Given a triangle patch with vertices [v1,v2,v3], provide coordinates of the new vertices [b_i, b_(i+1), ...] inserted inside the triangle patch via barycentric coordinates [(u_i, v_i, w_i), (u_(i+1), v_(i+1), w_(i+1)), ...] such that b_i = u_i*v1 + v_i*v2 + w_i*v3.