<_description>
A 3D immersion of of a Klein bottle that smoothly deforms between the
Etruscan Venus surface, the Roman surface, the Boy surface, and the
Ida surface. Topologically, all surfaces are Klein bottles, even the
Roman and Boy surfaces, which are doubly covered and therefore appear
to be an immersed real projective plane.
You can walk on the Klein bottle or rotate it in 3D. Since all the
surfaces except the Ida surfaces have points where the surface normal
is not well defined for some points, walking is performed on the Ida
surface. Furthermore, it is possible to smoothly deform the surface
between the Etruscan Venus surface, the Roman surface, the Boy
surface, and the Ida surface surface while turning it.
Inspired by George K. Francis's book "A Topological Picturebook",
Springer, 1987, George K. Francis's paper "The Etruscan Venus" in
P. Concus, R. Finn, and D. A. Hoffman: "Geometric Analysis and
Computer Graphics", Springer, 1991, and a video entitled "The Etruscan
Venus" by Donna J. Cox, George K. Francis, and Raymond L. Idaszak,
presented at SIGGRAPH 1989.
https://en.wikipedia.org/wiki/Boy%27s_surface
https://en.wikipedia.org/wiki/Roman_surface
https://en.wikipedia.org/wiki/Klein_bottle
http://mathworld.wolfram.com/BoySurface.html
http://mathworld.wolfram.com/RomanSurface.html
http://mathworld.wolfram.com/EtruscanVenusSurface.html
http://mathworld.wolfram.com/IdaSurface.html
Written by Carsten Steger; 2020.