Converting a rotation matrix on SO(3) to an unsigned unit quaternion: Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Description
It returns an unsigned unite quaternion in \(S^3\) (the four-dimensional sphere) from a \(3 \times 3\)
rotation matrix on SO(3).
Usage
rot2quat(X)
Value
A unsigned unite quaternion.
Arguments
X
A rotation matrix in SO(3).
Author
Anamul Sajib.
R implementation and documentation: Anamul Sajib <sajibstat@du.ac.bd>.
Details
Firstly construct a system of linear equations by equating the corresponding components of the theoretical rotation
matrix proposed by Prentice (1986), and given a rotation matrix. Finally, the system of linear equations are solved
by following the tricks mentioned in second reference here in order to achieve numerical accuracy to get quaternion values.
References
Prentice,M. J. (1986). Orientation statistics without parametric assumptions.Journal of the
Royal Statistical Society. Series B: Methodological 48(2). //http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm