SUBROUTINE iau_RV2M ( W, R ) *+ * - - - - - - - - - * i a u _ R V 2 M * - - - - - - - - - * * Form the r-matrix corresponding to a given r-vector. * * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: vector/matrix support routine. * * Given: * W d(3) rotation vector (Note 1) * * Returned: * R d(3,3) rotation matrix * * Notes: * * 1) A rotation matrix describes a rotation about some arbitrary axis. * The axis is called the Euler axis, and the angle through which * the reference frame rotates is called the Euler angle. The * "rotation vector" supplied to this routine has the same direction * as the Euler axis, and its magnitude is the Euler angle in * radians. * * 2) If W is null, the unit matrix is returned. * * 3) The reference frame rotates clockwise as seen looking along * the rotation vector from the origin. * * This revision: 2000 November 25 * * Copyright (C) 2001 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION W(3), R(3,3) DOUBLE PRECISION X, Y, Z, PHI, S, C, F * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Euler angle (magnitude of rotation vector) and functions. X = W(1) Y = W(2) Z = W(3) PHI = SQRT(X*X + Y*Y + Z*Z) S = SIN(PHI) C = COS(PHI) F = 1D0 - C * Euler axis (direction of rotation vector), perhaps null. IF ( PHI .NE. 0D0 ) THEN X = X / PHI Y = Y / PHI Z = Z / PHI END IF * Form the rotation matrix. R(1,1) = X*X*F + C R(1,2) = X*Y*F + Z*S R(1,3) = X*Z*F - Y*S R(2,1) = X*Y*F - Z*S R(2,2) = Y*Y*F + C R(2,3) = Y*Z*F + X*S R(3,1) = X*Z*F + Y*S R(3,2) = Y*Z*F - X*S R(3,3) = Z*Z*F + C * 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