genR: Generate rotations

In rotations: Working with Rotation Data

Generate rotations

Description

Generate rotations in matrix format using Rodrigues' formula or quaternions.

Usage

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

Arguments

r	vector of angles.
S	central orientation.
space	indicates the desired representation: rotation matrix "SO3" or quaternions "Q4."

Details

Given a vector U=(u1,u2,u3)' in R^3 of length one and angle of rotation r, a 3-by-3 rotation matrix is 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 matrix with upper triangular elements -u3, u2 and -u1 in that order.

For the same vector and angle a quaternion is formed according to

q=[cos(theta/2),sin(theta/2)U]'.

Value

A n-by-p matrix where each row is a random rotation matrix (p=9) or quaternion (p=4).

Examples

r <- rvmises(20, kappa = 0.01)
Rs <- genR(r, space = "SO3")
Qs <- genR(r, space = "Q4")

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