rotations (version 1.6.5)

log.SO3: Rotation logarithm

Description

Compute the logarithm of a rotation matrix, which results in a \(3\times 3\) skew-symmetric matrix. This function maps the lie group \(SO(3)\) into its tangent space, which is the space of all \(3\times 3\) skew symmetric matrices, the lie algebra \(so(3)\). For details see e.g. moakher02.

Usage

# S3 method for SO3
log(x, ...)

Value

Skew symmetric matrix \(\log(R)\).

Arguments

x

\(n\times 9\) matrix where each row corresponds to a random rotation matrix.

...

additional arguments.

Details

moakher02

Examples

Rs <- ruars(20, rcayley)

#Here we demonstrate how the logarithm can be used to determine the angle and
#axis corresponding to the provided sample

lRs <- log(Rs)               #Take the logarithm of the sample
Ws <- lRs[,c(6, 7, 2)]       #The appropriate diagonal entries are the axis*angle
lens <- sqrt(rowSums(Ws^2))
axes <- mis.axis(Rs)
angs <- mis.angle(Rs)
all.equal(axes, Ws/lens)
all.equal(angs, lens)