rotations (version 0.2)

Q4: Quaternions

Description

Creates or tests for objects of class "Q4."

Usage

Q4(q, ...)
  ## S3 method for class 'default':
Q4(q, theta = NULL, ...)
  ## S3 method for class 'SO3':
Q4(q, ...)
  ## S3 method for class 'Q4':
Q4(q, ...)
  as.Q4(q)
  is.Q4(q)
  id.Q4

Arguments

q

object to be coerced or tested.

theta

vector of rotation angles.

...

additional arguments.

Value

• as.Q4
  coerces its object into an Q4 type.
• is.Q4
  returns TRUE or False depending on whether its argument satifies the conditions to be an quaternion; namely it must be four-dimensional and of unit length.
• Q4.default
  returns an $n$-by-4 matrix where each row is a quaternion constructed from axis $U$ and angle theta.
• Q4.SO3
  returns $n$-by-4 matrix where each row is a quaternion constructed from the corresponding rotation matrix.

format

id.Q4 is the identity rotation given by the matrix $[1,0,0,0]^\top$.

Details

Construct a unit quaternion to represent a rotation. Each quaternion can be interpreted as a rotation of some reference frame about the axis $U$ (of unit length) through the angle $\theta$. For each axis and angle the quaternion is formed through $$q=[cos(\theta/2),sin(\theta/2)U]^\top.$$ If no angle is supplied then the length of each axis is taken to be the angle of rotation theta. If an SO3 object is given then this function will return the quaternion equivalent.