Relative to a given triangle of reference A₁ A₂ A₃ the areal coordinates of a point P inside, or on the boundary of, the triangle are (x₁, x₂, x₃), where x₁, x₂, x₃ are the areas of triangles PA₂A₃, PA₃A₁, PA₁A₂, respectively. In the usual case, where the triangle of reference is

Areal coordinates. The location of a point is specified by the areas of the component regions.

equilateral, the coordinates are called barycentric coordinates. The idea can be generalized to a tetrahedron of reference, using volumes, and to a simplex of reference.