3 · The Manifold — SO(2) & SO(3)

Each point on a manifold is one group element. Drag the point on each manifold — the cutaway (bottom-left) shows the coordinate frame it represents.

SO(2) — the set of all 2D rotations. Manifold represented as a circle.

SO(3) — the set of all 3D rotations. Manifold represented as a sphere.