SUBROUTINE iau_GC2GDE ( A, F, XYZ, ELONG, PHI, HEIGHT, J ) *+ * - - - - - - - - - - - * i a u _ G C 2 G D E * - - - - - - - - - - - * * Transform geocentric coordinates to geodetic for a reference * ellipsoid of specified form. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * A d equatorial radius (Notes 2,4) * F d flattening (Note 3) * XYZ d(3) geocentric vector (Note 4) * * Returned: * ELONG d longitude (radians, east +ve) * PHI d latitude (geodetic, radians) * HEIGHT d height above ellipsoid (geodetic, Note 4) * J i status: 0 = OK * -1 = illegal F * -2 = illegal A * * Notes: * * 1) This routine is closely based on the GCONV2H subroutine by * Toshio Fukushima (see reference). * * 2) The equatorial radius, A, can be in any units, but meters is * the conventional choice. * * 3) The flattening, F, is (for the Earth) a value around 0.00335, * i.e. around 1/298. * * 4) The equatorial radius, A, and the geocentric vector, XYZ, * must be given in the same units, and determine the units of * the returned height, HEIGHT. * * 5) If an error occurs (J<0), ELONG, PHI and HEIGHT are unchanged. * * 6) The inverse transformation is performed in the routine iau_GD2GCE. * * 7) The transformation for a standard ellipsoid (such as WGS84) can * more conveniently be performed by calling iau_GC2GD, which uses a * numerical code (1 for WGS84) to identify the required A and F * values. * * Reference: * * Fukushima, T., "Transformation from Cartesian to geodetic * coordinates accelerated by Halley's method", J.Geodesy (2006) * 79: 689-693 * * This revision: 2014 November 7 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION A, F, XYZ(3), ELONG, PHI, HEIGHT INTEGER J * Pi DOUBLE PRECISION DPI PARAMETER ( DPI = 3.141592653589793238462643D0 ) DOUBLE PRECISION AEPS2, E2, E4T, EC2, EC, B, X, Y, Z, P2, ABSZ, P, : S0, PN, ZC, C0, C02, C03, S02, S03, A02, A0, A03, : D0, F0, B0, S1, CC, S12, CC2 * ------------- * Preliminaries * ------------- * Validate ellipsoid parameters. IF ( F.LT.0D0 .OR. F.GE.1D0 ) THEN J = -1 GO TO 9999 ELSE IF ( A .LE. 0D0 ) THEN J = -2 GO TO 9999 END IF * Functions of ellipsoid parameters (with further validation of F). AEPS2 = A*A*1D-32 E2 = (2D0-F)*F E4T = E2*E2*1.5D0 EC2 = 1D0-E2 IF ( EC2 .LE. 0D0 ) THEN J = -1 GO TO 9999 END IF EC = SQRT(EC2) B = A*EC * Cartesian components. X = XYZ(1) Y = XYZ(2) Z = XYZ(3) * Distance from polar axis squared. P2 = X*X + Y*Y * Longitude. IF ( P2.GT.0D0 ) THEN ELONG = ATAN2(Y,X) ELSE ELONG = 0D0 END IF * Unsigned z-coordinate. ABSZ = ABS(Z) * Proceed unless polar case. IF ( P2.GT.AEPS2 ) THEN * Distance from polar axis. P = SQRT(P2) * Normalization. S0 = ABSZ/A PN = P/A ZC = EC*S0 * Prepare Newton correction factors. C0 = EC*PN C02 = C0*C0 C03 = C02*C0 S02 = S0*S0 S03 = S02*S0 A02 = C02+S02 A0 = SQRT(A02) A03 = A02*A0 D0 = ZC*A03 + E2*S03 F0 = PN*A03 - E2*C03 * Prepare Halley correction factor. B0 = E4T*S02*C02*PN*(A0-EC) S1 = D0*F0 - B0*S0 CC = EC*(F0*F0-B0*C0) * Evaluate latitude and height. PHI = ATAN(S1/CC) S12 = S1*S1 CC2 = CC*CC HEIGHT = (P*CC+ABSZ*S1-A*SQRT(EC2*S12+CC2))/SQRT(S12+CC2) ELSE * Exception: pole. PHI = DPI/2D0 HEIGHT = ABSZ-B END IF * Restore sign of latitude. IF ( Z.LT.0D0 ) PHI = -PHI * OK status. J = 0 * Finished. 9999 CONTINUE *+---------------------------------------------------------------------- * * Copyright (C) 2023 * Standards of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. 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The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END