Given is a 2D triangle with data values fo, fi, and f2 at the vertices x0, X₁, and x2 that are interpolated linearly on a triangle by f(x, y)=\alpha_{0}(x, y)

f_{0}+\alpha_{1}(x, y) f_{1}+\alpha_{2}(x, y) f_{2} using linear barycentric coordinates a; as basis functions. The constant gradient of this function \nabla f=\nabla \alpha_{0} f_{0}+\nabla \alpha_{1} f_{1}+\nabla \alpha_{2} f_{2} is represented as the linear combination of constant basis function gradient vectors Vai E R². Determine closed form expressions of all Vai with respect to the vertex coordinates xi. Is there a geometric interpretation of these basis function gradients?