It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane
 |
(1)
|
by defining the components of the unit normal vector 
,
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
and the constant
 |
(5)
|
Then the Hessian normal form of the plane is
 |
(6)
|
and 
is the distance of the plane from the origin (Gellert
et al. 1989, pp. 540-541). Here, the sign of 
determines the side of the plane on which the origin is located.
If 
,
it is in the half-space determined by the direction
of 
,
and if 
,
it is in the other half-space.
The point-plane distance from a point 
to a plane (6)
is given by the simple equation
 |
(7)
|
(Gellert et al. 1989, p. 541). If the point 
is in the half-space determined
by the direction of 
,
then 
;
if it is in the other half-space, then 
.
