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 * * Copyright (C) 2008 IAU SOFA Review 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) 2008 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 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 adapt the SOFA software and its * algorithms for your own purposes and you may copy and distribute * a resulting "derived work" to others on a world-wide, royalty-free * basis, provided that the derived work complies 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 contain * software provided by SOFA or software that has been distributed * by or endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon and/or differs from the * original SOFA software. * * c) The name(s) of all routine(s) that you distribute shall differ * from the SOFA names, even when the SOFA content has not been * otherwise changed. * * d) The routine-naming prefix "iau" shall not be used. * * e) 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. * * f) 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. * * 4. In any published work or commercial products which includes * results achieved by using the SOFA software, you shall acknowledge * that the SOFA software was used in obtaining those results. * * 5. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 6. The SOFA software is provided "as is" and the Board makes no * warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may obtain * by using the SOFA software. The Board 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 the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * 7. 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. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * *----------------------------------------------------------------------- END