These binary operators perform arithmetic on rotations in
quaternion or rotation matrix form (or objects which can
be coerced into them).
Usage
## S3 method for class 'SO3':
+(x, y)
## S3 method for class 'SO3':
-(x, y = NULL)
## S3 method for class 'Q4':
+(x, y)
## S3 method for class 'Q4':
-(x, y = NULL)
Arguments
x
first arguement
y
second arguement (optional for subtraction)
Value
+the result of rotating the identity frame
through x then y
-the difference of the
rotations, or the inverse rotation of only one arguement
is provided
Details
The rotation group SO(3) is a multiplicative group so
``adding" rotations $R_1$ and $R_2$
results in $R_1+R_2=R_2R_1$. Similarly,
the difference between rotations $R_1$ and
$R_2$ is $R_1-R_2=R_2^\top R_1$.
With this definiton it is clear that
$R_1+R_2-R_2=R_2^\top
R_2R_1=R_1$. If only one rotation is
provided to subtraction then the inverse (transpose) it
returned, e.g. $-R_2=R_2^\top$.