A
spotlight
is similar
to a point light source, but emits light in a specific direction in the shape
of a cone.

Source: Unity3d
A
spotlight radiates light within a cone.
In addition, light is modeled so that it is brightest along the
direction the spotlight is pointing.
For
this we required three additional light properties:
- a direction the
spotlight is pointing
- a cutoff
angle, used to define a cone around the direction vector
- an exponent,
describing how light falls off from the centre
When
rendering a point, we first check to see if it’s inside the cone. If it is not inside the cone, we just return
the ambient term.
If
the point is inside the cone, we determine the intensity of the spotlight at
the point based on the form