SUBROUTINE sla_DEULER (ORDER, PHI, THETA, PSI, RMAT) *+ * - - - - - - - * D E U L E R * - - - - - - - * * Form a rotation matrix from the Euler angles - three successive * rotations about specified Cartesian axes (double precision) * * Given: * ORDER c*(*) specifies about which axes the rotations occur * PHI d 1st rotation (radians) * THETA d 2nd rotation ( " ) * PSI d 3rd rotation ( " ) * * Returned: * RMAT d(3,3) rotation matrix * * A rotation is positive when the reference frame rotates * anticlockwise as seen looking towards the origin from the * positive region of the specified axis. * * The characters of ORDER define which axes the three successive * rotations are about. A typical value is 'ZXZ', indicating that * RMAT is to become the direction cosine matrix corresponding to * rotations of the reference frame through PHI radians about the * old Z-axis, followed by THETA radians about the resulting X-axis, * then PSI radians about the resulting Z-axis. * * The axis names can be any of the following, in any order or * combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal * axis labelling/numbering conventions apply; the xyz (=123) * triad is right-handed. Thus, the 'ZXZ' example given above * could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ'). ORDER * is terminated by length or by the first unrecognized character. * * Fewer than three rotations are acceptable, in which case the later * angle arguments are ignored. If all rotations are zero, the * identity matrix is produced. * * P.T.Wallace Starlink 23 May 1997 * * Copyright (C) 1997 Rutherford Appleton Laboratory * * License: * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program (see SLA_CONDITIONS); if not, write to the * Free Software Foundation, Inc., 59 Temple Place, Suite 330, * Boston, MA 02111-1307 USA * *- IMPLICIT NONE CHARACTER*(*) ORDER DOUBLE PRECISION PHI,THETA,PSI,RMAT(3,3) INTEGER J,I,L,N,K DOUBLE PRECISION RESULT(3,3),ROTN(3,3),ANGLE,S,C,W,WM(3,3) CHARACTER AXIS * Initialize result matrix DO J=1,3 DO I=1,3 IF (I.NE.J) THEN RESULT(I,J) = 0D0 ELSE RESULT(I,J) = 1D0 END IF END DO END DO * Establish length of axis string L = LEN(ORDER) * Look at each character of axis string until finished DO N=1,3 IF (N.LE.L) THEN * Initialize rotation matrix for the current rotation DO J=1,3 DO I=1,3 IF (I.NE.J) THEN ROTN(I,J) = 0D0 ELSE ROTN(I,J) = 1D0 END IF END DO END DO * Pick up the appropriate Euler angle and take sine & cosine IF (N.EQ.1) THEN ANGLE = PHI ELSE IF (N.EQ.2) THEN ANGLE = THETA ELSE ANGLE = PSI END IF S = SIN(ANGLE) C = COS(ANGLE) * Identify the axis AXIS = ORDER(N:N) IF (AXIS.EQ.'X'.OR. : AXIS.EQ.'x'.OR. : AXIS.EQ.'1') THEN * Matrix for x-rotation ROTN(2,2) = C ROTN(2,3) = S ROTN(3,2) = -S ROTN(3,3) = C ELSE IF (AXIS.EQ.'Y'.OR. : AXIS.EQ.'y'.OR. : AXIS.EQ.'2') THEN * Matrix for y-rotation ROTN(1,1) = C ROTN(1,3) = -S ROTN(3,1) = S ROTN(3,3) = C ELSE IF (AXIS.EQ.'Z'.OR. : AXIS.EQ.'z'.OR. : AXIS.EQ.'3') THEN * Matrix for z-rotation ROTN(1,1) = C ROTN(1,2) = S ROTN(2,1) = -S ROTN(2,2) = C ELSE * Unrecognized character - fake end of string L = 0 END IF * Apply the current rotation (matrix ROTN x matrix RESULT) DO I=1,3 DO J=1,3 W = 0D0 DO K=1,3 W = W+ROTN(I,K)*RESULT(K,J) END DO WM(I,J) = W END DO END DO DO J=1,3 DO I=1,3 RESULT(I,J) = WM(I,J) END DO END DO END IF END DO * Copy the result DO J=1,3 DO I=1,3 RMAT(I,J) = RESULT(I,J) END DO END DO END