1 | // License: GPL. For details, see LICENSE file.
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2 | package org.openstreetmap.josm.data.projection.proj;
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3 |
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4 | import static org.openstreetmap.josm.tools.I18n.tr;
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5 |
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6 | import org.openstreetmap.josm.data.Bounds;
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7 | import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
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8 |
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9 | /**
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10 | * Lambert Azimuthal Equal Area (EPSG code 9820).
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11 | * <p>
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12 | * This class has been derived from the implementation of the Geotools project;
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13 | * git 8cbf52d, org.geotools.referencing.operation.projection.LambertAzimuthalEqualArea
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14 | * at the time of migration.
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15 | * <p>
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16 | * <b>References:</b>
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17 | * <ul>
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18 | * <li> A. Annoni, C. Luzet, E.Gubler and J. Ihde - Map Projections for Europe</li>
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19 | * <li> John P. Snyder (Map Projections - A Working Manual,
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20 | * U.S. Geological Survey Professional Paper 1395)</li>
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21 | * </ul>
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22 | *
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23 | * @author Gerald Evenden (for original code in Proj4)
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24 | * @author Beate Stollberg
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25 | * @author Martin Desruisseaux
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26 | *
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27 | * @see <A HREF="http://mathworld.wolfram.com/LambertAzimuthalEqual-AreaProjection.html">Lambert Azimuthal Equal-Area Projection</A>
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28 | * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/lambert_azimuthal_equal_area.html">"Lambert_Azimuthal_Equal_Area"</A>
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29 | */
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30 | public class LambertAzimuthalEqualArea extends AbstractProj {
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31 |
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32 | /** Maximum difference allowed when comparing real numbers. */
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33 | private static final double EPSILON = 1E-7;
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34 |
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35 | /** Epsilon for the comparison of small quantities. */
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36 | private static final double FINE_EPSILON = 1E-10;
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37 |
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38 | /** Epsilon for the comparison of latitudes. */
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39 | private static final double EPSILON_LATITUDE = 1E-10;
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40 |
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41 | /** Constants for authalic latitude. */
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42 | private static final double P00 = 0.33333333333333333333;
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43 | private static final double P01 = 0.17222222222222222222;
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44 | private static final double P02 = 0.10257936507936507936;
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45 | private static final double P10 = 0.06388888888888888888;
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46 | private static final double P11 = 0.06640211640211640211;
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47 | private static final double P20 = 0.01641501294219154443;
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48 |
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49 | /** The projection mode. */
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50 | private enum Mode { OBLIQUE, EQUATORIAL, NORTH_POLE, SOUTH_POLE }
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51 |
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52 | /** The projection mode for this particular instance. */
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53 | private Mode mode;
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54 |
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55 | /** Constant parameters. */
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56 | private double sinb1, cosb1, xmf, ymf, qp, dd, rq;
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57 |
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58 | /** Coefficients for authalic latitude. */
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59 | private double aPA0, aPA1, aPA2;
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60 |
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61 | private double latitudeOfOrigin;
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62 |
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63 | @Override
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64 | public String getName() {
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65 | return tr("Lambert Azimuthal Equal Area");
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66 | }
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67 |
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68 | @Override
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69 | public String getProj4Id() {
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70 | return "laea";
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71 | }
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72 |
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73 | @Override
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74 | public void initialize(ProjParameters params) throws ProjectionConfigurationException {
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75 | super.initialize(params);
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76 |
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77 | if (params.lat0 == null)
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78 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
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79 |
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80 | latitudeOfOrigin = Math.toRadians(params.lat0);
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81 | /*
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82 | * Detects the mode (oblique, etc.).
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83 | */
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84 | final double t = Math.abs(latitudeOfOrigin);
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85 | if (Math.abs(t - Math.PI/2) < EPSILON_LATITUDE) {
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86 | mode = latitudeOfOrigin < 0.0 ? Mode.SOUTH_POLE : Mode.NORTH_POLE;
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87 | } else if (Math.abs(t) < EPSILON_LATITUDE) {
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88 | mode = Mode.EQUATORIAL;
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89 | } else {
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90 | mode = Mode.OBLIQUE;
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91 | }
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92 | /*
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93 | * Computes the constants for authalic latitude.
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94 | */
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95 | final double es2 = e2 * e2;
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96 | final double es3 = e2 * es2;
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97 | aPA0 = P02 * es3 + P01 * es2 + P00 * e2;
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98 | aPA1 = P11 * es3 + P10 * es2;
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99 | aPA2 = P20 * es3;
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100 |
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101 | final double sinphi;
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102 | qp = qsfn(1);
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103 | rq = Math.sqrt(0.5 * qp);
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104 | sinphi = Math.sin(latitudeOfOrigin);
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105 | sinb1 = qsfn(sinphi) / qp;
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106 | cosb1 = Math.sqrt(1.0 - sinb1 * sinb1);
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107 | switch (mode) {
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108 | case NORTH_POLE: // Fall through
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109 | case SOUTH_POLE: {
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110 | dd = 1.0;
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111 | xmf = ymf = rq;
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112 | break;
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113 | }
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114 | case EQUATORIAL: {
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115 | dd = 1.0 / rq;
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116 | xmf = 1.0;
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117 | ymf = 0.5 * qp;
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118 | break;
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119 | }
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120 | case OBLIQUE: {
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121 | dd = Math.cos(latitudeOfOrigin) /
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122 | (Math.sqrt(1.0 - e2 * sinphi * sinphi) * rq * cosb1);
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123 | xmf = rq * dd;
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124 | ymf = rq / dd;
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125 | break;
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126 | }
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127 | default: {
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128 | throw new AssertionError(mode);
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129 | }
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130 | }
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131 | }
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132 |
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133 | @Override
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134 | public double[] project(final double phi, final double lambda) {
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135 | final double coslam = Math.cos(lambda);
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136 | final double sinlam = Math.sin(lambda);
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137 | final double sinphi = Math.sin(phi);
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138 | double q = qsfn(sinphi);
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139 | final double sinb, cosb, b, c, x, y;
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140 | switch (mode) {
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141 | case OBLIQUE: {
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142 | sinb = q / qp;
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143 | cosb = Math.sqrt(1.0 - sinb * sinb);
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144 | c = 1.0 + sinb1 * sinb + cosb1 * cosb * coslam;
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145 | b = Math.sqrt(2.0 / c);
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146 | y = ymf * b * (cosb1 * sinb - sinb1 * cosb * coslam);
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147 | x = xmf * b * cosb * sinlam;
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148 | break;
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149 | }
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150 | case EQUATORIAL: {
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151 | sinb = q / qp;
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152 | cosb = Math.sqrt(1.0 - sinb * sinb);
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153 | c = 1.0 + cosb * coslam;
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154 | b = Math.sqrt(2.0 / c);
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155 | y = ymf * b * sinb;
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156 | x = xmf * b * cosb * sinlam;
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157 | break;
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158 | }
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159 | case NORTH_POLE: {
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160 | c = (Math.PI / 2) + phi;
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161 | q = qp - q;
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162 | if (q >= 0.0) {
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163 | b = Math.sqrt(q);
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164 | x = b * sinlam;
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165 | y = coslam * -b;
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166 | } else {
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167 | x = y = 0.;
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168 | }
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169 | break;
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170 | }
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171 | case SOUTH_POLE: {
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172 | c = phi - (Math.PI / 2);
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173 | q = qp + q;
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174 | if (q >= 0.0) {
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175 | b = Math.sqrt(q);
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176 | x = b * sinlam;
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177 | y = coslam * +b;
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178 | } else {
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179 | x = y = 0.;
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180 | }
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181 | break;
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182 | }
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183 | default: {
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184 | throw new AssertionError(mode);
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185 | }
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186 | }
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187 | if (Math.abs(c) < EPSILON_LATITUDE) {
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188 | return new double[] {0, 0}; // this is an error, we should handle it somehow
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189 | }
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190 | return new double[] {x, y};
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191 | }
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192 |
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193 | @Override
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194 | public double[] invproject(double x, double y) {
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195 | final double lambda, phi;
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196 | switch (mode) {
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197 | case EQUATORIAL: // Fall through
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198 | case OBLIQUE: {
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199 | x /= dd;
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200 | y *= dd;
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201 | final double rho = Math.hypot(x, y);
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202 | if (rho < FINE_EPSILON) {
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203 | lambda = 0.0;
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204 | phi = latitudeOfOrigin;
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205 | } else {
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206 | double sCe, cCe, ab;
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207 | sCe = 2.0 * Math.asin(0.5 * rho / rq);
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208 | cCe = Math.cos(sCe);
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209 | sCe = Math.sin(sCe);
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210 | x *= sCe;
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211 | if (mode == Mode.OBLIQUE) {
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212 | ab = cCe * sinb1 + y * sCe * cosb1 / rho;
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213 | y = rho * cosb1 * cCe - y * sinb1 * sCe;
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214 | } else {
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215 | ab = y * sCe / rho;
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216 | y = rho * cCe;
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217 | }
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218 | lambda = Math.atan2(x, y);
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219 | phi = authlat(Math.asin(ab));
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220 | }
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221 | break;
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222 | }
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223 | case NORTH_POLE: {
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224 | y = -y;
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225 | // Fall through
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226 | }
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227 | case SOUTH_POLE: {
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228 | final double q = x*x + y*y;
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229 | if (q == 0) {
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230 | lambda = 0.;
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231 | phi = latitudeOfOrigin;
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232 | } else {
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233 | double ab = 1.0 - q / qp;
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234 | if (mode == Mode.SOUTH_POLE) {
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235 | ab = -ab;
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236 | }
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237 | lambda = Math.atan2(x, y);
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238 | phi = authlat(Math.asin(ab));
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239 | }
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240 | break;
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241 | }
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242 | default: {
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243 | throw new AssertionError(mode);
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244 | }
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245 | }
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246 | return new double[] {phi, lambda};
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247 | }
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248 |
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249 |
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250 | /**
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251 | * Calculates <var>q</var>, Snyder equation (3-12)
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252 | *
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253 | * @param sinphi sin of the latitude <var>q</var> is calculated for.
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254 | * @return <var>q</var> from Snyder equation (3-12).
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255 | */
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256 | private double qsfn(final double sinphi) {
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257 | if (e >= EPSILON) {
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258 | final double con = e * sinphi;
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259 | return (1.0 - e2) * (sinphi / (1.0 - con*con) -
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260 | (0.5 / e) * Math.log((1.0 - con) / (1.0 + con)));
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261 | } else {
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262 | return sinphi + sinphi;
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263 | }
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264 | }
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265 |
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266 | /**
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267 | * Determines latitude from authalic latitude.
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268 | * @param beta authalic latitude
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269 | * @return corresponding latitude
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270 | */
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271 | private double authlat(final double beta) {
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272 | final double t = beta + beta;
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273 | return beta + aPA0 * Math.sin(t) + aPA1 * Math.sin(t+t) + aPA2 * Math.sin(t+t+t);
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274 | }
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275 |
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276 | @Override
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277 | public Bounds getAlgorithmBounds() {
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278 | return new Bounds(-89, -174, 89, 174, false);
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279 | }
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280 | }
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