Möbius

The Möbius strip.

$f(u, v) = (x, y, z)^T$ with

$x = a \cos(u) (c + v \cos(\frac{u}{2}))$
$y = a \sin(u) (c + v \cos(\frac{u}{2}))$
$z = a v\sin(\frac{u}{2})$

where $a$, and $c$ are scaling factors, $-\pi \le u \le \pi$, and $-0.5 \le v \le 0.5$.

The surface is non-orientable. A consequence is that no smooth varying normals exist. In the image a discontinuity can be seen where the normals 'jump' to the other side.

The blue and purple paths are in a diagonal direction, yet they terminate at the starting point.

The orange line along the surface also terminates a its starting point, showing there is just one edge. The orange edge path has double length, therefore it has normals on both sides.

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