1 | #include "erfa.h"
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2 |
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3 | int eraGc2gde ( double a, double f, double xyz[3],
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4 | double *elong, double *phi, double *height )
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5 | /*
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6 | ** - - - - - - - - - -
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7 | ** e r a G c 2 g d e
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8 | ** - - - - - - - - - -
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9 | **
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10 | ** Transform geocentric coordinates to geodetic for a reference
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11 | ** ellipsoid of specified form.
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12 | **
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13 | ** Given:
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14 | ** a double equatorial radius (Notes 2,4)
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15 | ** f double flattening (Note 3)
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16 | ** xyz double[3] geocentric vector (Note 4)
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17 | **
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18 | ** Returned:
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19 | ** elong double longitude (radians, east +ve)
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20 | ** phi double latitude (geodetic, radians)
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21 | ** height double height above ellipsoid (geodetic, Note 4)
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22 | **
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23 | ** Returned (function value):
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24 | ** int status: 0 = OK
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25 | ** -1 = illegal f
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26 | ** -2 = illegal a
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27 | **
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28 | ** Notes:
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29 | **
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30 | ** 1) This function is based on the GCONV2H Fortran subroutine by
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31 | ** Toshio Fukushima (see reference).
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32 | **
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33 | ** 2) The equatorial radius, a, can be in any units, but meters is
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34 | ** the conventional choice.
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35 | **
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36 | ** 3) The flattening, f, is (for the Earth) a value around 0.00335,
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37 | ** i.e. around 1/298.
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38 | **
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39 | ** 4) The equatorial radius, a, and the geocentric vector, xyz,
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40 | ** must be given in the same units, and determine the units of
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41 | ** the returned height, height.
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42 | **
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43 | ** 5) If an error occurs (status < 0), elong, phi and height are
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44 | ** unchanged.
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45 | **
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46 | ** 6) The inverse transformation is performed in the function
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47 | ** eraGd2gce.
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48 | **
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49 | ** 7) The transformation for a standard ellipsoid (such as ERFA_WGS84) can
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50 | ** more conveniently be performed by calling eraGc2gd, which uses a
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51 | ** numerical code to identify the required A and F values.
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52 | **
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53 | ** Reference:
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54 | **
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55 | ** Fukushima, T., "Transformation from Cartesian to geodetic
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56 | ** coordinates accelerated by Halley's method", J.Geodesy (2006)
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57 | ** 79: 689-693
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58 | **
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59 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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60 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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61 | */
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62 | {
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63 | double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
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64 | c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
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65 | cc, s12, cc2;
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66 |
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67 |
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68 | /* ------------- */
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69 | /* Preliminaries */
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70 | /* ------------- */
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71 |
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72 | /* Validate ellipsoid parameters. */
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73 | if ( f < 0.0 || f >= 1.0 ) return -1;
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74 | if ( a <= 0.0 ) return -2;
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75 |
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76 | /* Functions of ellipsoid parameters (with further validation of f). */
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77 | aeps2 = a*a * 1e-32;
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78 | e2 = (2.0 - f) * f;
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79 | e4t = e2*e2 * 1.5;
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80 | ec2 = 1.0 - e2;
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81 | if ( ec2 <= 0.0 ) return -1;
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82 | ec = sqrt(ec2);
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83 | b = a * ec;
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84 |
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85 | /* Cartesian components. */
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86 | x = xyz[0];
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87 | y = xyz[1];
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88 | z = xyz[2];
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89 |
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90 | /* Distance from polar axis squared. */
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91 | p2 = x*x + y*y;
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92 |
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93 | /* Longitude. */
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94 | *elong = p2 > 0.0 ? atan2(y, x) : 0.0;
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95 |
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96 | /* Unsigned z-coordinate. */
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97 | absz = fabs(z);
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98 |
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99 | /* Proceed unless polar case. */
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100 | if ( p2 > aeps2 ) {
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101 |
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102 | /* Distance from polar axis. */
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103 | p = sqrt(p2);
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104 |
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105 | /* Normalization. */
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106 | s0 = absz / a;
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107 | pn = p / a;
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108 | zc = ec * s0;
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109 |
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110 | /* Prepare Newton correction factors. */
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111 | c0 = ec * pn;
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112 | c02 = c0 * c0;
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113 | c03 = c02 * c0;
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114 | s02 = s0 * s0;
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115 | s03 = s02 * s0;
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116 | a02 = c02 + s02;
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117 | a0 = sqrt(a02);
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118 | a03 = a02 * a0;
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119 | d0 = zc*a03 + e2*s03;
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120 | f0 = pn*a03 - e2*c03;
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121 |
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122 | /* Prepare Halley correction factor. */
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123 | b0 = e4t * s02 * c02 * pn * (a0 - ec);
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124 | s1 = d0*f0 - b0*s0;
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125 | cc = ec * (f0*f0 - b0*c0);
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126 |
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127 | /* Evaluate latitude and height. */
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128 | *phi = atan(s1/cc);
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129 | s12 = s1 * s1;
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130 | cc2 = cc * cc;
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131 | *height = (p*cc + absz*s1 - a * sqrt(ec2*s12 + cc2)) /
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132 | sqrt(s12 + cc2);
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133 | } else {
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134 |
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135 | /* Exception: pole. */
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136 | *phi = ERFA_DPI / 2.0;
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137 | *height = absz - b;
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138 | }
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139 |
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140 | /* Restore sign of latitude. */
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141 | if ( z < 0 ) *phi = -*phi;
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142 |
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143 | /* OK status. */
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144 | return 0;
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145 |
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146 | }
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147 | /*----------------------------------------------------------------------
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148 | **
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149 | **
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150 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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151 | ** All rights reserved.
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152 | **
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153 | ** This library is derived, with permission, from the International
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154 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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155 | ** available from http://www.iausofa.org.
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156 | **
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157 | ** The ERFA version is intended to retain identical functionality to
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158 | ** the SOFA library, but made distinct through different function and
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159 | ** file names, as set out in the SOFA license conditions. The SOFA
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160 | ** original has a role as a reference standard for the IAU and IERS,
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161 | ** and consequently redistribution is permitted only in its unaltered
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162 | ** state. The ERFA version is not subject to this restriction and
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163 | ** therefore can be included in distributions which do not support the
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164 | ** concept of "read only" software.
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165 | **
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166 | ** Although the intent is to replicate the SOFA API (other than
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167 | ** replacement of prefix names) and results (with the exception of
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168 | ** bugs; any that are discovered will be fixed), SOFA is not
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169 | ** responsible for any errors found in this version of the library.
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170 | **
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171 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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172 | ** that you are using a library derived from SOFA, rather than SOFA
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173 | ** itself.
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174 | **
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175 | **
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176 | ** TERMS AND CONDITIONS
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177 | **
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178 | ** Redistribution and use in source and binary forms, with or without
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179 | ** modification, are permitted provided that the following conditions
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180 | ** are met:
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181 | **
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182 | ** 1 Redistributions of source code must retain the above copyright
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183 | ** notice, this list of conditions and the following disclaimer.
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184 | **
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185 | ** 2 Redistributions in binary form must reproduce the above copyright
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186 | ** notice, this list of conditions and the following disclaimer in
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187 | ** the documentation and/or other materials provided with the
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188 | ** distribution.
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189 | **
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190 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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191 | ** the International Astronomical Union nor the names of its
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192 | ** contributors may be used to endorse or promote products derived
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193 | ** from this software without specific prior written permission.
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194 | **
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195 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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196 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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197 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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198 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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199 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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200 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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201 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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202 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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203 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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204 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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205 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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206 | ** POSSIBILITY OF SUCH DAMAGE.
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207 | **
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208 | */
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