Subway

Subway is an algebraic surface, defined by an implicit equation, immersed.

algebraic aperiodic def-implicit immersed implemented tradition-gallery

Formula

x^{2} y^{2} - \left(z^{2} - 1\right)^{3} = 0

Properties

Family: algebraic
Given by: an implicit equation
Curvature: no condition imposed
Periodicity: not periodic
Ends: 0
Embedding: immersed
Fidelity: exact
Exactness: elementary

Sources

Closed form reproduced numerically against the shipped implementation (math_art/surfaces/algebraic.py) over 240 sample points: matches oracle x 1 over 240 points (worst 0).

H. Hauser, "Bildergalerie algebraischer Flaechen", Universitaet Wien. https://homepage.univie.ac.at/herwig.hauser/bildergalerie/
S. Amethyst, 3D-printed renderings of the same gallery, https://silviana.org/gallery/hauser/
H. Hauser, 'Bildergalerie algebraischer Flaechen', Universitaet Wien.