QUATERNIONS
Quaternion Arithmetic

QUATERNIONS is a FORTRAN90 library which carries out some simple arithmetic operations for quaternions.

Rotations in 3D can be represented in a number of ways, including quaternions, a rotation matrix, and a combination of a rotation axis and rotation angle. This library includes functions to convert a rotation from one representation to another, and to apply a rotation to a given vector.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

QUATERNIONS is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

C4LIB, a FORTRAN90 library which implements certain elementary functions for single precision complex (C4) variables.

C8LIB, a FORTRAN90 library which implements certain elementary functions for double precision complex (C8) variables;

COMPLEX_NUMBERS, a FORTRAN90 program which demonstrates some simple features involved in the use of complex numbers in MATLAB programming.

I4LIB, a FORTRAN90 library which contains many utility routines, using "I4" or "single precision integer" arithmetic.

R8LIB, a FORTRAN90 library which contains many utility routines, using "R8" or "double precision real" arithmetic.

Reference:

1. Jack Kuipers,
   Quaternions and Rotation Sequences,
   Princeton, 1998,
   ISBN: 0691102988,
   LC: QA196.K85.

Source Code:

• quaternions.f90, the source code.

Examples and Tests:

• quaternions_test.f90, a sample calling program.
• quaternions_test.txt, the output file.

List of Routines:

• DEGREES_TO_RADIANS converts an angle from degrees to radians.
• Q8_CONJUGATE conjugates a quaternion.
• Q8_EXPONENTIATE exponentiates a quaternion.
• Q8_INVERSE inverts a quaternion.
• Q8_MULTIPLY multiplies two quaternions.
• Q8_MULTIPLY2 multiplies two quaternions using a matrix format.
• Q8_NORM computes the norm of a quaternion.
• Q8_NORMAL_01 returns a normally distributed quaternion.
• Q8_TRANSPOSE_PRINT prints a Q8 "transposed".
• R8_ACOS computes the arc cosine function, with argument truncation.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• RADIANS_TO_DEGREES converts an angle from radians to degrees.
• ROTATION_AXIS_VECTOR rotates a vector around an axis vector in 3D.
• ROTATION_AXIS2MAT converts a rotation from axis to matrix format in 3D.
• ROTATION_AXIS2QUAT converts rotation from axis to quaternion form in 3D.
• ROTATION_MAT_VECTOR applies a marix rotation to a vector in 3d.
• ROTATION_MAT2AXIS converts a rotation from matrix to axis format in 3D.
• ROTATION_MAT2QUAT converts rotation from matrix to quaternion format.
• ROTATION_QUAT_VECTOR applies a quaternion rotation to a vector in 3D.
• ROTATION_QUAT2AXIS converts rotation from quaternion to axis form in 3D.
• ROTATION_QUAT2MAT converts rotation from quaternion to matrix form in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.