Stenciling - Introduction to 3D Game Programming with DirectX 9.0 - page 146

Then:

d n p

s p L

n L

8.3.2 Point Light Shadows

Figure 8.7: The shadow cast with respect
to a point light source

Figure 8.7 shows the shadow that an object casts with respect to a point
light source whose position is described by the point L . The light ray
from a point light through any vertex p is given by r ( t )= p + t ( p - L ).
The intersection point of the ray r ( t ) with the plane n p + d = 0 gives
s . The set of intersection points found by shooting r ( t ) through each of
the object's vertices with the plane defines the geometry of the shadow.
s can be solved for using the same technique (plane/ray intersection)
used in section 8.3.1.

Note: Notice that L serves different purposes for point and parallel
lights. For point lights we use L to define the position of the point light.
For parallel lights we use L to define the direction of the parallel light
rays.

8.3.3 The Shadow Matrix
Notice from Figure 8.6 that for a parallel light, the shadow is essentially
a parallel projection of the object onto the plane n p + d =0inthe
specified light direction. Similarly, Figure 8.7 shows that for a point
light, the shadow is essentially a perspective projection of the object
onto the plane n p + d = 0 from the viewpoint of the light source.
We can represent the transformation from a vertex p to its projec-
tion s with the plane n p + d = 0 with a matrix. Moreover, we can
represent both an orthogonal projection and a perspective projection
with the same matrix using some ingenuity.