The limit of a family of barycentric coordinates for quadrilaterals

Recently, Floater (2015) proposed a one-parameter family of generalized barycentric coordinates for quadrilaterals. In this note we gave a proof to his observation on the limit of such coordinates: the coordinates approach the piecewise linear coordinates obtained by triangulating the quadrilateral using one or other of the diagonals if the parameter ρ tends to 0 or infinity.