for comparison with de-facto stardard rotation definitions
This commit is contained in:
Martin Diehl
parent
1612343065
commit
e32b9d9ca8
116
src/math.f90
116
src/math.f90
|
|
@ -1384,35 +1384,37 @@ end function math_RtoQ
|
|||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief rotation matrix from Euler angles (in radians)
|
||||
!> @details rotation matrix 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)
|
||||
!> @brief rotation matrix from Bunge-Euler (3-1-3) angles (in radians)
|
||||
!> @details rotation matrix is meant to represent a PASSIVE rotation, composed of INTRINSIC
|
||||
!> @details rotations around the axes of the details rotating reference frame.
|
||||
!> @details similar to eu2om from "D Rowenhorst et al. Consistent representations of and conversions
|
||||
!> @details between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)", but R is transposed
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_EulerToR(Euler)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3), intent(in) :: Euler
|
||||
real(pReal), dimension(3,3) :: math_EulerToR
|
||||
real(pReal) c1, c, c2, s1, s, s2
|
||||
real(pReal) :: c1, C, c2, s1, S, s2
|
||||
|
||||
C1 = cos(Euler(1))
|
||||
c1 = cos(Euler(1))
|
||||
C = cos(Euler(2))
|
||||
C2 = cos(Euler(3))
|
||||
S1 = sin(Euler(1))
|
||||
c2 = cos(Euler(3))
|
||||
s1 = sin(Euler(1))
|
||||
S = sin(Euler(2))
|
||||
S2 = sin(Euler(3))
|
||||
s2 = sin(Euler(3))
|
||||
|
||||
math_EulerToR(1,1)=C1*C2-S1*S2*C
|
||||
math_EulerToR(1,2)=-C1*S2-S1*C2*C
|
||||
math_EulerToR(1,3)=S1*S
|
||||
math_EulerToR(2,1)=S1*C2+C1*S2*C
|
||||
math_EulerToR(2,2)=-S1*S2+C1*C2*C
|
||||
math_EulerToR(2,3)=-C1*S
|
||||
math_EulerToR(3,1)=S2*S
|
||||
math_EulerToR(3,2)=C2*S
|
||||
math_EulerToR(3,3)=C
|
||||
math_EulerToR(1,1) = c1*c2 -s1*C*s2
|
||||
math_EulerToR(1,2) = -c1*s2 -s1*C*c2
|
||||
math_EulerToR(1,3) = s1*S
|
||||
|
||||
math_EulerToR(2,1) = s1*c2 +c1*C*s2
|
||||
math_EulerToR(2,2) = -s1*s2 +c1*C*c2
|
||||
math_EulerToR(2,3) = -c1*S
|
||||
|
||||
math_EulerToR(3,1) = S*s2
|
||||
math_EulerToR(3,2) = S*c2
|
||||
math_EulerToR(3,3) = C
|
||||
|
||||
math_EulerToR = transpose(math_EulerToR) ! convert to passive rotation
|
||||
|
||||
|
|
@ -1420,29 +1422,29 @@ end function math_EulerToR
|
|||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief quaternion (w+ix+jy+kz) from 3-1-3 Euler angles (in radians)
|
||||
!> @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)
|
||||
!> @brief quaternion (w+ix+jy+kz) from Bunge-Euler (3-1-3) angles (in radians)
|
||||
!> @details rotation matrix is meant to represent a PASSIVE rotation, composed of INTRINSIC
|
||||
!> @details rotations around the axes of the details rotating reference frame.
|
||||
!> @details similar to eu2qu from "D Rowenhorst et al. Consistent representations of and
|
||||
!> @details conversions between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)", but
|
||||
!> @details Q is conjucated and Q is not reversed for Q(0) < 0.
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_EulerToQ(eulerangles)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3), intent(in) :: eulerangles
|
||||
real(pReal), dimension(4) :: math_EulerToQ
|
||||
real(pReal), dimension(3) :: halfangles
|
||||
real(pReal) :: c, s
|
||||
real(pReal) :: c, s, sigma, delta
|
||||
|
||||
halfangles = 0.5_pReal * eulerangles
|
||||
|
||||
c = cos(halfangles(2))
|
||||
s = sin(halfangles(2))
|
||||
|
||||
math_EulerToQ= [cos(halfangles(1)+halfangles(3)) * c, &
|
||||
cos(halfangles(1)-halfangles(3)) * s, &
|
||||
sin(halfangles(1)-halfangles(3)) * s, &
|
||||
sin(halfangles(1)+halfangles(3)) * c ]
|
||||
c = cos(0.5_pReal * eulerangles(2))
|
||||
s = sin(0.5_pReal * eulerangles(2))
|
||||
sigma = 0.5_pReal * (eulerangles(1)+eulerangles(3))
|
||||
delta = 0.5_pReal * (eulerangles(1)-eulerangles(3))
|
||||
|
||||
math_EulerToQ= [c * cos(sigma), &
|
||||
s * cos(delta), &
|
||||
s * sin(delta), &
|
||||
c * sin(sigma) ]
|
||||
math_EulerToQ = math_qConj(math_EulerToQ) ! convert to passive rotation
|
||||
|
||||
end function math_EulerToQ
|
||||
|
|
@ -1453,6 +1455,8 @@ end function math_EulerToQ
|
|||
!> @details rotation matrix is meant to represent a ACTIVE rotation
|
||||
!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
|
||||
!> @details formula for active rotation taken from http://mathworld.wolfram.com/RodriguesRotationFormula.html
|
||||
!> @details equivalent to eu2om (P=-1) from "D Rowenhorst et al. Consistent representations of and
|
||||
!> @details conversions between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)"
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_axisAngleToR(axis,omega)
|
||||
|
||||
|
|
@ -1460,31 +1464,31 @@ pure function math_axisAngleToR(axis,omega)
|
|||
real(pReal), dimension(3,3) :: math_axisAngleToR
|
||||
real(pReal), dimension(3), intent(in) :: axis
|
||||
real(pReal), intent(in) :: omega
|
||||
real(pReal), dimension(3) :: axisNrm
|
||||
real(pReal), dimension(3) :: n
|
||||
real(pReal) :: norm,s,c,c1
|
||||
|
||||
norm = norm2(axis)
|
||||
if (norm > 1.0e-8_pReal) then ! non-zero rotation
|
||||
axisNrm = axis/norm ! normalize axis to be sure
|
||||
wellDefined: if (norm > 1.0e-8_pReal) then
|
||||
n = axis/norm ! normalize axis to be sure
|
||||
|
||||
s = sin(omega)
|
||||
c = cos(omega)
|
||||
c1 = 1.0_pReal - c
|
||||
|
||||
math_axisAngleToR(1,1) = c + c1*axisNrm(1)**2.0_pReal
|
||||
math_axisAngleToR(1,2) = -s*axisNrm(3) + c1*axisNrm(1)*axisNrm(2)
|
||||
math_axisAngleToR(1,3) = s*axisNrm(2) + c1*axisNrm(1)*axisNrm(3)
|
||||
math_axisAngleToR(1,1) = c + c1*n(1)**2.0_pReal
|
||||
math_axisAngleToR(1,2) = c1*n(1)*n(2) - s*n(3)
|
||||
math_axisAngleToR(1,3) = c1*n(1)*n(3) + s*n(2)
|
||||
|
||||
math_axisAngleToR(2,1) = s*axisNrm(3) + c1*axisNrm(2)*axisNrm(1)
|
||||
math_axisAngleToR(2,2) = c + c1*axisNrm(2)**2.0_pReal
|
||||
math_axisAngleToR(2,3) = -s*axisNrm(1) + c1*axisNrm(2)*axisNrm(3)
|
||||
math_axisAngleToR(2,1) = c1*n(1)*n(2) + s*n(3)
|
||||
math_axisAngleToR(2,2) = c + c1*n(2)**2.0_pReal
|
||||
math_axisAngleToR(2,3) = c1*n(2)*n(3) - s*n(1)
|
||||
|
||||
math_axisAngleToR(3,1) = -s*axisNrm(2) + c1*axisNrm(3)*axisNrm(1)
|
||||
math_axisAngleToR(3,2) = s*axisNrm(1) + c1*axisNrm(3)*axisNrm(2)
|
||||
math_axisAngleToR(3,3) = c + c1*axisNrm(3)**2.0_pReal
|
||||
else
|
||||
math_axisAngleToR(3,1) = c1*n(1)*n(3) - s*n(2)
|
||||
math_axisAngleToR(3,2) = c1*n(2)*n(3) + s*n(1)
|
||||
math_axisAngleToR(3,3) = c + c1*n(3)**2.0_pReal
|
||||
else wellDefined
|
||||
math_axisAngleToR = math_I3
|
||||
endif
|
||||
endif wellDefined
|
||||
|
||||
end function math_axisAngleToR
|
||||
|
||||
|
|
@ -1493,6 +1497,8 @@ end function math_axisAngleToR
|
|||
!> @brief rotation matrix from axis and angle (in radians)
|
||||
!> @details rotation matrix is meant to represent a PASSIVE rotation
|
||||
!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
|
||||
!> @details eq-uivalent to eu2qu (P=+1) from "D Rowenhorst et al. Consistent representations of and
|
||||
!> @details conversions between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)"
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_EulerAxisAngleToR(axis,omega)
|
||||
|
||||
|
|
@ -1529,8 +1535,10 @@ end function math_EulerAxisAngleToQ
|
|||
!> @brief quaternion (w+ix+jy+kz) from axis and angle (in radians)
|
||||
!> @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 formula for active rotation taken from
|
||||
!> @details http://en.wikipedia.org/wiki/Rotation_representation_%28mathematics%29#Rodrigues_parameters
|
||||
!> @details equivalent to eu2qu (P=+1) from "D Rowenhorst et al. Consistent representations of and
|
||||
!> @details conversions between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)"
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_axisAngleToQ(axis,omega)
|
||||
|
||||
|
|
@ -1541,13 +1549,13 @@ pure function math_axisAngleToQ(axis,omega)
|
|||
real(pReal), dimension(3) :: axisNrm
|
||||
real(pReal) :: norm
|
||||
|
||||
norm = sqrt(math_mul3x3(axis,axis))
|
||||
rotation: if (norm > 1.0e-8_pReal) then
|
||||
norm = norm2(axis)
|
||||
wellDefined: if (norm > 1.0e-8_pReal) then
|
||||
axisNrm = axis/norm ! normalize axis to be sure
|
||||
math_axisAngleToQ = [cos(0.5_pReal*omega), sin(0.5_pReal*omega) * axisNrm(1:3)]
|
||||
else rotation
|
||||
else wellDefined
|
||||
math_axisAngleToQ = [1.0_pReal,0.0_pReal,0.0_pReal,0.0_pReal]
|
||||
endif rotation
|
||||
endif wellDefined
|
||||
|
||||
end function math_axisAngleToQ
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue