Directional (version 6.8)

Rotation matrix to rotate a spherical vector along the direction of another: Rotation matrix to rotate a spherical vector along the direction of another

Description

A rotation matrix is calculated to rotate a unit vector along the direction of another.

Usage

rotation(a, b)

Value

A rotation matrix whose dimension is equal to the length of the unit vectors.

Arguments

a

The initial unit vector.

b

The target unit vector.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

The function calcualtes a rotation matrix given two vectors. This rotation matrix is the connection between the two spherical only, vectors.

References

Amaral G.J.A., Dryden I.L. and Wood A.T.A. (2007). Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis. Journal of the American Statistical Association, 102(478): 695--707.

See Also

Arotation, rot.matrix, lambert, lambert.inv, rsop

Examples

a <- rnorm(3)
a <- a/sqrt(sum(a^2))
b <- rnorm(3)
b <- b/sqrt(sum(b^2))
A <- rotation(a, b)
A
a  ;  b
a %*% t(A)

a <- rnorm(7)
a <- a/sqrt(sum(a^2))
b <- rnorm(7)
b <- b/sqrt(sum(b^2))
A <- rotation(a, b)
A
a  ;  b
a %*% t(A)