actual trilinear coordinates

The trilinear coordinates α:β:γ of a point P relative to a reference triangle are proportional to the directed distances a' :b' :c' from P to the side lines of the triangle, but are undetermined up to a constant of proportionality k, i.e., a' | = | k α b' | = | k β c' | = | k γ. The constant k is given by k congruent (2Δ)/(a α + b β + c γ), where Δ = r s is the triangle area of Δ A B C, r is the inradius, s is the semiperimeter, and a, b, and c are the lengths of its sides.

areal coordinates | barycentric coordinates | reference triangle | trilinear coordinates