area_pix(picture_fi​lename)

Calculates the relation of areas of two domains by counting pixels.

An application: given a domain E and a disc D with area 1, you obtain the
area of E.

Give a picture containing
*E with one color
*D with another color (prefer white)
*black background

Since the relative areas are calculated, area(E)/area(D) applying an
affine transformation to the picture will not change the result.


Demo1:

urlwrite('http://integraali.com/stuff/kuvioD.png','kuva.png')
area_pix('picture.png')

Demo2:

t=linspace(0,2*pi,100);
x=cos(t).^3;
y=sin(t).^3;
h=figure;
plot(x,y,'k')
hold on
axis([-10 10 -10 10])
g=ginput(1);
a=g(1)+cos(t);
b=g(2)+sin(t);
plot(a,b,'k')
axis equal
box off
axis off
%edit the picture with Paint and apply Demo1