Elliptic Paraboloid

A Quadratic Surface which has Elliptical Cross-Section. The elliptic paraboloid of height $h$, Semimajor Axis $a$, and Semiminor Axis $b$ can be specified parametrically by

$$x = a \sqrt{u}\,\cos v$$

$$y = b \sqrt{u}\,\sin v$$

$$z = u.$$

for $v \in [0, 2\pi)$ and $u\in [0,h]$.

See also Elliptic Cone, Elliptic Cylinder, Paraboloid

References

Fischer, G. (Ed.). Plate 66 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 61, 1986.