紧急，双立方插值法放大，来个大神帮解决原理，百度的没说清

clc;
close all;
%f =rgb2gary(imread('1.jpg'));
f =imread('lena.bmp');
[mm,nn]=size(f);
m=mm/2;n=nn/2;
ff = zeros(m,n);
for i=1:m
for j=1:n
ff(i,j)=f(2*i,2*j);
end
end
k=4;
a=ff(1,:);
c=ff(m,:);
b=[ff(1,1),ff(1,1),ff(:,1)',ff(m,1),ff(m,1)];
d=[ff(1,n),ff(1,n),ff(:,n)',ff(m,n),ff(m,n)];
a1=[a;a;ff;c;c];
b1=[b;b;a1';d;d];
fff=b1';f1=double(fff);
g1 = zeros(k*m,k*n);
for i=1:k*m
u=rem(i,k)/k; i1=floor(i/k)+2;
A=[sw(1+u) sw(u) sw(1-u) sw(2-u)];
for j=1:k*n
v=rem(j,k)/k;j1=floor(j/k)+2;
C=[sw(1+v);sw(v);sw(1-v);sw(2-v)];
B=[f1(i1-1,j1-1) f1(i1-1,j1) f1(i1-1,j1+1) f1(i1-1,j1+2)
f1(i1,j1-1) f1(i1,j1) f1(i1,j1+1) f1(i1,j1+2)
f1(i1+1,j1-1) f1(i1+1,j1) f1(i1+1,j1+1) f1(i1+1,j1+2)
f1(i1+2,j1-1) f1(i1+2,j1) f1(i1+2,j1+1) f1(i1+2,j1+2)];
g1(i,j)=(A*B*C);
end
end
function A=sw(w1)
w=abs(w1);
if w<1&&w>=0
A=1-2*w^2+w^3;
elseif w>=1&&w<2
A=4-8*w+5*w^2-w^3;
else
A=0;
end
图像的缩小，再扩展后会成什么？是怎样插值的？