Right Conoid

Right Conoid is a ruled surface, given by a parametrisation, embedded or immersed depending on parameters.

Open Right Conoid in the interactive viewer →

aperiodic def-parametric implemented ruled tradition-classical

Formula

x(u, v)

v \cos\left(u\right)

y(u, v)

v \sin\left(u\right)

z(u, v)

0.5 \sin\left(2 u\right)

Properties

Family: ruled
Given by: a parametrisation
Curvature: no condition imposed
Periodicity: not periodic
Ends: 0
Embedding: embedded or immersed depending on parameters
Fidelity: exact
Exactness: elementary

Definition

the record's default variant, Plucker's conoid (cylindroid) h = 0.5 sin 2u with ruling half-length 1; the n-fold, Wallis, Zindler and Whitney variants share the operator but not this chart

Sources

Chart reproduced numerically against the shipped implementation: fwd max 0.32 of tol, 0.0% of oracle beyond tol (tol floor 2.5 x 0.05981).

J. Plucker, Neue Geometrie des Raumes (1868) -- the cylindroid.
J. Wallis, for the conical edge.
K. Zindler, for the conoid z(x^2 - y^2) = 2axy.