project.SO3 {rotations}

Projection into SO(3)

Description

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

Usage

project.SO3(M)

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.

Value

Projection of \bm M into SO(3).

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)