4 ms·
Only if you’re describing orientation as two orthogonal rotations. I’m saying think of it like a ‘pointing’ vector that defines the axis of rotation. And such a
by nighthawk454 2y ago
Only if you’re describing orientation as two orthogonal rotations. I’m saying think of it like a ‘pointing’ vector that defines the axis of rotation. And such a vector does require 3 components in 3d space
- creativenolo 2y agoIt’s possible to point in 3D space with two rotation components. For example, the first two components of a UV texture. But I agree it is helpful to think of quaternions as direction and spin.
- thaumasiotes 2y agoYes, a three-dimensional vector is a combination of a 3D orientation and a magnitude. An orientation by itself doesn't have three dimensions. The surface of a sphere is a two-dimensional space. > Only if you’re describing orientation as two orthogonal rotations. No, the space has the dimensionality it has. You may choose to describe a 3D orientation with more than two numbers, but you won't stop it from being a two-dimensional quantity that way. If you use more than two numbers, those numbers will fail to be independent of each other.
- oasisaimlessly 2y agoOrientation would conventionally be a member of SO(3), which is a 3-dimensional manifold. Your comment is essentially correct if you replace the word "orientation" with "direction", though.