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

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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<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.

See Also

rot2eul

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
det(X)

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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