61 | alfa = alfa2; |
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62 | } |
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63 | |||
64 | double ds2 = (R2 * dLat * dLat) +
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65 | (R2 * Math.cos(alfa) * Math.cos(alfa) * dLong * dLong); |
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66 | |||
67 | return Math.sqrt(ds2); |
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68 | } |
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69 | |||
70 | /* (non-Javadoc)
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71 | * @see org.cresques.impl.cts.GeoCalc#distanceEli(java.awt.geom.Point2D, java.awt.geom.Point2D)
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72 | */
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73 | public double distanceEli(Point2D pt1, Point2D pt2) { |
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74 | double lat1 = Math.toRadians(pt1.getY()); |
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75 | double lon1 = -Math.toRadians(pt1.getX()); |
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76 | double lat2 = Math.toRadians(pt2.getY()); |
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77 | double lon2 = -Math.toRadians(pt2.getX()); |
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78 | |||
79 | double F = (lat1 + lat2) / 2D; |
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80 | double G = (lat1 - lat2) / 2D; |
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81 | double L = (lon1 - lon2) / 2D; |
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82 | |||
83 | double sing = Math.sin(G); |
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84 | double cosl = Math.cos(L); |
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85 | double cosf = Math.cos(F); |
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86 | double sinl = Math.sin(L); |
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87 | double sinf = Math.sin(F); |
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88 | double cosg = Math.cos(G); |
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89 | |||
90 | double flat = 1D / proj.getDatum().getEIFlattening(); |
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91 | |||
92 | double S = (sing * sing * cosl * cosl) + (cosf * cosf * sinl * sinl);
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93 | double C = (cosg * cosg * cosl * cosl) + (sinf * sinf * sinl * sinl);
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94 | double W = Math.atan2(Math.sqrt(S), Math.sqrt(C)); |
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95 | double R = Math.sqrt((S * C)) / W; |
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96 | double H1 = ((3D * R) - 1D) / (2D * C); |
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97 | double H2 = ((3D * R) + 1D) / (2D * S); |
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98 | double D = 2D * W * proj.getDatum().getESemiMajorAxis(); |
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99 | |||
100 | return (D * ((1D + (flat * H1 * sinf * sinf * cosg * cosg)) - |
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101 | (flat * H2 * cosf * cosf * sing * sing))); |
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102 | } |
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103 | |||
104 | /**
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105 | * Algrothims from Geocentric Datum of Australia Technical Manual
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106 | *
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107 | * http://www.anzlic.org.au/icsm/gdatum/chapter4.html
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108 | *
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109 | * This page last updated 11 May 1999
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110 | *
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111 | * Computations on the Ellipsoid
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112 | *
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113 | * There are a number of formulae that are available
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114 | * to calculate accurate geodetic positions,
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115 | * azimuths and distances on the ellipsoid.
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116 | *
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117 | * Vincenty's formulae (Vincenty, 1975) may be used
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118 | * for lines ranging from a few cm to nearly 20,000 km,
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119 | * with millimetre accuracy.
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120 | * The formulae have been extensively tested
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121 | * for the Australian region, by comparison with results
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122 | * from other formulae (Rainsford, 1955 & Sodano, 1965).
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123 | *
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124 | * * Inverse problem: azimuth and distance from known
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125 | * latitudes and longitudes
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126 | * * Direct problem: Latitude and longitude from known
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127 | * position, azimuth and distance.
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128 | * * Sample data
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129 | * * Excel spreadsheet
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130 | *
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131 | * Vincenty's Inverse formulae
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132 | * Given: latitude and longitude of two points
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133 | * (phi1, lembda1 and phi2, lembda2),
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134 | * Calculate: the ellipsoidal distance (s) and
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135 | * forward and reverse azimuths between the points (alpha12, alpha21).
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136 | */
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137 | /* (non-Javadoc)
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138 | * @see org.cresques.impl.cts.GeoCalc#distanceVincenty(java.awt.geom.Point2D, java.awt.geom.Point2D)
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139 | */
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140 | public double distanceVincenty(Point2D pt1, Point2D pt2) { |
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141 | return distanceAzimutVincenty(pt1, pt2).dist;
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142 | } |
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143 | |||
144 | /**
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145 | * Returns the distance between two geographic points on the ellipsoid
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146 | * and the forward and reverse azimuths between these points.
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147 | * lats, longs and azimuths are in decimal degrees, distance in metres
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148 | * Returns ( s, alpha12, alpha21 ) as a tuple
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149 | * @param pt1
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150 | * @param pt2
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151 | * @return
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152 | */
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153 | protected GeoData distanceAzimutVincenty(Point2D pt1, Point2D pt2) { |
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154 | GeoData gd = new GeoData(0, 0); |
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155 | double f = 1D / proj.getDatum().getEIFlattening(); |
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156 | double a = proj.getDatum().getESemiMajorAxis();
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157 | double phi1 = pt1.getY();
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158 | double lembda1 = pt1.getX();
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159 | double phi2 = pt2.getY();
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160 | double lembda2 = pt2.getX();
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161 | |||
162 | if ((Math.abs(phi2 - phi1) < 1e-8) && |
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163 | (Math.abs(lembda2 - lembda1) < 1e-8)) { |
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164 | return gd;
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165 | } |
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166 | |||
167 | double piD4 = Math.atan(1.0); |
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168 | double two_pi = piD4 * 8.0; |
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169 | |||
170 | phi1 = (phi1 * piD4) / 45.0;
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171 | lembda1 = (lembda1 * piD4) / 45.0; // unfortunately lambda is a key word! |
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172 | phi2 = (phi2 * piD4) / 45.0;
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173 | lembda2 = (lembda2 * piD4) / 45.0;
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174 | |||
175 | double b = a * (1.0 - f); |
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176 | |||
177 | double TanU1 = (1 - f) * Math.tan(phi1); |
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178 | double TanU2 = (1 - f) * Math.tan(phi2); |
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179 | |||
180 | double U1 = Math.atan(TanU1); |
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181 | double U2 = Math.atan(TanU2); |
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182 | |||
183 | double lembda = lembda2 - lembda1;
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184 | double last_lembda = -4000000.0; // an impossibe value |
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185 | double omega = lembda;
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186 | |||
187 | // Iterate the following equations,
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188 | // until there is no significant change in lembda
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189 | double Sin_sigma = 0; |
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190 | |||
191 | // Iterate the following equations,
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192 | // until there is no significant change in lembda
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193 | double Cos_sigma = 0; |
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194 | double Cos2sigma_m = 0; |
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195 | double alpha = 0; |
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196 | double sigma = 0; |
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197 | double sqr_sin_sigma = 0; |
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198 | |||
199 | while ((last_lembda < -3000000.0) || |
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200 | ((lembda != 0) &&
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201 | (Math.abs((last_lembda - lembda) / lembda) > 1.0e-9))) { |
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202 | sqr_sin_sigma = Math.pow(Math.cos(U2) * Math.sin(lembda), 2) + |
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203 | Math.pow(((Math.cos(U1) * Math.sin(U2)) - |
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204 | (Math.sin(U1) * Math.cos(U2) * Math.cos(lembda))), |
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205 | 2);
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206 | |||
207 | Sin_sigma = Math.sqrt(sqr_sin_sigma);
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208 | |||
209 | Cos_sigma = (Math.sin(U1) * Math.sin(U2)) + |
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210 | (Math.cos(U1) * Math.cos(U2) * Math.cos(lembda)); |
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211 | |||
212 | sigma = Math.atan2(Sin_sigma, Cos_sigma);
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213 | |||
214 | double Sin_alpha = (Math.cos(U1) * Math.cos(U2) * Math.sin(lembda)) / Math.sin(sigma); |
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215 | alpha = Math.asin(Sin_alpha);
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216 | |||
217 | Cos2sigma_m = Math.cos(sigma) -
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218 | ((2 * Math.sin(U1) * Math.sin(U2)) / Math.pow(Math.cos(alpha), |
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219 | 2));
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220 | |||
221 | double C = (f / 16) * Math.pow(Math.cos(alpha), 2) * (4 + |
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222 | (f * (4 - (3 * Math.pow(Math.cos(alpha), 2))))); |
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223 | |||
224 | last_lembda = lembda; |
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225 | |||
226 | lembda = omega + |
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227 | ((1 - C) * f * Math.sin(alpha) * (sigma + |
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228 | (C * Math.sin(sigma) * (Cos2sigma_m +
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229 | (C * Math.cos(sigma) * (-1 + |
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230 | (2 * Math.pow(Cos2sigma_m, 2)))))))); |
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231 | } |
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232 | |||
233 | double u2 = (Math.pow(Math.cos(alpha), 2) * ((a * a) - (b * b))) / (b * b); |
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234 | |||
235 | double A = 1 + |
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236 | ((u2 / 16384) * (4096 + |
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237 | (u2 * (-768 + (u2 * (320 - (175 * u2))))))); |
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238 | |||
239 | double B = (u2 / 1024) * (256 + |
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240 | (u2 * (-128 + (u2 * (74 - (47 * u2)))))); |
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241 | |||
242 | double delta_sigma = B * Sin_sigma * (Cos2sigma_m +
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243 | ((B / 4) * ((Cos_sigma * (-1 + |
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244 | (2 * Math.pow(Cos2sigma_m, 2)))) - |
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245 | ((B / 6) * Cos2sigma_m * (-3 + |
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246 | (4 * sqr_sin_sigma)) * (-3 + |
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247 | (4 * Math.pow(Cos2sigma_m, 2))))))); |
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248 | |||
249 | double s = b * A * (sigma - delta_sigma);
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250 | |||
251 | double alpha12 = Math.atan2((Math.cos(U2) * Math.sin(lembda)), |
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252 | ((Math.cos(U1) * Math.sin(U2)) - |
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253 | (Math.sin(U1) * Math.cos(U2) * Math.cos(lembda)))); |
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254 | |||
255 | double alpha21 = Math.atan2((Math.cos(U1) * Math.sin(lembda)), |
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256 | ((-Math.sin(U1) * Math.cos(U2)) + |
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257 | (Math.cos(U1) * Math.sin(U2) * Math.cos(lembda)))); |
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258 | |||
259 | if (alpha12 < 0.0) { |
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260 | alpha12 = alpha12 + two_pi; |
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261 | } |
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262 | |||
263 | if (alpha12 > two_pi) {
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264 | alpha12 = alpha12 - two_pi; |
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265 | } |
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266 | |||
267 | alpha21 = alpha21 + (two_pi / 2.0);
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268 | |||
269 | if (alpha21 < 0.0) { |
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270 | alpha21 = alpha21 + two_pi; |
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271 | } |
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272 | |||
273 | if (alpha21 > two_pi) {
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274 | alpha21 = alpha21 - two_pi; |
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275 | } |
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276 | |||
277 | alpha12 = (alpha12 * 45.0) / piD4;
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278 | alpha21 = (alpha21 * 45.0) / piD4;
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279 | |||
280 | return new GeoData(0, 0, s, alpha12, alpha21); |
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281 | } |
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282 | |||
283 | /**
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284 | * Vincenty's Direct formulae
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285 | * Given: latitude and longitude of a point (phi1, lembda1) and
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286 | * the geodetic azimuth (alpha12)
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287 | * and ellipsoidal distance in metres (s) to a second point,
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288 | *
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289 | * Calculate: the latitude and longitude of the second point (phi2, lembda2)
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290 | * and the reverse azimuth (alpha21).
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291 | */
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292 | /**
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293 | * Returns the lat and long of projected point and reverse azimuth
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294 | * given a reference point and a distance and azimuth to project.
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295 | * lats, longs and azimuths are passed in decimal degrees.
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296 | * Returns ( phi2, lambda2, alpha21 ) as a tuple
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297 | * @param pt
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298 | * @param azimut
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299 | * @param dist
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300 | * @return
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301 | */
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302 | protected GeoData getPointVincenty(Point2D pt, double azimut, double dist) { |
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303 | GeoData ret = new GeoData(0, 0); |
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304 | double f = 1D / proj.getDatum().getEIFlattening(); |
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305 | double a = proj.getDatum().getESemiMajorAxis();
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306 | double phi1 = pt.getY();
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307 | double lembda1 = pt.getX();
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308 | double alpha12 = azimut;
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309 | double s = dist;
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310 | |||
311 | double piD4 = Math.atan(1.0); |
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312 | double two_pi = piD4 * 8.0; |
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313 | |||
314 | phi1 = (phi1 * piD4) / 45.0;
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315 | lembda1 = (lembda1 * piD4) / 45.0;
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316 | alpha12 = (alpha12 * piD4) / 45.0;
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317 | |||
318 | if (alpha12 < 0.0) { |
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319 | alpha12 = alpha12 + two_pi; |
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320 | } |
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321 | |||
322 | if (alpha12 > two_pi) {
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323 | alpha12 = alpha12 - two_pi; |
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324 | } |
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325 | |||
326 | double b = a * (1.0 - f); |
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327 | |||
328 | double TanU1 = (1 - f) * Math.tan(phi1); |
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329 | double U1 = Math.atan(TanU1); |
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330 | double sigma1 = Math.atan2(TanU1, Math.cos(alpha12)); |
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331 | double Sinalpha = Math.cos(U1) * Math.sin(alpha12); |
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332 | double cosalpha_sq = 1.0 - (Sinalpha * Sinalpha); |
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333 | |||
334 | double u2 = (cosalpha_sq * ((a * a) - (b * b))) / (b * b);
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335 | double A = 1.0 + |
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336 | ((u2 / 16384) * (4096 + |
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337 | (u2 * (-768 + (u2 * (320 - (175 * u2))))))); |
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338 | double B = (u2 / 1024) * (256 + |
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339 | (u2 * (-128 + (u2 * (74 - (47 * u2)))))); |
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340 | |||
341 | // Starting with the approximation
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342 | double sigma = (s / (b * A));
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343 | |||
344 | double last_sigma = (2.0 * sigma) + 2.0; // something impossible |
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345 | |||
346 | // Iterate the following three equations
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347 | // until there is no significant change in sigma
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348 | // two_sigma_m , delta_sigma
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349 | double two_sigma_m = 0; |
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350 | |||
351 | while (Math.abs((last_sigma - sigma) / sigma) > 1.0e-9) { |
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352 | two_sigma_m = (2 * sigma1) + sigma;
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353 | |||
354 | double delta_sigma = B * Math.sin(sigma) * (Math.cos(two_sigma_m) + |
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355 | ((B / 4) * (Math.cos(sigma) * ((-1 + |
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356 | (2 * Math.pow(Math.cos(two_sigma_m), 2))) - |
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357 | ((B / 6) * Math.cos(two_sigma_m) * (-3 + |
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358 | (4 * Math.pow(Math.sin(sigma), 2))) * (-3 + |
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359 | (4 * Math.pow(Math.cos(two_sigma_m), 2)))))))); |
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360 | |||
361 | last_sigma = sigma; |
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362 | sigma = (s / (b * A)) + delta_sigma; |
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363 | } |
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364 | |||
365 | double phi2 = Math.atan2(((Math.sin(U1) * Math.cos(sigma)) + |
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366 | (Math.cos(U1) * Math.sin(sigma) * Math.cos(alpha12))), |
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367 | ((1 - f) * Math.sqrt(Math.pow(Sinalpha, 2) + |
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368 | Math.pow((Math.sin(U1) * Math.sin(sigma)) - |
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369 | (Math.cos(U1) * Math.cos(sigma) * Math.cos(alpha12)), |
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370 | 2))));
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371 | |||
372 | double lembda = Math.atan2((Math.sin(sigma) * Math.sin(alpha12)), |
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373 | ((Math.cos(U1) * Math.cos(sigma)) - |
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374 | (Math.sin(U1) * Math.sin(sigma) * Math.cos(alpha12)))); |
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375 | |||
376 | double C = (f / 16) * cosalpha_sq * (4 + (f * (4 - (3 * cosalpha_sq)))); |
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377 | |||
378 | double omega = lembda -
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379 | ((1 - C) * f * Sinalpha * (sigma +
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380 | (C * Math.sin(sigma) * (Math.cos(two_sigma_m) + |
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381 | (C * Math.cos(sigma) * (-1 + |
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382 | (2 * Math.pow(Math.cos(two_sigma_m), 2)))))))); |
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383 | |||
384 | double lembda2 = lembda1 + omega;
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385 | |||
386 | double alpha21 = Math.atan2(Sinalpha, |
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387 | ((-Math.sin(U1) * Math.sin(sigma)) + |
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388 | (Math.cos(U1) * Math.cos(sigma) * Math.cos(alpha12)))); |
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389 | |||
390 | alpha21 = alpha21 + (two_pi / 2.0);
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391 | |||
392 | if (alpha21 < 0.0) { |
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393 | alpha21 = alpha21 + two_pi; |
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394 | } |
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395 | |||
396 | if (alpha21 > two_pi) {
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397 | alpha21 = alpha21 - two_pi; |
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398 | } |
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399 | |||
400 | phi2 = (phi2 * 45.0) / piD4;
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401 | lembda2 = (lembda2 * 45.0) / piD4;
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402 | alpha21 = (alpha21 * 45.0) / piD4;
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403 | |||
404 | ret.pt = new Point2D.Double(lembda2, phi2); |
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405 | ret.azimut = alpha21; |
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406 | |||
407 | return ret;
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408 | } |
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409 | |||
410 | /* (non-Javadoc)
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411 | * @see org.cresques.impl.cts.GeoCalc#surfaceSphere(java.awt.geom.Point2D, java.awt.geom.Point2D, java.awt.geom.Point2D)
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412 | */
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413 | public double surfaceSphere(Point2D pt1, Point2D pt2, Point2D pt3) { |
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414 | double sup = -1; |
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415 | double A = distanceGeo(pt1, pt2);
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416 | double B = distanceGeo(pt2, pt3);
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417 | double C = distanceGeo(pt3, pt1);
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418 | sup = (((A + B + C) - Math.toRadians(180D)) * Math.PI * proj.getDatum() |
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419 | .getESemiMajorAxis()) / Math.toRadians(180D); |
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420 | |||
421 | return sup;
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422 | } |
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423 | |||
424 | /*
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425 | * F?rmulas de Vincenty's.
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426 | * (pasadas de http://wegener.mechanik.tu-darmstadt.de/GMT-Help/Archiv/att-8710/Geodetic_py
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427 | * http://www.icsm.gov.au/icsm/gda/gdatm/index.html
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428 | */
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429 | protected class GeoData { |
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430 | Point2D pt;
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431 | double azimut;
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432 | double revAzimut;
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433 | double dist;
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434 | |||
435 | public GeoData(double x, double y) { |
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436 | pt = new Point2D.Double(x, y); |
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437 | azimut = revAzimut = dist = 0;
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438 | } |
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439 | |||
440 | public GeoData(double x, double y, double dist, double azi, double rAzi) { |
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441 | pt = new Point2D.Double(x, y); |
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442 | azimut = azi; |
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443 | revAzimut = rAzi; |
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444 | this.dist = dist;
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445 | } |
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446 | } |
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447 | } |