Math Art
Join of Two Tori

Join of Two Tori

Join of Two Tori is an algebraic surface, defined by an implicit equation, immersed.

Open Join of Two Tori in the interactive viewer →

algebraic aperiodic def-implicit immersed implemented tradition-gallery

Formula

(((x−1.1)2+y2+z2−1−0.12249999999999998)2+4⁢(z2−0.12249999999999998))⁢(((x+1.1)2+y2+z2−1−0.12249999999999998)2+4⁢(z2−0.12249999999999998))1+(x−1.1)2+(x+1.1)2+y2+z22−0.2=0\frac{\left(\left(\left(x - 1.1\right)^{2} + y^{2} + z^{2} - 1 - 0.12249999999999998\right)^{2} + 4 \left(z^{2} - 0.12249999999999998\right)\right) \left(\left(\left(x + 1.1\right)^{2} + y^{2} + z^{2} - 1 - 0.12249999999999998\right)^{2} + 4 \left(z^{2} - 0.12249999999999998\right)\right)}{1 + \left(x - 1.1\right)^{2} + \left(x + 1.1\right)^{2} + y^{2} + \frac{z^{2}}{2}} - 0.2 = 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 2.84e-14).