rotations (version 0.2)

genR: Generate rotations

Description

Generate rotations according to Rodrigues' formula.

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."

Value

• A $n\times p$matrix where each row is a random rotation matrix ($p=9$) or quaternion ($p=4$).

Details

Given a vector $U=(u_1,u_2,u_3)^\top\in R^3$ of length one and angle of rotation $r$, a rotation can be 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 matirix with upper triangular elements $-u_3$, $u_2$ and $-u_1$ in that order.

Examples

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