Download the contents of: http://www.math.udel.edu/~driscoll/SC/

use

scgui and name the polygon as "polygon" and the map as "map". Then copypaste the following to Matlab.

M=500;
p=0.9;
l=linspace(-1,1,M);
[X,Y]=meshgrid(l,l);
Z=X+1i*Y;
aper=ceil(max(0,1-abs(Z)));
Z=Z.*aper;
W=map(Z);
W=(W+4+4i)/8;
N=800;
A=zeros(N);
W=round(W*(N-1));
w1=real(W);w2=imag(W);
B=imread('chess.tif');
[C,col] = rgb2ind(B,1000);
[n,m]=size(C);
%C=double(C);
%Cmin=min(min(C));Cmax=max(max(C));
nn=min(n,m);
z1=real(Z);z2=imag(Z);
z1=round(nn/2+nn/2*p*z1);z2=round(nn/2+nn/2*p*z2);
R=zeros(N);
%Aper=zeros(n,m);
Aper=0*C;
for k=1:M
for j=1:M
Aper(z1(k,j),z2(k,j))=1;
R(w1(k,j),w2(k,j))=C(z1(k,j),z2(k,j));
end
end
CC=C.*Aper;
R=uint8(R);

%Crand0=round(rand(n,m));
%Crand=round((1-Crand0)*Cmin+Crand0*Cmax);
%CC=(1-Aper).*Crand+C.*Aper;

%figure
%image(R)
%colormap(col)
%figure
%image(CC);colormap(col)

subplot(1,2,1)
image(CC);colormap(col)
subplot(1,2,2)
image(R),colormap(col)