Cone of Revolution

Cone of Revolution is a quadric surface, defined by an implicit equation, immersed with singularities.

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aperiodic def-implicit implemented noncompact quadric singular tradition-classical

Formula

x^{2} + y^{2} - z^{2} = 0

Properties

Family: quadric
Given by: an implicit equation
Curvature: no condition imposed
Periodicity: not periodic
Ends: 0
Embedding: immersed with singularities
Orientable: yes
Fidelity: exact
Exactness: elementary

Definition

Revolution of a line secant to an axis about that axis; the special case of the elliptic cone (whose record already resolves ch1235) with circular cross-section.

Sources

Classical closed form, written directly in the exact language and checked by the validator.

Classical.
R. Ferreol, "Cone of revolution", Encyclopedie des formes mathematiques remarquables, mathcurve.com; local mirror chapter ch1229_conederevolution_2 (S:/data/math_art/references/websites/mathcurve/book/surfaces/ch1229_conederevolution_2.md).