SUBROUTINE iau_PAP ( A, B, THETA ) *+ * - - - - - - - - * i a u _ P A P * - - - - - - - - * * Position-angle from two p-vectors. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: vector/matrix support routine. * * Given: * A d(3) direction of reference point * B d(3) direction of point whose PA is required * * Returned: * THETA d position angle of B with respect to A (radians) * * Notes: * * 1) The result is the position angle, in radians, of direction B with * respect to direction A. It is in the range -pi to +pi. The sense * is such that if B is a small distance "north" of A the position * angle is approximately zero, and if B is a small distance "east" of * A the position angle is approximately +pi/2. * * 2) A and B need not be unit vectors. * * 3) Zero is returned if the two directions are the same or if either * vector is null. * * 4) If A is at a pole, the result is ill-defined. * * Called: * iau_PN decompose p-vector into modulus and direction * iau_PM modulus of p-vector * iau_PXP vector product of two p-vectors * iau_PMP p-vector minus p-vector * iau_PDP scalar product of two p-vectors * * This revision: 2006 November 13 * * SOFA release 2012-03-01 * * Copyright (C) 2012 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION A(3), B(3), THETA DOUBLE PRECISION AM, AU(3), BM, ST, CT, XA, YA, ZA, ETA(3), : XI(3), A2B(3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Modulus and direction of the A vector. CALL iau_PN ( A, AM, AU ) * Modulus of the B vector. CALL iau_PM ( B, BM ) * Deal with the case of a null vector. IF ( AM.EQ.0D0 .OR. BM.EQ.0D0 ) THEN ST = 0D0 CT = 1D0 ELSE * The "north" axis tangential from A (arbitrary length). XA = A(1) YA = A(2) ZA = A(3) ETA(1) = - XA * ZA ETA(2) = - YA * ZA ETA(3) = XA*XA + YA*YA * The "east" axis tangential from A (same length). CALL iau_PXP ( ETA, AU, XI ) * The vector from A to B. CALL iau_PMP ( B, A, A2B ) * Resolve into components along the north and east axes. CALL iau_PDP ( A2B, XI, ST ) CALL iau_PDP ( A2B, ETA, CT ) * Deal with degenerate cases. IF ( ST.EQ.0D0 .AND. CT.EQ.0D0 ) CT = 1D0 END IF * Position angle. THETA = ATAN2(ST,CT) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2012 * 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. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. 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