Design of complex Roof surface from AutoCad to Robot structural analysis Pro part 2

An elliptic paraboloid is shaped like an oval cup and has a maximum or minimum point when its axis is vertical. In a suitable coordinate system with three axes x, y, and z, it can be represented by the equation. where a and b are constants that dictate the level of curvature in the xz and yz planes respectively.
An elliptic paraboloid is a paraboloid whose vertical cross sections are all parabolas, while the horizontal cross sections are all ellipses. In its simplest form, an elliptic paraboloid can be generated via the rotation of a parabola around its axis of symmetry.

Elliptical constructions are grammatically incomplete for the deliberate purpose of concise prose. The term “elliptical” comes from “ellipsis” which indicates an omission, something left out. An elliptical construction delivers its meaning only if the context makes clear what the missing elements are.

a paraboloid that can be put into a position such that its sections parallel to one coordinate plane are ellipses, while its sections parallel to the other two coordinate planes are parabolas.