## 3.5 Other Quadrics

`pbrt` supports three more quadrics: cones, paraboloids, and
hyperboloids. They are implemented in the source files
`shapes/cone.h`,
`shapes/cone.cpp`,
`shapes/paraboloid.h`,
`shapes/paraboloid.cpp`,
`shapes/hyperboloid.h`, and
`shapes/hyperboloid.cpp`. We won’t
include their full implementations here, since the techniques used to
derive their quadratic intersection coefficients, parametric coordinates,
and partial derivatives should now be familiar. However, we will briefly
summarize the implicit and parametric forms of these shapes. A rendered
image of the three of them is in Figure 3.10.

Cones are also described parametrically:

The partial derivatives at a point on a cone are

and the second partial derivatives are

### 3.5.2 Paraboloids

The implicit equation of a paraboloid centered on the axis with radius and height is

and its parametric form is

The partial derivatives are

and

and the parametric form is

The partial derivatives are

and