polishing
This commit is contained in:
Martin Diehl
parent
9e0a0ee166
commit
9f4e354b12
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@ -27,7 +27,7 @@
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! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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! ###################################################################
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief rotation storage and conversion
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@ -44,7 +44,7 @@
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! Convention 5: the rotation angle ω is limited to the interval [0, π]
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! Convention 6: the real part of a quaternion is positive, Re(q) > 0
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! Convention 7: P = -1
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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module rotations
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use IO
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@ -111,60 +111,64 @@ subroutine rotations_init
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end subroutine rotations_init
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!---------------------------------------------------------------------------------------------------
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! Return rotation in different representations
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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! Return rotation in different representations.
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!--------------------------------------------------------------------------------------------------
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pure function asQuaternion(self)
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class(tRotation), intent(in) :: self
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real(pReal), dimension(4) :: asQuaternion
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asQuaternion = self%q
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end function asQuaternion
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function asEulers(self)
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class(tRotation), intent(in) :: self
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real(pReal), dimension(3) :: asEulers
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asEulers = qu2eu(self%q)
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end function asEulers
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function asAxisAngle(self)
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class(tRotation), intent(in) :: self
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real(pReal), dimension(4) :: asAxisAngle
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asAxisAngle = qu2ax(self%q)
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end function asAxisAngle
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function asMatrix(self)
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class(tRotation), intent(in) :: self
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real(pReal), dimension(3,3) :: asMatrix
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asMatrix = qu2om(self%q)
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end function asMatrix
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!---------------------------------------------------------------------------------------------------
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! Initialize rotation from different representations
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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! Initialize rotation from different representations.
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!--------------------------------------------------------------------------------------------------
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subroutine fromQuaternion(self,qu)
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class(tRotation), intent(out) :: self
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real(pReal), dimension(4), intent(in) :: qu
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if (dNeq(norm2(qu),1.0_pReal,1.0e-8_pReal)) call IO_error(402,ext_msg='fromQuaternion')
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self%q = qu
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end subroutine fromQuaternion
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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subroutine fromEulers(self,eu,degrees)
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class(tRotation), intent(out) :: self
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@ -173,6 +177,7 @@ subroutine fromEulers(self,eu,degrees)
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real(pReal), dimension(3) :: Eulers
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if (.not. present(degrees)) then
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Eulers = eu
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else
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@ -185,7 +190,7 @@ subroutine fromEulers(self,eu,degrees)
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self%q = eu2qu(Eulers)
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end subroutine fromEulers
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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subroutine fromAxisAngle(self,ax,degrees,P)
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class(tRotation), intent(out) :: self
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@ -196,6 +201,7 @@ subroutine fromAxisAngle(self,ax,degrees,P)
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real(pReal) :: angle
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real(pReal),dimension(3) :: axis
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if (.not. present(degrees)) then
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angle = ax(4)
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else
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@ -215,51 +221,54 @@ subroutine fromAxisAngle(self,ax,degrees,P)
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self%q = ax2qu([axis,angle])
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end subroutine fromAxisAngle
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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subroutine fromMatrix(self,om)
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class(tRotation), intent(out) :: self
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real(pReal), dimension(3,3), intent(in) :: om
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if (dNeq(math_det33(om),1.0_pReal,tol=1.0e-5_pReal)) &
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call IO_error(402,ext_msg='fromMatrix')
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self%q = om2qu(om)
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end subroutine fromMatrix
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!---------------------------------------------------------------------------------------------------
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!> @brief: Rotate a rotation
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @brief: Compose rotations.
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!--------------------------------------------------------------------------------------------------
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pure elemental function rotRot__(self,R) result(rRot)
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type(tRotation) :: rRot
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class(tRotation), intent(in) :: self,R
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rRot = tRotation(multiply_quaternion(self%q,R%q))
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rRot = tRotation(multiplyQuaternion(self%q,R%q))
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call rRot%standardize()
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end function rotRot__
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!---------------------------------------------------------------------------------------------------
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!> @brief quaternion representation with positive q
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @brief Convert to quaternion representation with positive q(1).
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!--------------------------------------------------------------------------------------------------
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pure elemental subroutine standardize(self)
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class(tRotation), intent(inout) :: self
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if (sign(1.0_pReal,self%q(1)) < 0.0_pReal) self%q = - self%q
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end subroutine standardize
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Rotate a vector passively (default) or actively.
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function rotVector(self,v,active) result(vRot)
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real(pReal), dimension(3) :: vRot
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@ -270,6 +279,7 @@ pure function rotVector(self,v,active) result(vRot)
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real(pReal), dimension(4) :: v_normed, q
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logical :: passive
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if (present(active)) then
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passive = .not. active
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else
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@ -280,22 +290,20 @@ pure function rotVector(self,v,active) result(vRot)
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vRot = v
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else
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v_normed = [0.0_pReal,v]/norm2(v)
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if (passive) then
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q = multiply_quaternion(self%q, multiply_quaternion(v_normed, conjugate_quaternion(self%q)))
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else
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q = multiply_quaternion(conjugate_quaternion(self%q), multiply_quaternion(v_normed, self%q))
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endif
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q = merge(multiplyQuaternion(self%q, multiplyQuaternion(v_normed, conjugateQuaternion(self%q))), &
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multiplyQuaternion(conjugateQuaternion(self%q), multiplyQuaternion(v_normed, self%q)), &
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passive)
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vRot = q(2:4)*norm2(v)
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endif
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end function rotVector
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Rotate a rank-2 tensor passively (default) or actively.
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!> @details: Rotation is based on rotation matrix
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function rotTensor2(self,T,active) result(tRot)
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real(pReal), dimension(3,3) :: tRot
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@ -319,11 +327,11 @@ pure function rotTensor2(self,T,active) result(tRot)
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end function rotTensor2
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @brief Rotate a rank-4 tensor passively (default) or actively.
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!> @details: rotation is based on rotation matrix
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!! ToDo: Need to check active/passive !!!
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function rotTensor4(self,T,active) result(tRot)
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real(pReal), dimension(3,3,3,3) :: tRot
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@ -351,11 +359,11 @@ pure function rotTensor4(self,T,active) result(tRot)
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end function rotTensor4
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @brief Rotate a rank-4 stiffness tensor in Voigt 6x6 notation passively (default) or actively.
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!> @details: https://scicomp.stackexchange.com/questions/35600
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!! ToDo: Need to check active/passive !!!
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function rotStiffness(self,C,active) result(cRot)
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real(pReal), dimension(6,6) :: cRot
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@ -391,24 +399,24 @@ pure function rotStiffness(self,C,active) result(cRot)
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end function rotStiffness
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!---------------------------------------------------------------------------------------------------
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!> @brief Misorientation.
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate misorientation.
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!--------------------------------------------------------------------------------------------------
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pure elemental function misorientation(self,other)
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type(tRotation) :: misorientation
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class(tRotation), intent(in) :: self, other
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misorientation%q = multiply_quaternion(other%q, conjugate_quaternion(self%q))
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misorientation%q = multiplyQuaternion(other%q, conjugateQuaternion(self%q))
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end function misorientation
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Convert unit quaternion to rotation matrix.
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function qu2om(qu) result(om)
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real(pReal), intent(in), dimension(4) :: qu
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@ -436,10 +444,10 @@ pure function qu2om(qu) result(om)
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end function qu2om
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Convert unit quaternion to Euler angles.
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert unit quaternion to Bunge Euler angles.
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!--------------------------------------------------------------------------------------------------
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pure function qu2eu(qu) result(eu)
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real(pReal), intent(in), dimension(4) :: qu
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@ -466,10 +474,10 @@ pure function qu2eu(qu) result(eu)
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end function qu2eu
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert unit quaternion to axis angle pair
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert unit quaternion to axis-angle pair.
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!--------------------------------------------------------------------------------------------------
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pure function qu2ax(qu) result(ax)
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real(pReal), intent(in), dimension(4) :: qu
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@ -477,6 +485,7 @@ pure function qu2ax(qu) result(ax)
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real(pReal) :: omega, s
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if (dEq0(sum(qu(2:4)**2))) then
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ax = [ 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal ] ! axis = [001]
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elseif (dNeq0(qu(1))) then
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@ -490,11 +499,11 @@ pure function qu2ax(qu) result(ax)
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end function qu2ax
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief convert rotation matrix to unit quaternion
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!> @brief Convert rotation matrix to unit quaternion.
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!> @details the original formulation (direct conversion) had (numerical?) issues
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function om2qu(om) result(qu)
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real(pReal), intent(in), dimension(3,3) :: om
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@ -503,6 +512,7 @@ pure function om2qu(om) result(qu)
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real(pReal) :: trace,s
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trace = math_trace33(om)
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if(trace > 0.0_pReal) then
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s = 0.5_pReal / sqrt(trace+1.0_pReal)
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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]
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@ -525,17 +535,18 @@ pure function om2qu(om) result(qu)
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end function om2qu
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert orientation matrix to Euler angles
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!> @brief Convert orientation matrix to Bunge Euler angles.
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!> @details Two step check for special cases to avoid invalid operations (not needed for python)
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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pure function om2eu(om) result(eu)
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real(pReal), intent(in), dimension(3,3) :: om
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real(pReal), dimension(3) :: eu
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real(pReal) :: zeta
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if (dNeq(abs(om(3,3)),1.0_pReal,1.e-8_pReal)) then
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zeta = 1.0_pReal/sqrt(math_clip(1.0_pReal-om(3,3)**2,1e-64_pReal,1.0_pReal))
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eu = [atan2(om(3,1)*zeta,-om(3,2)*zeta), &
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@ -550,10 +561,10 @@ pure function om2eu(om) result(eu)
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end function om2eu
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert orientation matrix to axis angle pair
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert orientation matrix to axis-angle pair.
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!--------------------------------------------------------------------------------------------------
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function om2ax(om) result(ax)
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real(pReal), intent(in), dimension(3,3) :: om
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@ -565,6 +576,7 @@ function om2ax(om) result(ax)
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real(pReal), dimension(3,3) :: VR, devNull, om_
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integer :: ierr, i
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om_ = om
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! first get the rotation angle
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@ -586,10 +598,10 @@ function om2ax(om) result(ax)
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end function om2ax
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Euler angles to unit quaternion
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert Bunge Euler angles to unit quaternion.
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!--------------------------------------------------------------------------------------------------
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pure function eu2qu(eu) result(qu)
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real(pReal), intent(in), dimension(3) :: eu
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@ -597,6 +609,7 @@ pure function eu2qu(eu) result(qu)
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real(pReal), dimension(3) :: ee
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real(pReal) :: cPhi, sPhi
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ee = 0.5_pReal*eu
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cPhi = cos(ee(2))
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@ -611,10 +624,10 @@ pure function eu2qu(eu) result(qu)
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end function eu2qu
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief Euler angles to orientation matrix
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert Euler angles to orientation matrix.
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!--------------------------------------------------------------------------------------------------
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pure function eu2om(eu) result(om)
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real(pReal), intent(in), dimension(3) :: eu
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@ -622,6 +635,7 @@ pure function eu2om(eu) result(om)
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real(pReal), dimension(3) :: c, s
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c = cos(eu)
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s = sin(eu)
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@ -640,10 +654,10 @@ pure function eu2om(eu) result(om)
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end function eu2om
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert euler to axis angle
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert Bunge Euler angles to axis-angle pair.
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!--------------------------------------------------------------------------------------------------
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pure function eu2ax(eu) result(ax)
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real(pReal), intent(in), dimension(3) :: eu
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@ -651,6 +665,7 @@ pure function eu2ax(eu) result(ax)
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real(pReal) :: t, delta, tau, alpha, sigma
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t = tan(eu(2)*0.5_pReal)
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sigma = 0.5_pReal*(eu(1)+eu(3))
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delta = 0.5_pReal*(eu(1)-eu(3))
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@ -669,10 +684,10 @@ pure function eu2ax(eu) result(ax)
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end function eu2ax
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert axis angle pair to quaternion
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert axis-angle pair to unit quaternion.
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!--------------------------------------------------------------------------------------------------
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pure function ax2qu(ax) result(qu)
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real(pReal), intent(in), dimension(4) :: ax
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@ -692,10 +707,10 @@ pure function ax2qu(ax) result(qu)
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end function ax2qu
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert axis angle pair to orientation matrix
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert axis-angle pair to orientation matrix.
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!--------------------------------------------------------------------------------------------------
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pure function ax2om(ax) result(om)
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real(pReal), intent(in), dimension(4) :: ax
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@ -703,6 +718,7 @@ pure function ax2om(ax) result(om)
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real(pReal) :: q, c, s, omc
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c = cos(ax(4))
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s = sin(ax(4))
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omc = 1.0_pReal-c
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@ -728,15 +744,16 @@ pure function ax2om(ax) result(om)
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end function ax2om
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!---------------------------------------------------------------------------------------------------
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!--------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert axis angle pair to Euler angles
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!---------------------------------------------------------------------------------------------------
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!> @brief Convert axis-angle pair to Bunge Euler angles.
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!--------------------------------------------------------------------------------------------------
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pure function ax2eu(ax) result(eu)
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|
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real(pReal), intent(in), dimension(4) :: ax
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||||
real(pReal), dimension(3) :: eu
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eu = om2eu(ax2om(ax))
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||||
end function ax2eu
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|
|
@ -745,33 +762,32 @@ end function ax2eu
|
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!--------------------------------------------------------------------------------------------------
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||||
!> @brief Multiply two quaternions.
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function multiply_quaternion(qu1,qu2)
|
||||
pure function multiplyQuaternion(qu1,qu2)
|
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|
||||
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)
|
||||
multiply_quaternion(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))
|
||||
multiply_quaternion(4) = qu1(1)*qu2(4) + qu1(4)*qu2(1) + P * (qu1(2)*qu2(3) - qu1(3)*qu2(2))
|
||||
multiplyQuaternion(1) = qu1(1)*qu2(1) - qu1(2)*qu2(2) - qu1(3)*qu2(3) - qu1(4)*qu2(4)
|
||||
multiplyQuaternion(2) = qu1(1)*qu2(2) + qu1(2)*qu2(1) + P * (qu1(3)*qu2(4) - qu1(4)*qu2(3))
|
||||
multiplyQuaternion(3) = qu1(1)*qu2(3) + qu1(3)*qu2(1) + P * (qu1(4)*qu2(2) - qu1(2)*qu2(4))
|
||||
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.
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function conjugate_quaternion(qu)
|
||||
pure function conjugateQuaternion(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 conjugate_quaternion
|
||||
end function conjugateQuaternion
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -780,8 +796,8 @@ end function conjugate_quaternion
|
|||
subroutine selfTest()
|
||||
|
||||
type(tRotation) :: R
|
||||
real(pReal), dimension(4) :: qu, ax, ro
|
||||
real(pReal), dimension(3) :: x, eu, ho, v3
|
||||
real(pReal), dimension(4) :: qu, ax
|
||||
real(pReal), dimension(3) :: x, eu, v3
|
||||
real(pReal), dimension(3,3) :: om, t33
|
||||
real(pReal), dimension(3,3,3,3) :: t3333
|
||||
real(pReal), dimension(6,6) :: C
|
||||
|
|
|
|||
Loading…
Reference in New Issue