Basic quaternion operations
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.


Author: Pierre de Buyl
License: 3-clause BSD

Build Status

fortran_quaternion is a Fortran module that provides some basic quaternion functions.

fortran_quaternion does not define any derived type, instead quaternions are provided as 4-element vectors storing the vector part first and the scalar part last.

  • qnew: return a quaternion from the scalar and vector input.
  • qvector: return the vector part of a quaternion.
  • qscalar: return the scalar part of a quaternion.
  • qnorm: return the norm.
  • qnormalize: return the normalized quaternion.
  • qconj: return the conjugate.
  • qinv: return the inverse.
  • qmul: return the product of two quaternions.

Example programs

Multiplication of two quaternions

program quaternion_usage
  use quaternion
  implicit none

  double precision :: q1(4), q2(4)

  q1 = qnew(v=[1.d0, 2.d0, 3.d0], s=4.d0)
  q2 = qnew(v=[6.d0, 7.d0, 8.d0], s=5.d0)

  write(*,'(4f5.2,a,4f5.2)') q1, ' x ', q2
  write(*,'(a,4f7.2)') '= ', qmul(q1, q2)

end program quaternion_usage

Rotation of a 3d vector about a given axis

program quaternion_rotation
  use quaternion
  implicit none

  double precision :: q(4), v(3)
  double precision :: axis(3), theta

  axis = [ 1, 1, 0 ]
  theta = 2*atan(1.d0) ! pi/2

  q = qnew(s=cos(theta/2), v=sin(theta/2)*axis/norm2(axis))

  v = [0, 0, 1]

  write(*,'(a,3f7.2)') 'v = ', v
  ! Rotate qv by q
  v = qvector(qmul(q, qmul(qnew(v=v), qconj(q))))
  write(*,'(a,3f7.2)') 'rotated v = ', v

end program quaternion_rotation


Copy the file src/quaternion.f90 or use cmake (with the add_subdirectory command) to add the library to your project.


Tests are defined in test/ and rely on fortran_tester, installed via git submodules:

git submodule init
git submodule update