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Elliptic Cone

A Cone with Elliptical Cross-Section. The parametric equations for an elliptic cone of height $h$, Semimajor Axis $a$, and Semiminor Axis $b$ are

$\displaystyle x$ $\textstyle =$ $\displaystyle (h-z)a\cos\theta$  
$\displaystyle y$ $\textstyle =$ $\displaystyle (h-z)b\sin\theta$  
$\displaystyle z$ $\textstyle =$ $\displaystyle z,$  

where $\theta\in [0,2\pi)$ and $z\in [0,h]$.

See also Cone, Elliptic Cylinder, Elliptic Paraboloid, Hyperbolic Paraboloid


Fischer, G. (Ed.). Plate 68 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 63, 1986.

© 1996-9 Eric W. Weisstein