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) * * Called: * iau_PN separate 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 * * 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. * * This revision: 2000 December 19 * * Copyright (C) 2001 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) 2001 * 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. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "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 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. * * 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