Hosted at https://so3-visualizer.vercel.app
The Lie group SO(3) is not simply connected; it is impossible to deform a 360-degree loop into the identity rotation. It is, however, possible to deform a 720-degree loop into the identity, as this website demonstrates. Topologically, this is because SO(3) is double-covered by the group of unit quaternions Spin(3), which is simply connected. It may seem like the sudden change in the axis of rotation is a discontinuity, but all axes of rotation are equivalent at the identity (which is where the switch occurs), so this is allowed.
This is a Next.js project bootstrapped with create-next-app, with Three.js used for the graphics.
Drag to rotate the camera, although this can be disorienting. I feel the default orientation is best for understanding what's going on.
First, run the development server:
npm run dev
# or
yarn dev
# or
pnpm dev
# or
bun devOpen http://localhost:3000 with your browser to see the result.
You can start editing the page by modifying app/page.tsx. The page auto-updates as you edit the file.