# Exact Trilinear Coordinates

Exact Trilinear Coordinates

Given a reference triangle , the trilinear coordinates of a point with respect to that triangle is any ordered triple of numbers proportional to the directed distances from to the directed sides (or their extensions as infinite directed lines) , , and , in that order. Exact trilinear coordinates are trilinear coordinates normalized to be the actual distances of to each of the three sides. The sign of a distance is taken as positive if 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 .

△ABC

P

P

AB

BC

CA

P

P

P