Combining Two 3D Rotations
Combining Two 3D Rotations
The concentric rotations and can be combined either by doing first and then , written as , or first and then , written as . This right-to-left notation comes from the algebra of dot products, ··v and ··v, where is a vector and and are the matrices representing the rotations and .
A
B
A
B
B∘A
B
A
A∘B
M
B
M
A
M
A
M
B
v
M
A
M
B
A
B
In general, .
A∘B≠B∘A
You can vary the axes of rotation by changing the spherical coordinates of their corresponding vectors.