Fixed bug in math rotations: passive and active rotations were not clearly distinguished and partly mixed up; yet, luckily, only resulted in wrong output of euler angles.
Now fixed with following convention: Rotation conversions do not switch implicitly from active to passive or vice versa EXCEPT when converting to or from any "Euler" type (Euler angles or Euler axis/angles). Those functions expect a passive rotation as input if converting to Euler type and return a passive rotation if converting from Euler type.
This commit is contained in:
Christoph Kords
parent
becacb675a
commit
622e2dcf15
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@ -1504,6 +1504,8 @@ subroutine IO_error(error_ID,e,i,g,ext_msg)
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msg = 'Dimension in nearest neigbor search wrong'
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case (408_pInt)
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msg = 'Polar decomposition error'
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case (409_pInt)
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msg = 'math_check: R*v == q*v failed'
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case (450_pInt)
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msg = 'unknown symmetry type specified'
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case (460_pInt)
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296
code/math.f90
296
code/math.f90
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@ -31,7 +31,7 @@ module math
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pInt
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implicit none
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public ! because FFTW is included in math.f90
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private ! because FFTW is included in math.f90
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real(pReal), parameter, public :: PI = 3.14159265358979323846264338327950288419716939937510_pReal !< ratio of a circle's circumference to its diameter
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real(pReal), parameter, public :: INDEG = 180.0_pReal/PI !< conversion from radian into degree
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real(pReal), parameter, public :: INRAD = PI/180.0_pReal !< conversion from degree into radian
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@ -196,10 +196,13 @@ real(pReal), dimension(4,36), parameter, private :: &
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math_RtoQ, &
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math_EulerToR, &
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math_EulerToQ, &
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math_AxisAngleToR, &
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math_AxisAngleToQ, &
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math_EulerAxisAngleToR, &
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math_axisAngleToR, &
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math_EulerAxisAngleToQ, &
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math_axisAngleToQ, &
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math_qToRodrig, &
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math_qToEuler, &
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math_qToEulerAxisAngle, &
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math_qToAxisAngle, &
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math_qToR, &
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math_EulerMisorientation, &
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@ -261,7 +264,7 @@ subroutine math_init
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implicit none
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integer(pInt) :: i
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real(pReal), dimension(3,3) :: R,R2
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real(pReal), dimension(3) :: Eulers
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real(pReal), dimension(3) :: Eulers,v
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real(pReal), dimension(4) :: q,q2,axisangle,randTest
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! the following variables are system dependend and shound NOT be pInt
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integer :: randSize ! gfortran requires a variable length to compile
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@ -305,10 +308,11 @@ subroutine math_init
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! --- check rotation dictionary ---
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q = math_qRand() ! random quaternion
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! +++ q -> a -> q +++
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q = math_qRand();
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axisangle = math_qToAxisAngle(q);
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q2 = math_AxisAngleToQ(axisangle(1:3),axisangle(4))
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axisangle = math_qToAxisAngle(q)
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q2 = math_axisAngleToQ(axisangle(1:3),axisangle(4))
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if ( any(abs( q-q2) > tol_math_check) .and. &
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any(abs(-q-q2) > tol_math_check) ) then
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write (error_msg, '(a,e14.6)' ) 'maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2)))
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@ -316,8 +320,8 @@ subroutine math_init
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endif
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! +++ q -> R -> q +++
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R = math_qToR(q);
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q2 = math_RToQ(R)
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R = math_qToR(q)
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q2 = math_RtoQ(R)
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if ( any(abs( q-q2) > tol_math_check) .and. &
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any(abs(-q-q2) > tol_math_check) ) then
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write (error_msg, '(a,e14.6)' ) 'maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2)))
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@ -325,7 +329,7 @@ subroutine math_init
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endif
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! +++ q -> euler -> q +++
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Eulers = math_qToEuler(q);
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Eulers = math_qToEuler(q)
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q2 = math_EulerToQ(Eulers)
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if ( any(abs( q-q2) > tol_math_check) .and. &
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any(abs(-q-q2) > tol_math_check) ) then
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@ -334,13 +338,23 @@ subroutine math_init
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endif
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! +++ R -> euler -> R +++
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Eulers = math_RToEuler(R);
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Eulers = math_RtoEuler(R)
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R2 = math_EulerToR(Eulers)
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if ( any(abs( R-R2) > tol_math_check) ) then
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write (error_msg, '(a,e14.6)' ) 'maximum deviation ',maxval(abs( R-R2))
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call IO_error(404_pInt,ext_msg=error_msg)
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endif
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! +++ check rotation sense of q and R +++
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q = math_qRand() ! random quaternion
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call halton(3_pInt,v) ! random vector
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R = math_qToR(q)
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if (any(abs(math_mul33x3(R,v) - math_qRot(q,v)) > tol_math_check)) then
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write(6,'(a,4(f8.3,x))') 'q',q
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call IO_error(409_pInt)
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endif
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end subroutine math_init
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@ -1365,8 +1379,14 @@ pure function math_qRot(Q,v)
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math_qRot = 2.0_pReal * math_qRot + v
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end function math_qRot
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!--------------------------------------------------------------------------------------------------
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!> @brief Euler angles (in radians) from rotation matrix
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!> @details rotation matrix is meant to represent a PASSIVE rotation,
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!> composed of INTRINSIC rotations around the axes of the
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!> rotating reference frame
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!> (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!--------------------------------------------------------------------------------------------------
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pure function math_RtoEuler(R)
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@ -1418,56 +1438,55 @@ end function math_RtoEuler
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!--------------------------------------------------------------------------------------------------
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!> @brief quaternion (w+ix+jy+kz) from orientation matrix
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!> @details math adopted from
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!> @details http://code.google.com/p/mtex/source/browse/trunk/geometry/geometry_tools/mat2quat.m
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!> @brief converts a rotation matrix into a quaternion (w+ix+jy+kz)
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!> @details math adopted from http://arxiv.org/pdf/math/0701759v1.pdf
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!--------------------------------------------------------------------------------------------------
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pure function math_RtoQ(R)
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implicit none
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real(pReal), dimension (3,3), intent(in) :: R
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real(pReal), dimension(3,3), intent(in) :: R
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real(pReal), dimension(4) :: absQ, math_RtoQ
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real(pReal) :: max_absQ
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integer, dimension(1) :: largest !no pInt, maxloc returns integer default
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absQ(1) = 1.0_pReal+R(1,1)+R(2,2)+R(3,3)
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absQ(2) = 1.0_pReal+R(1,1)-R(2,2)-R(3,3)
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absQ(3) = 1.0_pReal-R(1,1)+R(2,2)-R(3,3)
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absQ(4) = 1.0_pReal-R(1,1)-R(2,2)+R(3,3)
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math_RtoQ = 0.0_pReal
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absQ(1) = 1.0_pReal + R(1,1) + R(2,2) + R(3,3)
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absQ(2) = 1.0_pReal + R(1,1) - R(2,2) - R(3,3)
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absQ(3) = 1.0_pReal - R(1,1) + R(2,2) - R(3,3)
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absQ(4) = 1.0_pReal - R(1,1) - R(2,2) + R(3,3)
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largest = maxloc(absQ)
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max_absQ=0.5_pReal * sqrt(absQ(largest(1)))
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select case(largest(1))
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case (1_pInt)
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case (1)
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!1----------------------------------
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math_RtoQ(2) = R(2,3)-R(3,2)
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math_RtoQ(3) = R(3,1)-R(1,3)
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math_RtoQ(4) = R(1,2)-R(2,1)
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case (2_pInt)
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math_RtoQ(1) = R(2,3)-R(3,2)
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math_RtoQ(2) = R(3,2) - R(2,3)
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math_RtoQ(3) = R(1,3) - R(3,1)
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math_RtoQ(4) = R(2,1) - R(1,2)
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case (2)
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math_RtoQ(1) = R(3,2) - R(2,3)
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!2----------------------------------
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math_RtoQ(3) = R(1,2)+R(2,1)
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math_RtoQ(4) = R(3,1)+R(1,3)
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case (3_pInt)
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math_RtoQ(1) = R(3,1)-R(1,3)
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math_RtoQ(2) = R(1,2)+R(2,1)
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math_RtoQ(3) = R(2,1) + R(1,2)
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math_RtoQ(4) = R(1,3) + R(3,1)
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case (3)
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math_RtoQ(1) = R(1,3) - R(3,1)
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math_RtoQ(2) = R(2,1) + R(1,2)
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!3----------------------------------
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math_RtoQ(4) = R(2,3)+R(3,2)
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case (4_pInt)
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math_RtoQ (1) = R(1,2)-R(2,1)
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math_RtoQ (2) = R(3,1)+R(1,3)
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math_RtoQ (3) = R(3,2)+R(2,3)
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math_RtoQ(4) = R(3,2) + R(2,3)
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case (4)
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math_RtoQ(1) = R(2,1) - R(1,2)
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math_RtoQ(2) = R(1,3) + R(3,1)
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math_RtoQ(3) = R(2,3) + R(3,2)
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!4----------------------------------
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end select
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math_RtoQ = math_RtoQ*0.25_pReal/max_absQ
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max_absQ = 0.5_pReal * sqrt(absQ(largest(1)))
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math_RtoQ = math_RtoQ * 0.25_pReal / max_absQ
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math_RtoQ(largest(1)) = max_absQ
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end function math_RtoQ
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@ -1475,6 +1494,10 @@ end function math_RtoQ
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!--------------------------------------------------------------------------------------------------
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!> @brief rotation matrix from Euler angles (in radians)
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!> @details rotation matrix is meant to represent a PASSIVE rotation,
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!> @details composed of INTRINSIC rotations around the axes of the
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!> @details rotating reference frame
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!--------------------------------------------------------------------------------------------------
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pure function math_EulerToR(Euler)
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@ -1492,20 +1515,26 @@ pure function math_EulerToR(Euler)
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S2 = sin(Euler(3))
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math_EulerToR(1,1)=C1*C2-S1*S2*C
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math_EulerToR(1,2)=S1*C2+C1*S2*C
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math_EulerToR(1,3)=S2*S
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math_EulerToR(2,1)=-C1*S2-S1*C2*C
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math_EulerToR(1,2)=-C1*S2-S1*C2*C
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math_EulerToR(1,3)=S1*S
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math_EulerToR(2,1)=S1*C2+C1*S2*C
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math_EulerToR(2,2)=-S1*S2+C1*C2*C
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math_EulerToR(2,3)=C2*S
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math_EulerToR(3,1)=S1*S
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math_EulerToR(3,2)=-C1*S
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math_EulerToR(2,3)=-C1*S
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math_EulerToR(3,1)=S2*S
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math_EulerToR(3,2)=C2*S
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math_EulerToR(3,3)=C
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math_EulerToR = transpose(math_EulerToR) ! convert to passive rotation
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end function math_EulerToR
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!--------------------------------------------------------------------------------------------------
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!> @brief quaternion (w+ix+jy+kz) from 3-1-3 Euler angles (in radians)
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!> @details quaternion is meant to represent a PASSIVE rotation,
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!> @details composed of INTRINSIC rotations around the axes of the
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!> @details rotating reference frame
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!--------------------------------------------------------------------------------------------------
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pure function math_EulerToQ(eulerangles)
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@ -1525,17 +1554,21 @@ pure function math_EulerToQ(eulerangles)
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math_EulerToQ(2) = cos(halfangles(1)-halfangles(3)) * s
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math_EulerToQ(3) = sin(halfangles(1)-halfangles(3)) * s
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math_EulerToQ(4) = sin(halfangles(1)+halfangles(3)) * c
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math_EulerToQ = math_qConj(math_EulerToQ) ! convert to passive rotation
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end function math_EulerToQ
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!--------------------------------------------------------------------------------------------------
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!> @brief rotation matrix from axis and angle (in radians)
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!> @details rotation matrix is meant to represent a ACTIVE rotation
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!> @details formula for active rotation taken from http://mathworld.wolfram.com/RodriguesRotationFormula.html
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!--------------------------------------------------------------------------------------------------
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pure function math_AxisAngleToR(axis,omega)
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pure function math_axisAngleToR(axis,omega)
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implicit none
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real(pReal), dimension(3,3) :: math_AxisAngleToR
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real(pReal), dimension(3,3) :: math_axisAngleToR
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real(pReal), dimension(3), intent(in) :: axis
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real(pReal), intent(in) :: omega
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real(pReal), dimension(3) :: axisNrm
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@ -1549,35 +1582,71 @@ pure function math_AxisAngleToR(axis,omega)
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c = cos(omega)
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c1 = 1.0_pReal - c
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! formula for active rotation taken from http://mathworld.wolfram.com/RodriguesRotationFormula.html
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! below is transposed form to get passive rotation
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math_AxisAngleToR(1,1) = c + c1*axisNrm(1)**2.0_pReal
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math_AxisAngleToR(2,1) = -s*axisNrm(3) + c1*axisNrm(1)*axisNrm(2)
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math_AxisAngleToR(3,1) = s*axisNrm(2) + c1*axisNrm(1)*axisNrm(3)
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math_AxisAngleToR(1,2) = s*axisNrm(3) + c1*axisNrm(2)*axisNrm(1)
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math_AxisAngleToR(2,2) = c + c1*axisNrm(2)**2.0_pReal
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math_AxisAngleToR(3,2) = -s*axisNrm(1) + c1*axisNrm(2)*axisNrm(3)
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math_AxisAngleToR(1,3) = -s*axisNrm(2) + c1*axisNrm(3)*axisNrm(1)
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math_AxisAngleToR(2,3) = s*axisNrm(1) + c1*axisNrm(3)*axisNrm(2)
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math_AxisAngleToR(3,3) = c + c1*axisNrm(3)**2.0_pReal
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math_axisAngleToR(1,1) = c + c1*axisNrm(1)**2.0_pReal
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math_axisAngleToR(1,2) = -s*axisNrm(3) + c1*axisNrm(1)*axisNrm(2)
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math_axisAngleToR(1,3) = s*axisNrm(2) + c1*axisNrm(1)*axisNrm(3)
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math_axisAngleToR(2,1) = s*axisNrm(3) + c1*axisNrm(2)*axisNrm(1)
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math_axisAngleToR(2,2) = c + c1*axisNrm(2)**2.0_pReal
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math_axisAngleToR(2,3) = -s*axisNrm(1) + c1*axisNrm(2)*axisNrm(3)
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math_axisAngleToR(3,1) = -s*axisNrm(2) + c1*axisNrm(3)*axisNrm(1)
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math_axisAngleToR(3,2) = s*axisNrm(1) + c1*axisNrm(3)*axisNrm(2)
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math_axisAngleToR(3,3) = c + c1*axisNrm(3)**2.0_pReal
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else
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math_AxisAngleToR = math_I3
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math_axisAngleToR = math_I3
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endif
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end function math_axisAngleToR
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end function math_AxisAngleToR
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!--------------------------------------------------------------------------------------------------
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!> @brief rotation matrix from axis and angle (in radians)
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!> @details rotation matrix is meant to represent a PASSIVE rotation
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!--------------------------------------------------------------------------------------------------
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pure function math_EulerAxisAngleToR(axis,omega)
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implicit none
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real(pReal), dimension(3,3) :: math_EulerAxisAngleToR
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real(pReal), dimension(3), intent(in) :: axis
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real(pReal), intent(in) :: omega
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math_EulerAxisAngleToR = transpose(math_axisAngleToR(axis,omega)) ! convert to passive rotation
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end function math_EulerAxisAngleToR
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!--------------------------------------------------------------------------------------------------
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!> @brief quaternion (w+ix+jy+kz) from Euler axis and angle (in radians)
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!> @details quaternion is meant to represent a PASSIVE rotation
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!> @details formula for active rotation taken from
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!> @details http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
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!--------------------------------------------------------------------------------------------------
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pure function math_EulerAxisAngleToQ(axis,omega)
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implicit none
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real(pReal), dimension(4) :: math_EulerAxisAngleToQ
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real(pReal), dimension(3), intent(in) :: axis
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real(pReal), intent(in) :: omega
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math_EulerAxisAngleToQ = math_qConj(math_axisAngleToQ(axis,omega)) ! convert to passive rotation
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end function math_EulerAxisAngleToQ
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!--------------------------------------------------------------------------------------------------
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!> @brief quaternion (w+ix+jy+kz) from axis and angle (in radians)
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!> @details quaternion is meant to represent an ACTIVE rotation
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!> @details formula for active rotation taken from
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!> @details http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
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!--------------------------------------------------------------------------------------------------
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pure function math_AxisAngleToQ(axis,omega)
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pure function math_axisAngleToQ(axis,omega)
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implicit none
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real(pReal), dimension(4) :: math_AxisAngleToQ
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real(pReal), dimension(4) :: math_axisAngleToQ
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real(pReal), dimension(3), intent(in) :: axis
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real(pReal), intent(in) :: omega
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real(pReal), dimension(3) :: axisNrm
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@ -1586,79 +1655,89 @@ pure function math_AxisAngleToQ(axis,omega)
|
|||
norm = sqrt(math_mul3x3(axis,axis))
|
||||
if (norm > 1.0e-8_pReal) then ! non-zero rotation
|
||||
axisNrm = axis/norm ! normalize axis to be sure
|
||||
! formula taken from http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
|
||||
s = sin(0.5_pReal*omega)
|
||||
c = cos(0.5_pReal*omega)
|
||||
math_AxisAngleToQ(1) = c
|
||||
math_AxisAngleToQ(2:4) = s * axisNrm(1:3)
|
||||
math_axisAngleToQ(1) = c
|
||||
math_axisAngleToQ(2:4) = s * axisNrm(1:3)
|
||||
else
|
||||
math_AxisAngleToQ = [1.0_pReal,0.0_pReal,0.0_pReal,0.0_pReal] ! no rotation
|
||||
math_axisAngleToQ = [1.0_pReal,0.0_pReal,0.0_pReal,0.0_pReal] ! no rotation
|
||||
endif
|
||||
|
||||
end function math_AxisAngleToQ
|
||||
end function math_axisAngleToQ
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief orientation matrix from quaternion (w+ix+jy+kz)
|
||||
!> @details taken from http://arxiv.org/pdf/math/0701759v1.pdf
|
||||
!> @dteails see also http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_qToR(Q)
|
||||
pure function math_qToR(q)
|
||||
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(4), intent(in) :: q
|
||||
real(pReal), dimension(3,3) :: math_qToR, T,S
|
||||
integer(pInt) :: i, j
|
||||
|
||||
forall (i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) &
|
||||
T(i,j) = Q(i+1_pInt) * Q(j+1_pInt)
|
||||
S = reshape( (/0.0_pReal, Q(4), -Q(3), &
|
||||
-Q(4),0.0_pReal, +Q(2), &
|
||||
Q(3), -Q(2),0.0_pReal/),(/3,3/)) ! notation is transposed!
|
||||
T(i,j) = q(i+1_pInt) * q(j+1_pInt)
|
||||
S = reshape( [0.0_pReal, -q(4), q(3), &
|
||||
q(4), 0.0_pReal, -q(2), &
|
||||
-q(3), q(2), 0.0_pReal],[3,3]) ! notation is transposed!
|
||||
|
||||
math_qToR = (2.0_pReal * Q(1)*Q(1) - 1.0_pReal) * math_I3 + &
|
||||
2.0_pReal * T - &
|
||||
2.0_pReal * Q(1) * S
|
||||
math_qToR = (2.0_pReal * q(1)*q(1) - 1.0_pReal) * math_I3 &
|
||||
+ 2.0_pReal * T - 2.0_pReal * q(1) * S
|
||||
|
||||
end function math_qToR
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief 3-1-3 Euler angles (in radians) from quaternion (w+ix+jy+kz)
|
||||
!> @details quaternion is meant to represent a PASSIVE rotation,
|
||||
!> @details composed of INTRINSIC rotations around the axes of the
|
||||
!> @details rotating reference frame
|
||||
!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_qToEuler(Q)
|
||||
pure function math_qToEuler(qPassive)
|
||||
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(4), intent(in) :: qPassive
|
||||
real(pReal), dimension(4) :: q
|
||||
real(pReal), dimension(3) :: math_qToEuler
|
||||
real(pReal) :: acos_arg
|
||||
|
||||
math_qToEuler(2) = acos(1.0_pReal-2.0_pReal*(Q(2)*Q(2)+Q(3)*Q(3)))
|
||||
q = math_qConj(qPassive) ! convert to active rotation, since formulas are defined for active rotations
|
||||
|
||||
if (abs(math_qToEuler(2)) < 1.0e-3_pReal) then
|
||||
acos_arg=Q(1)
|
||||
if(acos_arg > 1.0_pReal)acos_arg = 1.0_pReal
|
||||
if(acos_arg < -1.0_pReal)acos_arg = -1.0_pReal
|
||||
math_qToEuler(1) = 2.0_pReal*acos(acos_arg)
|
||||
math_qToEuler(2) = acos(1.0_pReal-2.0_pReal*(q(2)*q(2)+q(3)*q(3)))
|
||||
|
||||
if (abs(math_qToEuler(2)) < 1.0e-6_pReal) then
|
||||
acos_arg = q(1)
|
||||
if(acos_arg > 1.0_pReal) acos_arg = 1.0_pReal
|
||||
if(acos_arg < -1.0_pReal) acos_arg = -1.0_pReal
|
||||
math_qToEuler(1) = sign(2.0_pReal * acos(acos_arg),q(4))
|
||||
math_qToEuler(3) = 0.0_pReal
|
||||
else
|
||||
math_qToEuler(1) = atan2(Q(1)*Q(3)+Q(2)*Q(4), Q(1)*Q(2)-Q(3)*Q(4))
|
||||
if (math_qToEuler(1) < 0.0_pReal) &
|
||||
math_qToEuler(1) = math_qToEuler(1) + 2.0_pReal * pi
|
||||
|
||||
math_qToEuler(3) = atan2(-Q(1)*Q(3)+Q(2)*Q(4), Q(1)*Q(2)+Q(3)*Q(4))
|
||||
if (math_qToEuler(3) < 0.0_pReal) &
|
||||
math_qToEuler(3) = math_qToEuler(3) + 2.0_pReal * pi
|
||||
math_qToEuler(1) = atan2(q(1)*q(3)+q(2)*q(4), q(1)*q(2)-q(3)*q(4))
|
||||
math_qToEuler(3) = atan2(-q(1)*q(3)+q(2)*q(4), q(1)*q(2)+q(3)*q(4))
|
||||
endif
|
||||
|
||||
if (math_qToEuler(1) < 0.0_pReal) &
|
||||
math_qToEuler(1) = math_qToEuler(1) + 2.0_pReal * pi
|
||||
if (math_qToEuler(2) < 0.0_pReal) &
|
||||
math_qToEuler(2) = math_qToEuler(2) + pi
|
||||
if (math_qToEuler(3) < 0.0_pReal) &
|
||||
math_qToEuler(3) = math_qToEuler(3) + 2.0_pReal * pi
|
||||
|
||||
end function math_qToEuler
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief axis-angle (x, y, z, ang in radians) from quaternion (w+ix+jy+kz)
|
||||
!> @details quaternion is meant to represent an ACTIVE rotation
|
||||
!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
|
||||
!> @details formula for active rotation taken from
|
||||
!> @details http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_qToAxisAngle(Q)
|
||||
|
||||
|
|
@ -1681,6 +1760,25 @@ pure function math_qToAxisAngle(Q)
|
|||
end function math_qToAxisAngle
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief Euler axis-angle (x, y, z, ang in radians) from quaternion (w+ix+jy+kz)
|
||||
!> @details quaternion is meant to represent a PASSIVE rotation
|
||||
!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_qToEulerAxisAngle(qPassive)
|
||||
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: qPassive
|
||||
real(pReal), dimension(4) :: q
|
||||
real(pReal), dimension(4) :: math_qToEulerAxisAngle
|
||||
|
||||
q = math_qConj(qPassive) ! convert to active rotation
|
||||
math_qToEulerAxisAngle = math_qToAxisAngle(q)
|
||||
|
||||
end function math_qToEulerAxisAngle
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief Rodrigues vector (x, y, z) from unit quaternion (w+ix+jy+kz)
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -1890,7 +1988,7 @@ function math_sampleFiberOri(alpha,beta,noise)
|
|||
if(angle /= 0.0_pReal) then
|
||||
! rotation axis between sample and crystal system (cross product)
|
||||
forall(i=1_pInt:3_pInt) axis(i) = fiberInC(rotMap(1,i))*fiberInS(rotMap(2,i))-fiberInC(rotMap(2,i))*fiberInS(rotMap(1,i))
|
||||
oRot = math_AxisAngleToR(math_vectorproduct(fiberInC,fiberInS),angle)
|
||||
oRot = math_EulerAxisAngleToR(math_vectorproduct(fiberInC,fiberInS),angle)
|
||||
else
|
||||
oRot = math_I3
|
||||
end if
|
||||
|
|
@ -1898,7 +1996,7 @@ function math_sampleFiberOri(alpha,beta,noise)
|
|||
! ---# rotation matrix about fiber axis (random angle) #---
|
||||
do
|
||||
call halton(6_pInt,rnd)
|
||||
fRot = math_AxisAngleToR(fiberInS,rnd(1)*2.0_pReal*pi)
|
||||
fRot = math_EulerAxisAngleToR(fiberInS,rnd(1)*2.0_pReal*pi)
|
||||
|
||||
! ---# rotation about random axis perpend to fiber #---
|
||||
! random axis pependicular to fiber axis
|
||||
|
|
@ -1924,7 +2022,7 @@ function math_sampleFiberOri(alpha,beta,noise)
|
|||
enddo
|
||||
if (rnd(6) <= 0.5) angle = -angle
|
||||
|
||||
pRot = math_AxisAngleToR(axis,angle)
|
||||
pRot = math_EulerAxisAngleToR(axis,angle)
|
||||
|
||||
! ---# apply the three rotations #---
|
||||
math_sampleFiberOri = math_RtoEuler(math_mul33x33(pRot,math_mul33x33(fRot,oRot)))
|
||||
|
|
|
|||
Loading…
Reference in New Issue