Smooth fractal surfaces derived from bicubic rational fractal interpolation functions

where δ is a positive real number, which we specify later. It can easily be verified that this metric is equivalent to the Euclidean metric on R3. Denote Ri,j(x, y) = Pi,j(φi(x), φj(y))−si,jBi,j(x, y), due to the C1-continuous functions Pi,j(x, y) and Bi,j(x, y), the function Ri,j(x, y) is C 1-continuous over Ω. So, a constant number μi,j exists, such that: |Ri,j(x, y)−Ri,j(x, y′)| < μi,j(|x− x′|+ |y − y′|).