What Are Barycentric Coordinates?
What Are Barycentric Coordinates? Barycentric coordinates provide a way to describe any point inside a triangle using the triangle’s own vertices as a reference. Instead of relying on the usual x–y axes, we express a point as a weighted combination of the three corners. The Core Idea Let a triangle have vertices A , B and C . Any point P inside (or on) the triangle can be written as P = αA + βB + γC The numbers α, β and γ are the barycentric coordinates of P. They indicate how strongly each vertex contributes to P. For this expression to make geometric sense, the three weights must satisfy α + β + γ = 1 This condition ensures that P behaves like a weighted average — a “blend” of A, B and C — rather than drifting away from the triangle. As long as all three values are non-negative ( α, β, γ ≥ 0 ), the point lies somewhere within the triangle. Examples α = 1 , β = γ = 0 → P = A α = β = 0.5 , γ = 0 → midpoint of AB α = ...