The signed distance from a point to an oriented hyperplane is the perpendicular distance with a sign determined by which side contains the point. It is positive on the side toward which the unit normal vector points, negative on the opposite side, and zero on the hyperplane.
If 
is the unit normal vector and 
is any point of the hyperplane,
the signed distance of 
is the dot product
 |
Reversing 
reverses the sign of 
(Georgiades 1992).
On a line with a unit-scale coordinate 
increasing in the chosen direction, the
signed distance from 
to 
is 
.
For a triangle traversed in the order 
, 
, 
, take the left side of the line
directed from 
to 
as positive. The signed distance of 
from that line is the signed height
in the signed area formula.
In trilinear coordinates, each sideline of the reference triangle is oriented by the unit normal vector pointing toward the opposite polygon vertex.
