function re_im = dthird(im, p, q)
%双三次插值法实现图像缩放，输入目标图像和行缩放、纵缩放倍数
im = imread('test.jpg')
p = 4
q = 4
im = im2double(im);
[m,n] = size(im);
im_R = im(:,:,1);
im_G = im(:,:,2);
im_B = im(:,:,3);
l = round(m*p);
h = round(n*q)/3;
re_R = zeros(l,h);
re_G = zeros(l,h);
re_B = zeros(l,h);
for dstx = 1:l
for dsty = 1:h
x = floor(dstx/p); u = dstx/p - x;
y = floor(dsty/q); v = dsty/q - y;
%逼近函数，A = s[]
sa = 4 - 8*abs(u+1) + 5*abs(u+1)^2 - abs(u+1)^3;
sb = 1 - 2*abs(u)^2 + abs(u)^3;
sc = 1 - 2*abs(u-1)^2 + abs(u-1)^3;
sd = 4 - 8*abs(u-2) + 5*abs(u-2)^2 - abs(u-2)^3;
A = [sa, sb, sc, sd];
%逼近函数，C = s[]
sa = 4 - 8*abs(v+1) + 5*abs(v+1)^2 - abs(v+1)^3;
sb = 1 - 2*abs(v)^2 + abs(v)^3;
sc = 1 - 2*abs(v-1)^2 + abs(v-1)^3;
sd = 4 - 8*abs(v-2) + 5*abs(v-2)^2 - abs(v-2)^3;
C = [sa; sb; sc; sd];
%考虑到边界像素，分类讨论得到插值计算区域矩阵 B[]
xi = max(1,x-1); xx = max(1,x); xa = min(m,x+1); xaa = min(m,x+2);
yi = max(1,y-1); yy = max(1,y); ya = min(n/3,y+1); yaa = min(n/3,y+2);
if xi~=x-1||yi~=y-1||xaa~=x+2||yaa~=y+2
BR = [im_R(xi,yi),im_R(xi,yy),im_R(xi,ya),im_R(xi,yaa);im_R(xx,yi),im_R(xx,yy),im_R(xx,ya),im_R(xx,yaa);
im_R(xa,yi),im_R(xa,yy),im_R(xa,ya),im_R(xa,yaa);im_R(xaa,yi),im_R(xaa,yy),im_R(xaa,ya),im_R(xaa,yaa)];
BG = [im_G(xi,yi),im_G(xi,yy),im_G(xi,ya),im_G(xi,yaa);im_G(xx,yi),im_G(xx,yy),im_G(xx,ya),im_G(xx,yaa);
im_G(xa,yi),im_G(xa,yy),im_G(xa,ya),im_G(xa,yaa);im_G(xaa,yi),im_G(xaa,yy),im_G(xaa,ya),im_G(xaa,yaa)];
BB = [im_B(xi,yi),im_B(xi,yy),im_B(xi,ya),im_B(xi,yaa);im_B(xx,yi),im_B(xx,yy),im_B(xx,ya),im_B(xx,yaa);
im_B(xa,yi),im_B(xa,yy),im_B(xa,ya),im_B(xa,yaa);im_B(xaa,yi),im_B(xaa,yy),im_B(xaa,ya),im_B(xaa,yaa)];
else
BR = im_R(xi:xaa,yi:yaa);
BG = im_G(xi:xaa,yi:yaa);
BB = im_B(xi:xaa,yi:yaa);
end
%插值主运算 A*B*C
re_R(dstx,dsty) = (A*BR)*C;
re_G(dstx,dsty) = (A*BG)*C;
re_B(dstx,dsty) = (A*BB*C);
end
end
rm = cat(3,re_R,re_G,re_B);
re_im = im2uint8(rm);
figure,imshow(re_im);
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