| genR {rotations} | R Documentation |
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=(u_1,u_2,u_3)^\top\in R^3 of length one and angle of rotation r, a 3\times 3 rotation
matrix is formed using Rodrigues' formula
\cos(r)I_{3\times 3}+\sin(r)\Phi(U)+(1-\cos(r))UU^\top
where I_{3\times 3} is the 3\times 3 identity matrix, \Phi(U) is a 3\times 3 skew-symmetric matrix
with upper triangular elements -u_3, u_2 and -u_1 in that order.
For the same vector and angle a quaternion is formed according to
q=[cos(\theta/2),sin(\theta/2)U]^\top.
Value
A n\times 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")