{"id":782,"date":"2020-02-06T18:13:53","date_gmt":"2020-02-06T22:13:53","guid":{"rendered":"https:\/\/www2.whoi.edu\/site\/aomip\/?page_id=782"},"modified":"2021-06-18T09:26:49","modified_gmt":"2021-06-18T13:26:49","slug":"euler-rotation-fortran-code","status":"publish","type":"page","link":"https:\/\/www2.whoi.edu\/site\/aomip\/models\/euler-rotation-fortran-code\/","title":{"rendered":"Euler Rotation – Fortran Code"},"content":{"rendered":"\n\n\t

Euler Rotation – Fortran Code<\/h1>\n

Fortran Module<\/h2>\n

MODULE C_MODULE_EULER_ROTATION<\/p>\n!———————————————————————–
\n! euler rotation of model geometry
\n!———————————————————————–
\n!
\n! C_ALPHA : rotation about z-axis
\n! C_BETA\u00a0 : rotation about new y-axis
\n! C_GAMMA : rotation about new z-axis
\n!
\n! C_FORWARD : rotation matricies to geographic coordinates
\n! C_REVERSE : rotation matricies to model coordinates
\n!
\n!———————————————————————–\nREAL (TYPE_REAL_8) ::
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 C_ALPHA\u00a0 = 000.0\nREAL (TYPE_REAL_8) ::
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 C_BETA\u00a0\u00a0 = 000.0\nREAL (TYPE_REAL_8) ::
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 C_GAMMA\u00a0 = 000.0\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 DIMENSION (1:3, 1:3) ::
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 C_FORWARD = 0.0\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 DIMENSION (1:3, 1:3) ::
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 C_REVERSE = 0.0\n

!———————————————————————–<\/p>\n

END MODULE C_MODULE_EULER_ROTATION<\/p>\n

Euler Matrix<\/h2>\n

SUBROUTINE C_EULER_ROTATION_MATRIX<\/p>\n!———————————————————————–
\n! purpose: compute euler rotation matrix
\n!———————————————————————–
\n!
\n! C_ALPHA\u00a0\u00a0 : rotation about z-axis
\n! C_BETA\u00a0\u00a0\u00a0 : rotation about new y-axis
\n! C_GAMMA\u00a0\u00a0 : rotation about new z-axis
\n! C_REVERSE : rotation to model coordinates
\n! C_FORWARD : rotation to geographic coordinates
\n!
\n!———————————————————————–\n!local vars
\nREAL (TYPE_REAL_8) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 COSA,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 SINA,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 COSB,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 SINB,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 COSG,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 SING\n

!———————————————————————–<\/p>\n!compute sin and cos of all angles in degrees
\nCOSA\u00a0 = C_COSD (C_ALPHA )
\nSINA\u00a0 = C_SIND (C_ALPHA )
\nCOSB\u00a0 = C_COSD (C_BETA\u00a0 )
\nSINB\u00a0 = C_SIND (C_BETA\u00a0 )
\nCOSG\u00a0 = C_COSD (C_GAMMA )
\nSING\u00a0 = C_SIND (C_GAMMA )\n!compute rotation matrix into model coordinates
\nC_REVERSE (1,1) =\u00a0\u00a0 COSA * COSB * COSG\u00a0 –\u00a0 SINA * SING
\nC_REVERSE (1,2) =\u00a0\u00a0 SINA * COSB * COSG\u00a0 +\u00a0 COSA * SING
\nC_REVERSE (1,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – SINB * COSG
\nC_REVERSE (2,1) = – COSA * COSB * SING\u00a0 –\u00a0 SINA * COSG
\nC_REVERSE (2,2) = – SINA * COSB * SING\u00a0 +\u00a0 COSA * COSG
\nC_REVERSE (2,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SINB * SING
\nC_REVERSE (3,1) =\u00a0\u00a0 COSA * SINB
\nC_REVERSE (3,2) =\u00a0\u00a0 SINA * SINB
\nC_REVERSE (3,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 COSB\n!compute rotation matrix into geographical coordinates
\nC_FORWARD (1,1) =\u00a0\u00a0 COSG * COSB * COSA\u00a0 –\u00a0 SING * SINA
\nC_FORWARD (1,2) = – SING * COSB * COSA\u00a0 –\u00a0 COSG * SINA
\nC_FORWARD (1,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SINB * COSA
\nC_FORWARD (2,1) =\u00a0\u00a0 COSG * COSB * SINA\u00a0 +\u00a0 SING * COSA
\nC_FORWARD (2,2) = – SING * COSB * SINA\u00a0 +\u00a0 COSG * COSA
\nC_FORWARD (2,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SINB * SINA
\nC_FORWARD (3,1) = – COSG * SINB
\nC_FORWARD (3,2) =\u00a0\u00a0 SING * SINB
\nC_FORWARD (3,3) =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 COSB\n

!———————————————————————–<\/p>\n

END SUBROUTINE C_EULER_ROTATION_MATRIX<\/p>\n

Native-Grid -> AOMIP-Grid<\/h2>\nSUBROUTINE C_GEO_TO_MODEL (X_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Y_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X_OUT_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Y_OUT_ANGLE)\n!——————————————————————–
\n! purpose: a coordinate transformation from geographic coordinates
\n!\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 to model coordinates
\n!——————————————————————–
\n!
\n! variables
\n!
\n! X_IN_ANGLE\u00a0 : X-COORDINATE IN GEOGRAPHICAL SYSTEM.
\n! Y_IN_ANGLE\u00a0 : Y-COORDINATE IN GEOGRAPHICAL SYSTEM.
\n! X_OUT_ANGLE : X-COORDINATE IN MODEL SYSTEM.
\n! Y_OUT_ANGLE : Y-COORDINATE IN MODEL SYSTEM.
\n!
\n!———————————————————————\n!passed arguments
\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 INTENT (IN) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_IN_ANGLE\n!passed arguments
\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 INTENT (OUT) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_OUT_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_OUT_ANGLE\n!local vars
\nREAL (TYPE_REAL_8) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_TMP_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_TMP_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 XX,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 YY,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 ZZ,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 XNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 YNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 ZNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 COSTN,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 PHI_NEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 THETA_NEW\n

!———————————————————————<\/p>\n!initial angles of rotation
\nX_TMP_ANGLE = X_IN_ANGLE
\nY_TMP_ANGLE = Y_IN_ANGLE\n!avoid trouble of an exactly zero angle by adding offset
\nX_TMP_ANGLE = X_TMP_ANGLE + C_EPSILON
\nY_TMP_ANGLE = Y_TMP_ANGLE + C_EPSILON\n!spherical to cartesian
\nXX = C_COSD (Y_TMP_ANGLE) * C_COSD (X_TMP_ANGLE)
\nYY = C_COSD (Y_TMP_ANGLE) * C_SIND (X_TMP_ANGLE)
\nZZ = C_SIND (Y_TMP_ANGLE)\n!new cartesian coordinates are given by
\nXNEW = C_REVERSE (1,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (1,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (1,3) * ZZ
\nYNEW = C_REVERSE (2,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (2,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (2,3) * ZZ
\nZNEW = C_REVERSE (3,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (3,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_REVERSE (3,3) * ZZ\nTHETA_NEW\u00a0 = C_INV_SIND (ZNEW)
\nCOSTN = SQRT (1.0 – ZNEW ** 2)\n

IF ((XNEW > 0.0).AND.(YNEW > 0.0)) THEN<\/p>\nIF (XNEW < YNEW) THEN
\nPHI_NEW= C_INV_COSD (XNEW\/COSTN)
\nELSE
\nPHI_NEW= C_INV_SIND (YNEW\/COSTN)
\nENDIF\n

ELSEIF ((XNEW < 0.0).AND.(YNEW > 0.0)) THEN<\/p>\nIF (ABS(XNEW) < YNEW) THEN
\nPHI_NEW = 180.0 – C_INV_COSD (ABS(XNEW)\/COSTN)
\nELSE
\nPHI_NEW = 180.0 – C_INV_SIND (YNEW\/COSTN)
\nENDIF\n

ELSEIF ((XNEW < 0.0).AND.(YNEW < 0.0)) THEN<\/p>\nIF (ABS(XNEW) < ABS(YNEW)) THEN
\nPHI_NEW =-180.0 + C_INV_COSD (ABS(XNEW)\/COSTN)
\nELSE
\nPHI_NEW =-180.0 + C_INV_SIND (ABS(YNEW)\/COSTN)
\nENDIF\n

ELSEIF ((XNEW > 0.0) .AND. (YNEW < 0.0)) THEN<\/p>\nIF (\u00a0\u00a0\u00a0 XNEW\u00a0 < ABS(YNEW)) THEN
\nPHI_NEW =-C_INV_COSD (ABS(XNEW)\/COSTN)
\nELSE
\nPHI_NEW =-C_INV_SIND (ABS(YNEW)\/COSTN)
\nENDIF\n

ENDIF<\/p>\n!new spherical coordinates are
\nY_OUT_ANGLE = THETA_NEW
\nX_OUT_ANGLE = PHI_NEW\n

IF (X_OUT_ANGLE < 0.0) X_OUT_ANGLE = X_OUT_ANGLE + 360.0<\/p>\n!avoid trouble of an exactly zero angle by subtracting offset
\nX_OUT_ANGLE = X_OUT_ANGLE – C_EPSILON
\nY_OUT_ANGLE = Y_OUT_ANGLE – C_EPSILON\n

!———————————————————————<\/p>\n

END SUBROUTINE C_GEO_TO_MODEL<\/p>\n

AOMIP-Grid -> Native_Grid<\/h2>\nSUBROUTINE C_MODEL_TO_GEO (X_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Y_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 X_OUT_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Y_OUT_ANGLE)\n!———————————————————————
\n! purpose: a coordinate trnansformation from model coordinates
\n!\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 to geographic coordinates
\n!——————————————————————–
\n!
\n! variables
\n!
\n! X_IN_ANGLE\u00a0 : X-COORDINATE IN MODEL SYSTEM.
\n! Y_IN_ANGLE\u00a0 : Y-COORDINATE IN MODEL SYSTEM.
\n! X_OUT_ANGLE : X-COORDINATE IN GEOGRAPHICAL SYSTEM.
\n! Y_OUT_ANGLE : Y-COORDINATE IN GEOGRAPHICAL SYSTEM.
\n!
\n! THE ROTATION FROM THE COORDINATE SYSTEM,
\n! X”’,Y”’,Z”’ BACK TO THE ORIGINAL COORDINATE SYTEM
\n! CAN BE PERFORMED BY DOING THE ROTATION IN
\n! REVERSED ORDER AND WITH OPPOSITE SIGN ON THE ROTATED ANGLES.
\n!
\n!———————————————————————\n!passed arguments
\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 INTENT (IN) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_IN_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_IN_ANGLE\n!passed arguments
\nREAL (TYPE_REAL_8),
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 INTENT (OUT) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_OUT_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_OUT_ANGLE\n!local vars
\nREAL (TYPE_REAL_8) ::
\n&
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 X_TMP_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 Y_TMP_ANGLE,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 XX,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 YY,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 ZZ,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 XNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 YNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 ZNEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 COSTN,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 PHI_NEW,
\n&\u00a0\u00a0\u00a0\u00a0\u00a0 THETA_NEW\n

!———————————————————————<\/p>\n!initial angles of rotation
\nX_TMP_ANGLE = X_IN_ANGLE
\nY_TMP_ANGLE = Y_IN_ANGLE\n!avoid trouble of an exactly zero angle by adding offset
\nX_TMP_ANGLE = X_TMP_ANGLE + C_EPSILON
\nY_TMP_ANGLE = Y_TMP_ANGLE + C_EPSILON\n!spherical coordiantes to cartesian coordinates
\nXX = C_COSD (Y_TMP_ANGLE) * C_COSD (X_TMP_ANGLE)
\nYY = C_COSD (Y_TMP_ANGLE) * C_SIND (X_TMP_ANGLE)
\nZZ = C_SIND (Y_TMP_ANGLE)\n!new cartesian coordinates are given by
\nXNEW = C_FORWARD (1,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (1,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (1,3) * ZZ
\nYNEW = C_FORWARD (2,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (2,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (2,3) * ZZ
\nZNEW = C_FORWARD (3,1) * XX
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (3,2) * YY
\n&\u00a0\u00a0\u00a0\u00a0 + C_FORWARD (3,3) * ZZ\n!obtain new angles THETA_NEW,COSTN,PHI_NEW
\nTHETA_NEW\u00a0 = C_INV_SIND (ZNEW)
\nCOSTN = SQRT (1.0 – ZNEW**2)\n

IF\u00a0\u00a0\u00a0 ((XNEW > 0.0) .AND. (YNEW > 0.0)) THEN<\/p>\nIF (XNEW < YNEW) THEN
\nPHI_NEW = C_INV_COSD (XNEW\/COSTN)
\nELSE
\nPHI_NEW = C_INV_SIND (YNEW\/COSTN)
\nENDIF\n

ELSEIF ((XNEW < 0.0) .AND. (YNEW > 0.0)) THEN<\/p>\nIF (ABS (XNEW) < YNEW) THEN
\nPHI_NEW = 180.0 – C_INV_COSD (ABS (XNEW)\/COSTN)
\nELSE
\nPHI_NEW = 180.0 – C_INV_SIND (YNEW\/COSTN)
\nENDIF\n

ELSEIF ((XNEW < 0.0) .AND. (YNEW < 0.0)) THEN<\/p>\nIF (ABS (XNEW) < ABS (YNEW)) THEN
\nPHI_NEW =-180.0 + C_INV_COSD (ABS (XNEW)\/COSTN)
\nELSE
\nPHI_NEW =-180.0 + C_INV_SIND (ABS (YNEW)\/COSTN)
\nENDIF\n

ELSEIF ((XNEW > 0.0) .AND. (YNEW < 0.0)) THEN<\/p>\nIF(\u00a0\u00a0\u00a0 XNEW\u00a0 < ABS (YNEW)) THEN
\nPHI_NEW =\u00a0\u00a0\u00a0 – C_INV_COSD (ABS (XNEW)\/COSTN)
\nELSE
\nPHI_NEW =\u00a0\u00a0\u00a0 – C_INV_SIND (ABS (YNEW)\/COSTN)
\nENDIF\n

ENDIF<\/p>\n!new spherical coordinates
\nX_OUT_ANGLE = PHI_NEW
\nY_OUT_ANGLE = THETA_NEW\n

IF (X_OUT_ANGLE < 0.0) X_OUT_ANGLE = X_OUT_ANGLE + 360.0<\/p>\n!avoid trouble of an exactly zero angle by subtracting offset
\nX_OUT_ANGLE = X_OUT_ANGLE – C_EPSILON
\nY_OUT_ANGLE = Y_OUT_ANGLE – C_EPSILON\n

!———————————————————————–<\/p>\n

END SUBROUTINE C_MODEL_TO_GEO<\/p>\n\n","protected":false},"excerpt":{"rendered":"

Euler Rotation – Fortran Code Fortran Module MODULE C_MODULE_EULER_ROTATION !———————————————————————– ! euler rotation of model geometry !———————————————————————– ! ! C_ALPHA : rotation about z-axis ! C_BETA\u00a0 : rotation about new y-axis ! C_GAMMA : rotation about new z-axis ! ! C_FORWARD : rotation matricies to geographic coordinates ! C_REVERSE : rotation matricies to model coordinates…<\/p>\n","protected":false},"author":83,"featured_media":0,"parent":628,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"tpl-sidebar.php","meta":{"advanced-sidebar-menu\/link-title":"","advanced-sidebar-menu\/exclude-page":false},"_links":{"self":[{"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/pages\/782"}],"collection":[{"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/users\/83"}],"replies":[{"embeddable":true,"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/comments?post=782"}],"version-history":[{"count":3,"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/pages\/782\/revisions"}],"predecessor-version":[{"id":1687,"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/pages\/782\/revisions\/1687"}],"up":[{"embeddable":true,"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/pages\/628"}],"wp:attachment":[{"href":"https:\/\/www2.whoi.edu\/site\/aomip\/wp-json\/wp\/v2\/media?parent=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}