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.coor.LatLon;
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8 | import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
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9 | import org.openstreetmap.josm.tools.Utils;
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10 |
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11 | /**
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12 | * Oblique Mercator Projection. A conformal, oblique, cylindrical projection with the cylinder
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13 | * touching the ellipsoid (or sphere) along a great circle path (the central line). The
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14 | * {@linkplain Mercator} and {@linkplain TransverseMercator Transverse Mercator} projections can
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15 | * be thought of as special cases of the oblique mercator, where the central line is along the
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16 | * equator or a meridian, respectively. The Oblique Mercator projection has been used in
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17 | * Switzerland, Hungary, Madagascar, Malaysia, Borneo and the panhandle of Alaska.
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18 | * <p>
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19 | * The Oblique Mercator projection uses a (<var>U</var>,<var>V</var>) coordinate system, with the
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20 | * <var>U</var> axis along the central line. During the forward projection, coordinates from the
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21 | * ellipsoid are projected conformally to a sphere of constant total curvature, called the
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22 | * "aposphere", before being projected onto the plane. The projection coordinates are further
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23 | * convented to a (<var>X</var>,<var>Y</var>) coordinate system by rotating the calculated
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24 | * (<var>u</var>,<var>v</var>) coordinates to give output (<var>x</var>,<var>y</var>) coordinates.
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25 | * The rotation value is usually the same as the projection azimuth (the angle, east of north, of
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26 | * the central line), but some cases allow a separate rotation parameter.
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27 | * <p>
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28 | * There are two forms of the oblique mercator, differing in the origin of their grid coordinates.
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29 | * The Hotine Oblique Mercator (EPSG code 9812) has grid coordinates start at the intersection of
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30 | * the central line and the equator of the aposphere.
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31 | * The Oblique Mercator (EPSG code 9815) is the same, except the grid coordinates begin at the
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32 | * central point (where the latitude of center and central line intersect). ESRI separates these
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33 | * two case by appending {@code "Natural_Origin"} (for the {@code "Hotine_Oblique_Mercator"}) and
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34 | * {@code "Center"} (for the {@code "Oblique_Mercator"}) to the projection names.
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35 | * <p>
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36 | * Two different methods are used to specify the central line for the oblique mercator:
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37 | * 1) a central point and an azimuth, east of north, describing the central line and
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38 | * 2) two points on the central line. The EPSG does not use the two point method,
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39 | * while ESRI separates the two cases by putting {@code "Azimuth"} and {@code "Two_Point"}
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40 | * in their projection names. Both cases use the point where the {@code "latitude_of_center"}
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41 | * parameter crosses the central line as the projection's central point.
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42 | * The {@linkplain #centralMeridian central meridian} is not a projection parameter,
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43 | * and is instead calculated as the intersection between the central line and the
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44 | * equator of the aposphere.
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45 | * <p>
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46 | * For the azimuth method, the central latitude cannot be ±90.0 degrees
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47 | * and the central line cannot be at a maximum or minimum latitude at the central point.
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48 | * In the two point method, the latitude of the first and second points cannot be
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49 | * equal. Also, the latitude of the first point and central point cannot be
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50 | * ±90.0 degrees. Furthermore, the latitude of the first point cannot be 0.0 and
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51 | * the latitude of the second point cannot be -90.0 degrees. A change of
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52 | * 10<sup>-7</sup> radians can allow calculation at these special cases. Snyder's restriction
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53 | * of the central latitude being 0.0 has been removed, since the equations appear
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54 | * to work correctly in this case.
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55 | * <p>
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56 | * Azimuth values of 0.0 and ±90.0 degrees are allowed (and used in Hungary
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57 | * and Switzerland), though these cases would usually use a Mercator or
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58 | * Transverse Mercator projection instead. Azimuth values > 90 degrees cause
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59 | * errors in the equations.
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60 | * <p>
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61 | * The oblique mercator is also called the "Rectified Skew Orthomorphic" (RSO). It appears
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62 | * is that the only difference from the oblique mercator is that the RSO allows the rotation
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63 | * from the (<var>U</var>,<var>V</var>) to (<var>X</var>,<var>Y</var>) coordinate system to
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64 | * be different from the azimuth. This separate parameter is called
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65 | * {@code "rectified_grid_angle"} (or {@code "XY_Plane_Rotation"} by ESRI) and is also
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66 | * included in the EPSG's parameters for the Oblique Mercator and Hotine Oblique Mercator.
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67 | * The rotation parameter is optional in all the non-two point projections and will be
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68 | * set to the azimuth if not specified.
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69 | * <p>
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70 | * Projection cases and aliases implemented by the {@link ObliqueMercator} are:
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71 | * <ul>
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72 | * <li>{@code Oblique_Mercator} (EPSG code 9815)<br>
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73 | * grid coordinates begin at the central point,
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74 | * has {@code "rectified_grid_angle"} parameter.</li>
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75 | * <li>{@code Hotine_Oblique_Mercator_Azimuth_Center} (ESRI)<br>
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76 | * grid coordinates begin at the central point.</li>
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77 | * <li>{@code Rectified_Skew_Orthomorphic_Center} (ESRI)<br>
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78 | * grid coordinates begin at the central point,
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79 | * has {@code "rectified_grid_angle"} parameter.</li>
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80 | *
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81 | * <li>{@code Hotine_Oblique_Mercator} (EPSG code 9812)<br>
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82 | * grid coordinates begin at the interseciton of the central line and aposphere equator,
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83 | * has {@code "rectified_grid_angle"} parameter.</li>
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84 | * <li>{@code Hotine_Oblique_Mercator_Azimuth_Natural_Origin} (ESRI)<br>
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85 | * grid coordinates begin at the interseciton of the central line and aposphere equator.</li>
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86 | * <li>{@code Rectified_Skew_Orthomorphic_Natural_Origin} (ESRI)<br>
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87 | * grid coordinates begin at the interseciton of the central line and aposphere equator,
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88 | * has {@code "rectified_grid_angle"} parameter.</li>
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89 | *
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90 | * <li>{@code Hotine_Oblique_Mercator_Two_Point_Center} (ESRI)<br>
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91 | * grid coordinates begin at the central point.</li>
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92 | * <li>{@code Hotine_Oblique_Mercator_Two_Point_Natural_Origin} (ESRI)<br>
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93 | * grid coordinates begin at the interseciton of the central line and aposphere equator.</li>
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94 | * </ul>
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95 | * <p>
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96 | * This class has been derived from the implementation of the Geotools project;
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97 | * git 8cbf52d, org.geotools.referencing.operation.projection.ObliqueMercator
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98 | * at the time of migration.
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99 | * <p>
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100 | * Note that automatic calculation of bounds is very limited for this projection,
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101 | * since the central line can have any orientation.
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102 | * <p>
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103 | * <b>References:</b>
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104 | * <ul>
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105 | * <li>{@code libproj4} is available at
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106 | * <A HREF="http://members.bellatlantic.net/~vze2hc4d/proj4/">libproj4 Miscellanea</A><br>
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107 | * Relevent files are: {@code PJ_omerc.c}, {@code pj_tsfn.c},
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108 | * {@code pj_fwd.c}, {@code pj_inv.c} and {@code lib_proj.h}</li>
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109 | * <li>John P. Snyder (Map Projections - A Working Manual,
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110 | * U.S. Geological Survey Professional Paper 1395, 1987)</li>
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111 | * <li>"Coordinate Conversions and Transformations including Formulas",
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112 | * EPSG Guidence Note Number 7 part 2, Version 24.</li>
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113 | * <li>Gerald Evenden, 2004, <a href="http://members.verizon.net/~vze2hc4d/proj4/omerc.pdf">
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114 | * Documentation of revised Oblique Mercator</a></li>
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115 | * </ul>
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116 | *
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117 | * @author Gerald I. Evenden (for original code in Proj4)
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118 | * @author Rueben Schulz
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119 | *
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120 | * @see <A HREF="http://mathworld.wolfram.com/MercatorProjection.html">Oblique Mercator projection on MathWorld</A>
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121 | * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/hotine_oblique_mercator.html">"hotine_oblique_mercator" on RemoteSensing.org</A>
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122 | * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/oblique_mercator.html">"oblique_mercator" on RemoteSensing.org</A>
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123 | */
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124 | public class ObliqueMercator extends AbstractProj implements ICentralMeridianProvider {
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125 |
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126 | /**
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127 | * Maximum difference allowed when comparing real numbers.
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128 | */
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129 | private static final double EPSILON = 1E-6;
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130 |
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131 | /**
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132 | * Maximum difference allowed when comparing latitudes.
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133 | */
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134 | private static final double EPSILON_LATITUDE = 1E-10;
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135 |
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136 | //////
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137 | ////// Map projection parameters. The following are NOT used by the transformation
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138 | ////// methods, but are stored in order to restitute them in WKT formatting. They
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139 | ////// are made visible ('protected' access) for documentation purpose and because
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140 | ////// they are user-supplied parameters, not derived coefficients.
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141 | //////
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142 |
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143 | /**
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144 | * The azimuth of the central line passing throught the centre of the projection, in radians.
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145 | */
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146 | protected double azimuth;
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147 |
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148 | /**
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149 | * The rectified bearing of the central line, in radians. This is equals to the
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150 | * {@linkplain #azimuth} if the parameter value is not set.
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151 | */
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152 | protected double rectifiedGridAngle;
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153 |
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154 | //////
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155 | ////// Map projection coefficients computed from the above parameters.
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156 | ////// They are the fields used for coordinate transformations.
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157 | //////
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158 |
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159 | /**
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160 | * Constants used in the transformation.
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161 | */
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162 | private double b, g;
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163 |
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164 | /**
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165 | * Convenience value equal to {@code a} / {@link #b}.
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166 | */
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167 | private double arb;
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168 |
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169 | /**
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170 | * Convenience value equal to {@code a}×{@link #b}.
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171 | */
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172 | private double ab;
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173 |
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174 | /**
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175 | * Convenience value equal to {@link #b} / {@code a}.
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176 | */
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177 | private double bra;
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178 |
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179 | /**
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180 | * <var>v</var> values when the input latitude is a pole.
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181 | */
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182 | private double vPoleN, vPoleS;
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183 |
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184 | /**
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185 | * Sine and Cosine values for gamma0 (the angle between the meridian
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186 | * and central line at the intersection between the central line and
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187 | * the Earth equator on aposphere).
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188 | */
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189 | private double singamma0, cosgamma0;
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190 |
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191 | /**
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192 | * Sine and Cosine values for the rotation between (U,V) and
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193 | * (X,Y) coordinate systems
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194 | */
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195 | private double sinrot, cosrot;
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196 |
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197 | /**
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198 | * <var>u</var> value (in (U,V) coordinate system) of the central point. Used in
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199 | * the oblique mercator case. The <var>v</var> value of the central point is 0.0.
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200 | */
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201 | private double uc;
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202 |
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203 | /**
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204 | * Central longitude in <u>radians</u>. Default value is 0, the Greenwich meridian.
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205 | * This is called '<var>lambda0</var>' in Snyder.
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206 | */
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207 | protected double centralMeridian;
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208 |
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209 | /**
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210 | * A reference point, which is known to be on the central line.
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211 | */
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212 | private LatLon referencePoint;
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213 |
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214 | @Override
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215 | public String getName() {
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216 | return tr("Oblique Mercator");
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217 | }
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218 |
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219 | @Override
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220 | public String getProj4Id() {
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221 | return "omerc";
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222 | }
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223 |
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224 | @Override
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225 | public void initialize(ProjParameters params) throws ProjectionConfigurationException {
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226 | super.initialize(params);
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227 | boolean twoPoint = params.alpha == null;
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228 |
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229 | double latCenter = 0;
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230 | if (params.lat0 != null) {
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231 | latCenter = Utils.toRadians(params.lat0);
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232 | }
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233 |
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234 | final double com = Math.sqrt(1.0 - e2);
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235 | double sinph0 = Math.sin(latCenter);
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236 | double cosph0 = Math.cos(latCenter);
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237 | final double con = 1. - e2 * sinph0 * sinph0;
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238 | double temp = cosph0 * cosph0;
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239 | b = Math.sqrt(1.0 + e2 * (temp * temp) / (1.0 - e2));
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240 | double a = b * com / con;
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241 | final double d = b * com / (cosph0 * Math.sqrt(con));
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242 | double f = d * d - 1.0;
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243 | if (f < 0.0) {
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244 | f = 0.0;
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245 | } else {
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246 | f = Math.sqrt(f);
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247 | if (latCenter < 0.0) {
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248 | f = -f;
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249 | }
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250 | }
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251 | g = f += d;
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252 | g = f * Math.pow(tsfn(latCenter, sinph0), b);
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253 |
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254 | /*
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255 | * Computes the constants that depend on the "twoPoint" vs "azimuth" case. In the
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256 | * two points case, we compute them from (LAT_OF_1ST_POINT, LONG_OF_1ST_POINT) and
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257 | * (LAT_OF_2ND_POINT, LONG_OF_2ND_POINT). For the "azimuth" case, we compute them
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258 | * from LONGITUDE_OF_CENTRE and AZIMUTH.
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259 | */
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260 | final double gamma0;
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261 | Double lonCenter = null;
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262 | if (twoPoint) {
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263 | if (params.lon1 == null)
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264 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lon_1"));
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265 | if (params.lat1 == null)
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266 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_1"));
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267 | if (params.lon2 == null)
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268 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lon_2"));
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269 | if (params.lat2 == null)
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270 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_2"));
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271 | referencePoint = new LatLon(params.lat1, params.lat2);
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272 | double lon1 = Utils.toRadians(params.lon1);
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273 | double lat1 = Utils.toRadians(params.lat1);
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274 | double lon2 = Utils.toRadians(params.lon2);
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275 | double lat2 = Utils.toRadians(params.lat2);
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276 |
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277 | if (Math.abs(lat1 - lat2) <= EPSILON ||
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278 | Math.abs(lat1) <= EPSILON ||
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279 | Math.abs(Math.abs(lat1) - Math.PI / 2) <= EPSILON ||
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280 | Math.abs(Math.abs(latCenter) - Math.PI / 2) <= EPSILON ||
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281 | Math.abs(Math.abs(lat2) - Math.PI / 2) <= EPSILON) {
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282 | throw new ProjectionConfigurationException(
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283 | tr("Unsuitable parameters ''{0}'' and ''{1}'' for two point method.", "lat_1", "lat_2"));
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284 | }
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285 | /*
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286 | * The coefficients for the "two points" case.
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287 | */
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288 | final double h = Math.pow(tsfn(lat1, Math.sin(lat1)), b);
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289 | final double l = Math.pow(tsfn(lat2, Math.sin(lat2)), b);
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290 | final double fp = g / h;
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291 | final double p = (l - h) / (l + h);
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292 | double j = g * g;
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293 | j = (j - l * h) / (j + l * h);
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294 | double diff = lon1 - lon2;
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295 | if (diff < -Math.PI) {
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296 | lon2 -= 2.0 * Math.PI;
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297 | } else if (diff > Math.PI) {
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298 | lon2 += 2.0 * Math.PI;
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299 | }
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300 | centralMeridian = normalizeLonRad(0.5 * (lon1 + lon2) -
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301 | Math.atan(j * Math.tan(0.5 * b * (lon1 - lon2)) / p) / b);
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302 | gamma0 = Math.atan(2.0 * Math.sin(b * normalizeLonRad(lon1 - centralMeridian)) /
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303 | (fp - 1.0 / fp));
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304 | azimuth = Math.asin(d * Math.sin(gamma0));
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305 | rectifiedGridAngle = azimuth;
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306 | } else {
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307 | if (params.lonc == null)
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308 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lonc"));
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309 | if (params.lat0 == null)
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310 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
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311 | if (params.alpha == null)
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312 | throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "alpha"));
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313 | referencePoint = new LatLon(params.lat0, params.lonc);
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314 |
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315 | lonCenter = Utils.toRadians(params.lonc);
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316 | azimuth = Utils.toRadians(params.alpha);
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317 | // CHECKSTYLE.OFF: SingleSpaceSeparator
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318 | if ((azimuth > -1.5*Math.PI && azimuth < -0.5*Math.PI) ||
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319 | (azimuth > 0.5*Math.PI && azimuth < 1.5*Math.PI)) {
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320 | throw new ProjectionConfigurationException(
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321 | tr("Illegal value for parameter ''{0}'': {1}", "alpha", Double.toString(params.alpha)));
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322 | }
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323 | // CHECKSTYLE.ON: SingleSpaceSeparator
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324 | if (params.gamma != null) {
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325 | rectifiedGridAngle = Utils.toRadians(params.gamma);
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326 | } else {
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327 | rectifiedGridAngle = azimuth;
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328 | }
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329 | gamma0 = Math.asin(Math.sin(azimuth) / d);
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330 | // Check for asin(+-1.00000001)
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331 | temp = 0.5 * (f - 1.0 / f) * Math.tan(gamma0);
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332 | if (Math.abs(temp) > 1.0) {
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333 | if (Math.abs(Math.abs(temp) - 1.0) > EPSILON) {
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334 | throw new ProjectionConfigurationException(tr("error in initialization"));
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335 | }
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336 | temp = (temp > 0) ? 1.0 : -1.0;
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337 | }
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338 | centralMeridian = lonCenter - Math.asin(temp) / b;
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339 | }
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340 |
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341 | /*
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342 | * More coefficients common to all kind of oblique mercator.
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343 | */
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344 | singamma0 = Math.sin(gamma0);
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345 | cosgamma0 = Math.cos(gamma0);
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346 | sinrot = Math.sin(rectifiedGridAngle);
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347 | cosrot = Math.cos(rectifiedGridAngle);
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348 | arb = a / b;
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349 | ab = a * b;
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350 | bra = b / a;
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351 | vPoleN = arb * Math.log(Math.tan(0.5 * (Math.PI/2.0 - gamma0)));
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352 | vPoleS = arb * Math.log(Math.tan(0.5 * (Math.PI/2.0 + gamma0)));
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353 | boolean hotine = params.no_off != null && params.no_off;
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354 | if (hotine) {
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355 | uc = 0.0;
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356 | } else {
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357 | if (Math.abs(Math.abs(azimuth) - Math.PI/2.0) < EPSILON_LATITUDE) {
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358 | // lonCenter == null in twoPoint, but azimuth cannot be 90 here (lat1 != lat2)
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359 | if (lonCenter == null) {
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360 | throw new ProjectionConfigurationException("assertion error");
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361 | }
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362 | uc = a * (lonCenter - centralMeridian);
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363 | } else {
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364 | double uC = Math.abs(arb * Math.atan2(Math.sqrt(d * d - 1.0), Math.cos(azimuth)));
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365 | if (latCenter < 0.0) {
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366 | uC = -uC;
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367 | }
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368 | this.uc = uC;
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369 | }
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370 | }
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371 | }
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372 |
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373 | private static double normalizeLonRad(double a) {
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374 | return Utils.toRadians(LatLon.normalizeLon(Utils.toDegrees(a)));
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375 | }
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376 |
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377 | @Override
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378 | public double[] project(double y, double x) {
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379 | double u, v;
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380 | if (Math.abs(Math.abs(y) - Math.PI/2.0) > EPSILON) {
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381 | double q = g / Math.pow(tsfn(y, Math.sin(y)), b);
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382 | double temp = 1.0 / q;
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383 | double s = 0.5 * (q - temp);
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384 | double v2 = Math.sin(b * x);
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385 | double u2 = (s * singamma0 - v2 * cosgamma0) / (0.5 * (q + temp));
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386 | if (Math.abs(Math.abs(u2) - 1.0) < EPSILON) {
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387 | v = 0; // this is actually an error and should be reported to the caller somehow
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388 | } else {
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389 | v = 0.5 * arb * Math.log((1.0 - u2) / (1.0 + u2));
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390 | }
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391 | temp = Math.cos(b * x);
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392 | if (Math.abs(temp) < EPSILON_LATITUDE) {
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393 | u = ab * x;
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394 | } else {
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395 | u = arb * Math.atan2(s * cosgamma0 + v2 * singamma0, temp);
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396 | }
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397 | } else {
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398 | v = y > 0 ? vPoleN : vPoleS;
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399 | u = arb * y;
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400 | }
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401 | u -= uc;
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402 | x = v * cosrot + u * sinrot;
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403 | y = u * cosrot - v * sinrot;
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404 | return new double[] {x, y};
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405 | }
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406 |
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407 | @Override
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408 | public double[] invproject(double x, double y) {
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409 | double v = x * cosrot - y * sinrot;
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410 | double u = y * cosrot + x * sinrot + uc;
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411 | double qp = Math.exp(-bra * v);
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412 | double temp = 1.0 / qp;
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413 | double sp = 0.5 * (qp - temp);
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414 | double vp = Math.sin(bra * u);
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415 | double up = (vp * cosgamma0 + sp * singamma0) / (0.5 * (qp + temp));
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416 | if (Math.abs(Math.abs(up) - 1.0) < EPSILON) {
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417 | return new double[] {
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418 | up < 0.0 ? -(Math.PI / 2.0) : (Math.PI / 2.0),
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419 | 0.0};
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420 | } else {
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421 | return new double[] {
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422 | cphi2(Math.pow(g / Math.sqrt((1. + up) / (1. - up)), 1.0 / b)), //calculate t
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423 | -Math.atan2(sp * cosgamma0 - vp * singamma0, Math.cos(bra * u)) / b};
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424 | }
|
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425 | }
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426 |
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427 | @Override
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428 | public Bounds getAlgorithmBounds() {
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429 | // The central line of this projection can be oriented in any direction.
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430 | // Moreover, the projection doesn't work too well very far off the central line.
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431 | // This makes it hard to choose proper bounds automatically.
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432 | //
|
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433 | // We return a small box around a reference point. This default box is
|
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434 | // probably too small for most applications. If this is the case, the
|
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435 | // bounds should be configured explicitly.
|
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436 | double lat = referencePoint.lat();
|
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437 | double dLat = 3.0;
|
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438 | double lon = referencePoint.lon() - Utils.toDegrees(centralMeridian);
|
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439 | double dLon = 3.0;
|
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440 | return new Bounds(lat - dLat, lon - dLon, lat + dLat, lon + dLon, false);
|
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441 | }
|
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442 |
|
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443 | @Override
|
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444 | public double getCentralMeridian() {
|
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445 | return Utils.toDegrees(centralMeridian);
|
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446 | }
|
---|
447 | }
|
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