223031012
/
DAMASK_EICMD
mirror of https://github.com/achalhp/DAMASK_EICMD.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

polishing

This commit is contained in:
Martin Diehl 2022-06-11 23:12:30 +02:00
parent 9e0a0ee166
commit 9f4e354b12
1 changed files with 105 additions and 89 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

194
src/rotations.f90
View File

@ -27,7 +27,7 @@
! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
! ################################################################### ! ###################################################################
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief rotation storage and conversion !> @brief rotation storage and conversion
@ -44,7 +44,7 @@
! Convention 5: the rotation angle ω is limited to the interval [0, π] ! Convention 5: the rotation angle ω is limited to the interval [0, π]
! Convention 6: the real part of a quaternion is positive, Re(q) > 0 ! Convention 6: the real part of a quaternion is positive, Re(q) > 0
! Convention 7: P = -1 ! Convention 7: P = -1
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
module rotations module rotations
use IO use IO
@ -111,60 +111,64 @@ subroutine rotations_init
end subroutine rotations_init end subroutine rotations_init
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! Return rotation in different representations ! Return rotation in different representations.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function asQuaternion(self) pure function asQuaternion(self)
class(tRotation), intent(in) :: self class(tRotation), intent(in) :: self
real(pReal), dimension(4) :: asQuaternion real(pReal), dimension(4) :: asQuaternion
asQuaternion = self%q asQuaternion = self%q
end function asQuaternion end function asQuaternion
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function asEulers(self) pure function asEulers(self)
class(tRotation), intent(in) :: self class(tRotation), intent(in) :: self
real(pReal), dimension(3) :: asEulers real(pReal), dimension(3) :: asEulers
asEulers = qu2eu(self%q) asEulers = qu2eu(self%q)
end function asEulers end function asEulers
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function asAxisAngle(self) pure function asAxisAngle(self)
class(tRotation), intent(in) :: self class(tRotation), intent(in) :: self
real(pReal), dimension(4) :: asAxisAngle real(pReal), dimension(4) :: asAxisAngle
asAxisAngle = qu2ax(self%q) asAxisAngle = qu2ax(self%q)
end function asAxisAngle end function asAxisAngle
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function asMatrix(self) pure function asMatrix(self)
class(tRotation), intent(in) :: self class(tRotation), intent(in) :: self
real(pReal), dimension(3,3) :: asMatrix real(pReal), dimension(3,3) :: asMatrix
asMatrix = qu2om(self%q) asMatrix = qu2om(self%q)
end function asMatrix end function asMatrix
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------- ! Initialize rotation from different representations.
! Initialize rotation from different representations !--------------------------------------------------------------------------------------------------
!---------------------------------------------------------------------------------------------------
subroutine fromQuaternion(self,qu) subroutine fromQuaternion(self,qu)
class(tRotation), intent(out) :: self class(tRotation), intent(out) :: self
real(pReal), dimension(4), intent(in) :: qu real(pReal), dimension(4), intent(in) :: qu
if (dNeq(norm2(qu),1.0_pReal,1.0e-8_pReal)) call IO_error(402,ext_msg='fromQuaternion') if (dNeq(norm2(qu),1.0_pReal,1.0e-8_pReal)) call IO_error(402,ext_msg='fromQuaternion')
self%q = qu self%q = qu
end subroutine fromQuaternion end subroutine fromQuaternion
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine fromEulers(self,eu,degrees) subroutine fromEulers(self,eu,degrees)
class(tRotation), intent(out) :: self class(tRotation), intent(out) :: self
@ -173,6 +177,7 @@ subroutine fromEulers(self,eu,degrees)
real(pReal), dimension(3) :: Eulers real(pReal), dimension(3) :: Eulers
if (.not. present(degrees)) then if (.not. present(degrees)) then
Eulers = eu Eulers = eu
else else
@ -185,7 +190,7 @@ subroutine fromEulers(self,eu,degrees)
self%q = eu2qu(Eulers) self%q = eu2qu(Eulers)
end subroutine fromEulers end subroutine fromEulers
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine fromAxisAngle(self,ax,degrees,P) subroutine fromAxisAngle(self,ax,degrees,P)
class(tRotation), intent(out) :: self class(tRotation), intent(out) :: self
@ -196,6 +201,7 @@ subroutine fromAxisAngle(self,ax,degrees,P)
real(pReal) :: angle real(pReal) :: angle
real(pReal),dimension(3) :: axis real(pReal),dimension(3) :: axis
if (.not. present(degrees)) then if (.not. present(degrees)) then
angle = ax(4) angle = ax(4)
else else
@ -215,51 +221,54 @@ subroutine fromAxisAngle(self,ax,degrees,P)
self%q = ax2qu([axis,angle]) self%q = ax2qu([axis,angle])
end subroutine fromAxisAngle end subroutine fromAxisAngle
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine fromMatrix(self,om) subroutine fromMatrix(self,om)
class(tRotation), intent(out) :: self class(tRotation), intent(out) :: self
real(pReal), dimension(3,3), intent(in) :: om real(pReal), dimension(3,3), intent(in) :: om
if (dNeq(math_det33(om),1.0_pReal,tol=1.0e-5_pReal)) & if (dNeq(math_det33(om),1.0_pReal,tol=1.0e-5_pReal)) &
call IO_error(402,ext_msg='fromMatrix') call IO_error(402,ext_msg='fromMatrix')
self%q = om2qu(om) self%q = om2qu(om)
end subroutine fromMatrix end subroutine fromMatrix
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief: Rotate a rotation !> @brief: Compose rotations.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure elemental function rotRot__(self,R) result(rRot) pure elemental function rotRot__(self,R) result(rRot)
type(tRotation) :: rRot type(tRotation) :: rRot
class(tRotation), intent(in) :: self,R class(tRotation), intent(in) :: self,R
rRot = tRotation(multiply_quaternion(self%q,R%q))
rRot = tRotation(multiplyQuaternion(self%q,R%q))
call rRot%standardize() call rRot%standardize()
end function rotRot__ end function rotRot__
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief quaternion representation with positive q !> @brief Convert to quaternion representation with positive q(1).
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure elemental subroutine standardize(self) pure elemental subroutine standardize(self)
class(tRotation), intent(inout) :: self class(tRotation), intent(inout) :: self
if (sign(1.0_pReal,self%q(1)) < 0.0_pReal) self%q = - self%q if (sign(1.0_pReal,self%q(1)) < 0.0_pReal) self%q = - self%q
end subroutine standardize end subroutine standardize
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Rotate a vector passively (default) or actively. !> @brief Rotate a vector passively (default) or actively.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function rotVector(self,v,active) result(vRot) pure function rotVector(self,v,active) result(vRot)
real(pReal), dimension(3) :: vRot real(pReal), dimension(3) :: vRot
@ -270,6 +279,7 @@ pure function rotVector(self,v,active) result(vRot)
real(pReal), dimension(4) :: v_normed, q real(pReal), dimension(4) :: v_normed, q
logical :: passive logical :: passive
if (present(active)) then if (present(active)) then
passive = .not. active passive = .not. active
else else
@ -280,22 +290,20 @@ pure function rotVector(self,v,active) result(vRot)
vRot = v vRot = v
else else
v_normed = [0.0_pReal,v]/norm2(v) v_normed = [0.0_pReal,v]/norm2(v)
if (passive) then q = merge(multiplyQuaternion(self%q, multiplyQuaternion(v_normed, conjugateQuaternion(self%q))), &
q = multiply_quaternion(self%q, multiply_quaternion(v_normed, conjugate_quaternion(self%q))) multiplyQuaternion(conjugateQuaternion(self%q), multiplyQuaternion(v_normed, self%q)), &
else passive)
q = multiply_quaternion(conjugate_quaternion(self%q), multiply_quaternion(v_normed, self%q))
endif
vRot = q(2:4)*norm2(v) vRot = q(2:4)*norm2(v)
endif endif
end function rotVector end function rotVector
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Rotate a rank-2 tensor passively (default) or actively. !> @brief Rotate a rank-2 tensor passively (default) or actively.
!> @details: Rotation is based on rotation matrix !> @details: Rotation is based on rotation matrix
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function rotTensor2(self,T,active) result(tRot) pure function rotTensor2(self,T,active) result(tRot)
real(pReal), dimension(3,3) :: tRot real(pReal), dimension(3,3) :: tRot
@ -319,11 +327,11 @@ pure function rotTensor2(self,T,active) result(tRot)
end function rotTensor2 end function rotTensor2
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Rotate a rank-4 tensor passively (default) or actively. !> @brief Rotate a rank-4 tensor passively (default) or actively.
!> @details: rotation is based on rotation matrix !> @details: rotation is based on rotation matrix
!! ToDo: Need to check active/passive !!! !! ToDo: Need to check active/passive !!!
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function rotTensor4(self,T,active) result(tRot) pure function rotTensor4(self,T,active) result(tRot)
real(pReal), dimension(3,3,3,3) :: tRot real(pReal), dimension(3,3,3,3) :: tRot
@ -351,11 +359,11 @@ pure function rotTensor4(self,T,active) result(tRot)
end function rotTensor4 end function rotTensor4
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Rotate a rank-4 stiffness tensor in Voigt 6x6 notation passively (default) or actively. !> @brief Rotate a rank-4 stiffness tensor in Voigt 6x6 notation passively (default) or actively.
!> @details: https://scicomp.stackexchange.com/questions/35600 !> @details: https://scicomp.stackexchange.com/questions/35600
!! ToDo: Need to check active/passive !!! !! ToDo: Need to check active/passive !!!
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function rotStiffness(self,C,active) result(cRot) pure function rotStiffness(self,C,active) result(cRot)
real(pReal), dimension(6,6) :: cRot real(pReal), dimension(6,6) :: cRot
@ -391,24 +399,24 @@ pure function rotStiffness(self,C,active) result(cRot)
end function rotStiffness end function rotStiffness
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Misorientation. !> @brief Calculate misorientation.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure elemental function misorientation(self,other) pure elemental function misorientation(self,other)
type(tRotation) :: misorientation type(tRotation) :: misorientation
class(tRotation), intent(in) :: self, other class(tRotation), intent(in) :: self, other
misorientation%q = multiply_quaternion(other%q, conjugate_quaternion(self%q)) misorientation%q = multiplyQuaternion(other%q, conjugateQuaternion(self%q))
end function misorientation end function misorientation
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Convert unit quaternion to rotation matrix. !> @brief Convert unit quaternion to rotation matrix.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function qu2om(qu) result(om) pure function qu2om(qu) result(om)
real(pReal), intent(in), dimension(4) :: qu real(pReal), intent(in), dimension(4) :: qu
@ -436,10 +444,10 @@ pure function qu2om(qu) result(om)
end function qu2om end function qu2om
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Convert unit quaternion to Euler angles. !> @brief Convert unit quaternion to Bunge Euler angles.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function qu2eu(qu) result(eu) pure function qu2eu(qu) result(eu)
real(pReal), intent(in), dimension(4) :: qu real(pReal), intent(in), dimension(4) :: qu
@ -466,10 +474,10 @@ pure function qu2eu(qu) result(eu)
end function qu2eu end function qu2eu
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert unit quaternion to axis angle pair !> @brief Convert unit quaternion to axis-angle pair.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function qu2ax(qu) result(ax) pure function qu2ax(qu) result(ax)
real(pReal), intent(in), dimension(4) :: qu real(pReal), intent(in), dimension(4) :: qu
@ -477,6 +485,7 @@ pure function qu2ax(qu) result(ax)
real(pReal) :: omega, s real(pReal) :: omega, s
if (dEq0(sum(qu(2:4)**2))) then if (dEq0(sum(qu(2:4)**2))) then
ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ] ! axis = [001] ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ] ! axis = [001]
elseif (dNeq0(qu(1))) then elseif (dNeq0(qu(1))) then
@ -490,11 +499,11 @@ pure function qu2ax(qu) result(ax)
end function qu2ax end function qu2ax
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief convert rotation matrix to unit quaternion !> @brief Convert rotation matrix to unit quaternion.
!> @details the original formulation (direct conversion) had (numerical?) issues !> @details the original formulation (direct conversion) had (numerical?) issues
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function om2qu(om) result(qu) pure function om2qu(om) result(qu)
real(pReal), intent(in), dimension(3,3) :: om real(pReal), intent(in), dimension(3,3) :: om
@ -503,6 +512,7 @@ pure function om2qu(om) result(qu)
real(pReal) :: trace,s real(pReal) :: trace,s
trace = math_trace33(om) trace = math_trace33(om)
if(trace > 0.0_pReal) then if(trace > 0.0_pReal) then
s = 0.5_pReal / sqrt(trace+1.0_pReal) s = 0.5_pReal / sqrt(trace+1.0_pReal)
qu = [0.25_pReal/s, (om(3,2)-om(2,3))*s,(om(1,3)-om(3,1))*s,(om(2,1)-om(1,2))*s] qu = [0.25_pReal/s, (om(3,2)-om(2,3))*s,(om(1,3)-om(3,1))*s,(om(2,1)-om(1,2))*s]
@ -525,17 +535,18 @@ pure function om2qu(om) result(qu)
end function om2qu end function om2qu
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert orientation matrix to Euler angles !> @brief Convert orientation matrix to Bunge Euler angles.
!> @details Two step check for special cases to avoid invalid operations (not needed for python) !> @details Two step check for special cases to avoid invalid operations (not needed for python)
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function om2eu(om) result(eu) pure function om2eu(om) result(eu)
real(pReal), intent(in), dimension(3,3) :: om real(pReal), intent(in), dimension(3,3) :: om
real(pReal), dimension(3) :: eu real(pReal), dimension(3) :: eu
real(pReal) :: zeta real(pReal) :: zeta
if (dNeq(abs(om(3,3)),1.0_pReal,1.e-8_pReal)) then if (dNeq(abs(om(3,3)),1.0_pReal,1.e-8_pReal)) then
zeta = 1.0_pReal/sqrt(math_clip(1.0_pReal-om(3,3)**2,1e-64_pReal,1.0_pReal)) zeta = 1.0_pReal/sqrt(math_clip(1.0_pReal-om(3,3)**2,1e-64_pReal,1.0_pReal))
eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), & eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), &
@ -550,10 +561,10 @@ pure function om2eu(om) result(eu)
end function om2eu end function om2eu
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert orientation matrix to axis angle pair !> @brief Convert orientation matrix to axis-angle pair.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function om2ax(om) result(ax) function om2ax(om) result(ax)
real(pReal), intent(in), dimension(3,3) :: om real(pReal), intent(in), dimension(3,3) :: om
@ -565,6 +576,7 @@ function om2ax(om) result(ax)
real(pReal), dimension(3,3) :: VR, devNull, om_ real(pReal), dimension(3,3) :: VR, devNull, om_
integer :: ierr, i integer :: ierr, i
om_ = om om_ = om
! first get the rotation angle ! first get the rotation angle
@ -586,10 +598,10 @@ function om2ax(om) result(ax)
end function om2ax end function om2ax
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Euler angles to unit quaternion !> @brief Convert Bunge Euler angles to unit quaternion.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function eu2qu(eu) result(qu) pure function eu2qu(eu) result(qu)
real(pReal), intent(in), dimension(3) :: eu real(pReal), intent(in), dimension(3) :: eu
@ -597,6 +609,7 @@ pure function eu2qu(eu) result(qu)
real(pReal), dimension(3) :: ee real(pReal), dimension(3) :: ee
real(pReal) :: cPhi, sPhi real(pReal) :: cPhi, sPhi
ee = 0.5_pReal*eu ee = 0.5_pReal*eu
cPhi = cos(ee(2)) cPhi = cos(ee(2))
@ -611,10 +624,10 @@ pure function eu2qu(eu) result(qu)
end function eu2qu end function eu2qu
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief Euler angles to orientation matrix !> @brief Convert Euler angles to orientation matrix.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function eu2om(eu) result(om) pure function eu2om(eu) result(om)
real(pReal), intent(in), dimension(3) :: eu real(pReal), intent(in), dimension(3) :: eu
@ -622,6 +635,7 @@ pure function eu2om(eu) result(om)
real(pReal), dimension(3) :: c, s real(pReal), dimension(3) :: c, s
c = cos(eu) c = cos(eu)
s = sin(eu) s = sin(eu)
@ -640,10 +654,10 @@ pure function eu2om(eu) result(om)
end function eu2om end function eu2om
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert euler to axis angle !> @brief Convert Bunge Euler angles to axis-angle pair.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function eu2ax(eu) result(ax) pure function eu2ax(eu) result(ax)
real(pReal), intent(in), dimension(3) :: eu real(pReal), intent(in), dimension(3) :: eu
@ -651,6 +665,7 @@ pure function eu2ax(eu) result(ax)
real(pReal) :: t, delta, tau, alpha, sigma real(pReal) :: t, delta, tau, alpha, sigma
t = tan(eu(2)*0.5_pReal) t = tan(eu(2)*0.5_pReal)
sigma = 0.5_pReal*(eu(1)+eu(3)) sigma = 0.5_pReal*(eu(1)+eu(3))
delta = 0.5_pReal*(eu(1)-eu(3)) delta = 0.5_pReal*(eu(1)-eu(3))
@ -669,10 +684,10 @@ pure function eu2ax(eu) result(ax)
end function eu2ax end function eu2ax
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert axis angle pair to quaternion !> @brief Convert axis-angle pair to unit quaternion.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function ax2qu(ax) result(qu) pure function ax2qu(ax) result(qu)
real(pReal), intent(in), dimension(4) :: ax real(pReal), intent(in), dimension(4) :: ax
@ -692,10 +707,10 @@ pure function ax2qu(ax) result(qu)
end function ax2qu end function ax2qu
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert axis angle pair to orientation matrix !> @brief Convert axis-angle pair to orientation matrix.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function ax2om(ax) result(om) pure function ax2om(ax) result(om)
real(pReal), intent(in), dimension(4) :: ax real(pReal), intent(in), dimension(4) :: ax
@ -703,6 +718,7 @@ pure function ax2om(ax) result(om)
real(pReal) :: q, c, s, omc real(pReal) :: q, c, s, omc
c = cos(ax(4)) c = cos(ax(4))
s = sin(ax(4)) s = sin(ax(4))
omc = 1.0_pReal-c omc = 1.0_pReal-c
@ -728,15 +744,16 @@ pure function ax2om(ax) result(om)
end function ax2om end function ax2om
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @author Marc De Graef, Carnegie Mellon University !> @author Marc De Graef, Carnegie Mellon University
!> @brief convert axis angle pair to Euler angles !> @brief Convert axis-angle pair to Bunge Euler angles.
!--------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function ax2eu(ax) result(eu) pure function ax2eu(ax) result(eu)
real(pReal), intent(in), dimension(4) :: ax real(pReal), intent(in), dimension(4) :: ax
real(pReal), dimension(3) :: eu real(pReal), dimension(3) :: eu
eu = om2eu(ax2om(ax)) eu = om2eu(ax2om(ax))
end function ax2eu end function ax2eu
@ -745,33 +762,32 @@ end function ax2eu
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Multiply two quaternions. !> @brief Multiply two quaternions.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function multiply_quaternion(qu1,qu2) pure function multiplyQuaternion(qu1,qu2)
real(pReal), dimension(4), intent(in) :: qu1, qu2 real(pReal), dimension(4), intent(in) :: qu1, qu2
real(pReal), dimension(4) :: multiply_quaternion real(pReal), dimension(4) :: multiplyQuaternion
multiply_quaternion(1) = qu1(1)*qu2(1) - qu1(2)*qu2(2) - qu1(3)*qu2(3) - qu1(4)*qu2(4) multiplyQuaternion(1) = qu1(1)*qu2(1) - qu1(2)*qu2(2) - qu1(3)*qu2(3) - qu1(4)*qu2(4)
multiply_quaternion(2) = qu1(1)*qu2(2) + qu1(2)*qu2(1) + P * (qu1(3)*qu2(4) - qu1(4)*qu2(3)) multiplyQuaternion(2) = qu1(1)*qu2(2) + qu1(2)*qu2(1) + P * (qu1(3)*qu2(4) - qu1(4)*qu2(3))
multiply_quaternion(3) = qu1(1)*qu2(3) + qu1(3)*qu2(1) + P * (qu1(4)*qu2(2) - qu1(2)*qu2(4)) multiplyQuaternion(3) = qu1(1)*qu2(3) + qu1(3)*qu2(1) + P * (qu1(4)*qu2(2) - qu1(2)*qu2(4))
multiply_quaternion(4) = qu1(1)*qu2(4) + qu1(4)*qu2(1) + P * (qu1(2)*qu2(3) - qu1(3)*qu2(2)) multiplyQuaternion(4) = qu1(1)*qu2(4) + qu1(4)*qu2(1) + P * (qu1(2)*qu2(3) - qu1(3)*qu2(2))
end function multiply_quaternion end function multiplyQuaternion
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Calculate conjugate complex of a quaternion. !> @brief Calculate conjugate complex of a quaternion.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function conjugate_quaternion(qu) pure function conjugateQuaternion(qu)
real(pReal), dimension(4), intent(in) :: qu real(pReal), dimension(4), intent(in) :: qu
real(pReal), dimension(4) :: conjugate_quaternion real(pReal), dimension(4) :: conjugateQuaternion
conjugate_quaternion = [qu(1), -qu(2), -qu(3), -qu(4)] conjugateQuaternion = [qu(1), -qu(2), -qu(3), -qu(4)]
end function conjugateQuaternion
end function conjugate_quaternion
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -780,8 +796,8 @@ end function conjugate_quaternion
subroutine selfTest() subroutine selfTest()
type(tRotation) :: R type(tRotation) :: R
real(pReal), dimension(4) :: qu, ax, ro real(pReal), dimension(4) :: qu, ax
real(pReal), dimension(3) :: x, eu, ho, v3 real(pReal), dimension(3) :: x, eu, v3
real(pReal), dimension(3,3) :: om, t33 real(pReal), dimension(3,3) :: om, t33
real(pReal), dimension(3,3,3,3) :: t3333 real(pReal), dimension(3,3,3,3) :: t3333
real(pReal), dimension(6,6) :: C real(pReal), dimension(6,6) :: C