eul2rot: Construct a rotation matrix on SO(3) from the Euler angles.

View source: R/eul2rot.R

Rotation matrix on SO(3) from three Euler anglesR Documentation

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 (θ_{12}, θ_{13}, θ_{23}), 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

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

Arguments

theta.12

An Euler angle, a number which must lie in (-π, π).

theta.23

An Euler angle, a number which must lie in (-π, π).

theta.13

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

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.

Value

A roation matrix.

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.

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

Directional documentation built on Sept. 22, 2022, 9:06 a.m.