Math Art
Morin's Surface

Morin's Surface

Morin's Surface is a topological surface, given by a parametrisation, immersed.

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aperiodic closed closed-orientable def-parametric immersed implemented topological tradition-classical tradition-sculptural

Formula

x(u, v)
cos⁡(u)⁢(2⁢cos⁡(u)+2⁢sin⁡(u))⁢cos⁡(v)2−sin⁡(2⁢u)⁢sin⁡(2⁢v)\frac{\cos\left(u\right) \left(2 \cos\left(u\right) + \sqrt{2} \sin\left(u\right)\right) \cos\left(v\right)}{\sqrt{2} - \sin\left(2 u\right) \sin\left(2 v\right)}
y(u, v)
cos⁡(u)⁢(2⁢cos⁡(u)−2⁢sin⁡(u))⁢sin⁡(v)2−sin⁡(2⁢u)⁢sin⁡(2⁢v)\frac{\cos\left(u\right) \left(2 \cos\left(u\right) - \sqrt{2} \sin\left(u\right)\right) \sin\left(v\right)}{\sqrt{2} - \sin\left(2 u\right) \sin\left(2 v\right)}
z(u, v)
cos⁡(u)22−sin⁡(2⁢u)⁢sin⁡(2⁢v)\frac{\cos\left(u\right)^{2}}{\sqrt{2} - \sin\left(2 u\right) \sin\left(2 v\right)}

Properties

Family
topological
Given by
a parametrisation
Curvature
no condition imposed
Periodicity
not periodic
Ends
0
Embedding
immersed
Orientable
yes
Fidelity
exact
Exactness
elementary

Definition

Apery order n = 2 (Morin's own halfway model, an immersed sphere) and pinch k = 1 fixed to the operator defaults; u = +-pi/2 collapse to the triple point

Sources

Chart reproduced numerically against the shipped implementation: fwd max 0.64 of tol, 0.0% of oracle beyond tol (tol floor 2.5 x 0.04064).