Directional (version 2.2)

Rotation matrix on SO(3) from three Euler angles: Construct a rotation matrix on SO(3) from the Euler angles.

Description

It forms a rotation matrix X on SO(3) by using three Euler angles $(\theta_{12}, \theta_{13}, \theta_{23})$, where X is defined as $X=R_z(\theta_{12}) \times R_y(\theta_{13}) \times R_x( \theta_{23} )$. Here $R_x (\theta_{23})$ means a rotation of $\theta_{23}$ radians about the x axis.

Usage

eul2rot(theta.12, theta.23, theta.13)

Arguments

theta.12

An Euler angle, a number which must lie in $(-\pi, \pi)$.

theta.23

An Euler angle, a number which must lie in $(-\pi, \pi)$.

theta.13

An Euler angle, a number which must lie in $(-\pi/2, \pi/2)$.

Value

A roation matrix.

Details

Given three euler angles a rotation matrix X on SO(3) is formed using the transformation according to Green and Mardia (2006) which is defined above.

References

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

See Also

rot2eul

Examples

# 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
det(X)

e <- rot2eul(X)$v1

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

theta.12 ; theta.23 ; theta.13