Math Art
Kuen Surface

Kuen Surface

Kuen Surface is a surface of constant negative Gaussian curvature, given by a parametrisation, self-intersecting.

Open Kuen Surface in the interactive viewer →

aperiodic constant-curvature def-parametric implemented k-const-negative self-intersecting tradition-classical tradition-physical-model

Formula

x(u, v)
2⁢(cos⁡(u)+u⁢sin⁡(u))⁢sin⁡(v)1+u2⁢sin⁡(v)2\frac{2 \left(\cos\left(u\right) + u \sin\left(u\right)\right) \sin\left(v\right)}{1 + u^{2} \sin\left(v\right)^{2}}
y(u, v)
2⁢(sin⁡(u)−u⁢cos⁡(u))⁢sin⁡(v)1+u2⁢sin⁡(v)2\frac{2 \left(\sin\left(u\right) - u \cos\left(u\right)\right) \sin\left(v\right)}{1 + u^{2} \sin\left(v\right)^{2}}
z(u, v)
log⁡(tan⁡(v2))+2⁢cos⁡(v)1+u2⁢sin⁡(v)2\log\left(\tan\left(\frac{v}{2}\right)\right) + \frac{2 \cos\left(v\right)}{1 + u^{2} \sin\left(v\right)^{2}}

Properties

Family
constant-curvature
Given by
a parametrisation
Curvature
constant negative Gaussian curvature
Periodicity
not periodic
Ends
0
Embedding
self-intersecting
Fidelity
exact
Exactness
elementary

Sources

Chart as curated in tools/surfdb/charts.py, verified numerically against the curvature condition the record claims (measured over the chart by the validator and the charts self-test).