genR: Generate Rotations

In heike/rotations: Tools for working with rotational data

Description

Generate rotations according to the Uniform-Axis Random Spin methodology

Usage

  genR(r, S = NULL, space = "SO3")

Arguments

r	vector of angles
S	The principle direction
space	Indicates the desired representation: matrix in SO3, quaternion, or Euler angles

Details

Given a vector u in R^2 of length one and angle of rotation r, a rotation can be formed using Rodrigues formula

cos(r)I+sin(r)Φ(u)+(1-cos(r))uu'

where I is the 3-by-3 identity matrix,Φ(u) is a 3-by-3 skew-symmetric matirix with upper triangular elements -u3, u2 and -u1 in that order.

Value

a matrix where each row is a sample point in the desired space

References

Bingham M, Nordman D and Vardeman S (2009). "Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in three Dimensions." _Journal of the American Statistical Association_, *104*(488), pp. 1385-1397.

Examples

r<-rvmises(20,0.01)
genR(r)

heike/rotations documentation built on May 17, 2019, 3:24 p.m.