Compute the Euler angles from a rotation matrix on SO(3).

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Description

It calculates three euler angles (θ_{12}, θ_{13}, θ_{23}) from a (3 \times 3) rotation matrix X, where X is defined as X = R_z(θ_{12})\times R_y(θ_{13}) \times R_x(θ_{23}). Here R_x(θ_{23}) means a rotation of θ_{23} radians about the x axis.

Usage

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Arguments

X

A rotation matrix which is defined as a product of three elementary rotations mentioned above. Here θ_{12}, θ_{23} \in (-π, π) and and θ_{13} \in (-π/2, π/2).

Details

Given a rotation matrix X, euler angles are computed by equating each element in X with the corresponding element in the matrix product defined above. This results in nine equations that can be used to find the euler angles.

Value

For a given rotation matrix, there are two eqivalent sets of euler angles.

Author(s)

Anamul Sajib<pmxahsa@nottingham.ac.uk>

R implementation and documentation: Anamul Sajib<pmxahsa@nottingham.ac.uk>

References

Green, P. J. \& Mardia, K. V. (2006). Bayesian alignment using hierarchical models, with applications in proteins bioinformatics. Biometrika, 93(2):235–254.

http://www.staff.city.ac.uk/~sbbh653/publications/euler.pdf

See Also

eul2rot

Examples

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# three euler angles

theta.12 <- sample( seq(-3, 3, 0.3), 1 )
theta.23 <- sample( seq(-3, 3, 0.3), 1 )
theta.13 <- sample( seq(-1.4, 1.4, 0.3), 1 )

theta.12 ; theta.23 ; theta.13

X <- eul2rot(theta.12, theta.23, theta.13)
X  ##  A rotation matrix

e <- rot2eul(X)$v1

theta.12 <- e[3]
theta.23 <- e[2]
theta.13 <- e[1]

theta.12 ; theta.23 ; theta.13

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