How do I add shadings when overlapping polygons?

 figure();
 x = [0 1 1 0];
 y = [0 0 1 1];
 xy = polyshape(x,y); hold on;
 xx = [0 0.5 0.5 0];
 yy = [0 0 0.5 0.5];
 xxyy = polyshape(xx,yy); 
 xxx = [0.25 0.75 0.75 0.25];
 yyy = [0.25 0.25 0.75 0.75];
 xxxyyy = polyshape(xxx,yyy); 
 
 L = linspace(0,2.*pi,100);
 kx = 0.2*cos(L)'+0.7;
 ky = 0.2*sin(L)'+0.7;
 kreis = polyshape(kx(1:end-1),ky(1:end-1));
 
 plot(xy)
 plot(xxyy)
 plot(xxxyyy)
 plot(kreis)
 axis equal;

I have a variety of polygons. Now I need to know how to either shade the overlapping areas according to a grayscale (the the more polygons overlapping the darker the intersecting area) or to otherwise gain information about the overlapping areas. Thanks

Answer 1

[Matt J]

Why not just create a grayscale image?

 t= linspace(0,1,300);
 [X,Y]=meshgrid(t); 
 sz=size(X);
 X=X(:);Y=Y(:);
 I=xy.isinterior(X,Y)+xxyy.isinterior(X,Y)+xxxyyy.isinterior(X,Y)+...
   kreis.isinterior(X,Y);

  imagesc((reshape(I,sz)),'XData',t,'YData',t); 
  colormap(gray)
  axis image
  set(gca,'YDir','normal');
  

[Dominik Wienerroither]

Thank you!

Answer 2

[Steven Lord]

To determine if two polyshape objects overlap, use the overlaps function (introduced in release R2018a) or the intersect function (release R2017b, when polyshape was introduced.)