Math Art
Ida Surface

Ida Surface

Ida Surface is a topological surface, given by a parametrisation, immersed.

Open Ida Surface in the interactive viewer →

aperiodic closed def-parametric immersed implemented topological tradition-sculptural

Formula

x(u, v)
cos⁡(v)⁢cos⁡(2⁢u)+sin⁡(v)⁢cos⁡(u)1−12⁢sin⁡(3⁢u)⁢sin⁡(2⁢v)\frac{\cos\left(v\right) \cos\left(2 u\right) + \sin\left(v\right) \cos\left(u\right)}{1 - \frac{1}{\sqrt{2}} \sin\left(3 u\right) \sin\left(2 v\right)}
y(u, v)
cos⁡(v)⁢sin⁡(2⁢u)−sin⁡(v)⁢sin⁡(u)1−12⁢sin⁡(3⁢u)⁢sin⁡(2⁢v)\frac{\cos\left(v\right) \sin\left(2 u\right) - \sin\left(v\right) \sin\left(u\right)}{1 - \frac{1}{\sqrt{2}} \sin\left(3 u\right) \sin\left(2 v\right)}
z(u, v)
2⁢cos⁡(v)1−12⁢sin⁡(3⁢u)⁢sin⁡(2⁢v)\frac{2 \cos\left(v\right)}{1 - \frac{1}{\sqrt{2}} \sin\left(3 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
Fidelity
exact
Exactness
elementary

Definition

Francis's ovalesque sweep F(1, 1): the same sweep as the Etruscan Venus with the quartic's denominator switched on, which separates the Venus's pinch points and leaves a smoothly immersed Klein bottle. Waist r1 = 1 and height r2 = 2 at the operator's defaults

Sources

Chart reproduced numerically against the shipped implementation: fwd max 0.73 of tol, 0.0% of oracle beyond tol (tol floor 2.5 x 0.06468).