Conformal mesh deformations with Möbius transformations | ACM Transactions on Graphics

What makes a Möbius strip so special? This mathematical surface has only one side and one edge! If you start walking along the edge, you won’t return to your starting point after one full rotation — you’ll need two. In this reel, we compute the arc length of the edge of a Möbius using calculus. Because of the half-twist, the parameter runs from 0 to 4π instead of 2π. And in the thin-strip approximation (major radius much larger than width), the edge length comes out to be approximately 4πR — abo

14. Transformations of the Complex Plane: Möbius Transformations | Emmanuel Jesuyon Dansu