rotations (version 1.6.5)

project.SO3: Projection into SO(3)

Description

Project an arbitrary \(3\times 3\) matrix into \(SO(3)\).

Usage

project.SO3(M)

Value

Projection of \(\bm M\) into \(SO(3)\).

Arguments

M

\(3\times 3\) matrix to project into \(SO(3)\).

Details

This function uses the process detailed in Section 3.1 of moakher02 to project an arbitrary \(3\times 3\) matrix into \(SO(3)\). More specifically it finds the closest orthogonal 3-by-3 matrix with determinant one to the provided matrix.

See Also

mean.SO3, median.SO3

Examples

#Project an arbitrary 3x3 matrix into SO(3)
M<-matrix(rnorm(9), 3, 3)
project.SO3(M)

#Project a sample arithmetic mean into SO(3), same as 'mean'
Rs <- ruars(20, rcayley)
Rbar <- colSums(Rs)/nrow(Rs)
project.SO3(Rbar)              #The following is equivalent
mean(Rs)