project.SO3: Projection into SO(3)
In rotations: Working with Rotation Data

project.SO3

R Documentation

Projection into SO(3)

Description

Project an arbitrary 3-by-3 matrix into SO(3).

Usage

project.SO3(M)

Arguments

`M`	3-by-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-by-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 M into SO(3).

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)

rotations documentation built on June 25, 2022, 1:06 a.m.