WOLFRAM|DEMONSTRATIONS PROJECT

Exact Trilinear Coordinates

​
2.74 : 1.47 : 1.02
Given a reference triangle
△ABC
, the trilinear coordinates of a point
P
with respect to that triangle is any ordered triple of numbers proportional to the directed distances from
P
to the directed sides (or their extensions as infinite directed lines)
AB
,
BC
, and
CA
, in that order. Exact trilinear coordinates are trilinear coordinates normalized to be the actual distances of
P
to each of the three sides. The sign of a distance is taken as positive if
P
is on the same side of the directed triangle as the triangle and negative otherwise. You can drag the vertices to modify the triangle and the point
P
.