Written by Paul Bourke
July 1996

The following are the formulae for some of the more common quadrics, that is, surfaces formed by an equation in x and y of at most degree 2.

Ellipsoid, real (Special case: Sphere)

Ellipsoid, imaginary

Cone, real

Cone, imaginary

Cylinder, real (Elliptic)

Cylinder, imaginary (Elliptic)

Cylinder (Hyperbolic)

Cylinder (Parabolic)

Paraboloid (Elliptic)

Paraboloid (Hyperbolic)

Hyperboloid (Single sheet)

Hyperboloid (Double sheet)