# rot2eul: Compute the Euler angles from a rotation matrix on SO(3). In Directional: A Collection of Functions for Directional Data Analysis

 Euler angles from a rotation matrix on SO(3) R Documentation

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

### Description

It calculates three euler angles (\theta_{12}, \theta_{13}, \theta_{23}) from a (3 \times 3) rotation matrix X, 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

rot2eul(X)


### Arguments

 X A rotation matrix which is defined as a product of three elementary rotations mentioned above. Here  \theta_{12}, \theta_{23} \in (-\pi, \pi) and and \theta_{13} \in (-\pi/2, \pi/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 <sajibstat@du.ac.bd>.

R implementation and documentation: Anamul Sajib <sajibstat@du.ac.bd>.

### References

Green, P. J. and 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

eul2rot 

### 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

e <- rot2eul(X)\$v1

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

theta.12 ; theta.23 ; theta.13


Directional documentation built on Oct. 12, 2023, 1:07 a.m.