QUATERNIONS
Quaternion Arithmetic

QUATERNIONS is a Python 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 Python library which implements certain elementary functions for single precision complex (C4) variables.

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

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

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

R8LIB, a Python 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:

• degrees_to_radians.m, converts an angle in degrees to one in radians;
• q8_conjugate.m, conjugates a quaternion;
• q8_exponentiate.m, exponentiates a quaternion;
• q8_inverse.m, inverts a quaternion;
• q8_multiply.m, multiplies two quaternions;
• q8_multiply2.m, multiplies two quaternions using a matrix;
• q8_norm.m, computes the L2 norm of a quaternion;
• q8_normal_01.m, selects a normally distributed quaternion;
• q8_transpose_print.m, prints a quaterion "transposed", or as a row vector.
• r8_acos.m, computes the inverse cosine of C;
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8vec_print.m, prints an R8VEC;
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• radians_to_degrees.m, converts an angle in radians to one in degrees;
• rotation_axis_vector.m, rotates a vector about an axis vector in 3D;
• rotation_axis2mat.m, converts a rotation from axis to matrix format in 3D;
• rotation_axis2quat.m, converts a rotation from axis to quaternion format in 3D;
• rotation_mat_vector.m, applies a matrix rotation to a vector in 3D;
• rotation_mat2axis.m, converts a rotation from matrix to axis format in 3D;
• rotation_mat2quat.m, converts a rotation from matrix to quaternion format in 3D;
• rotation_quat_vector.m, applies a quaternion rotation to a vector in 3D;
• rotation_quat2axis.m, converts a rotation from quaternion to axis format in 3D;
• rotation_quat2mat.m, converts a rotation from quaternion to matrix format in 3D;
• timestamp.m, prints the current YMDHMS date as a timestamp.

Examples and Tests:

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

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