How to evaluate the union area of the multiple circles plotted in matrix form of centers and radii?

Specially looking for the area inside the rectangle covered by the union of circles...

Answer 1

[Matt J]

An approximate calculation can be made as follows,

C={centreG1,centreG2,centreG3,centreG4,centreG5,centreG6};

p=cellfun(@polycircle,C,{radii});

Area=area(union(p))

function p=polycircle(center,R)

   p=translate( nsidedpoly(1e4,'Radius',R), center);

end

[Rohan Shinde]

can you fix the error?

[Matt J]

I fixed it (see above).

[Rohan Shinde]

yes but if we want the area inside the square only as mentioned earlier...

something like area(Union(all circles)) intersection area(rectangle)

[Matt J]

A simple change,

rect=polyshape(vertices); %rectangle polyshape

area( intersection(union(p),rect) )

but you would have to put the rectangle in polyshape form.

[Rohan Shinde]

error is invalid expression

[Rohan Shinde]

and also what if the N in the above solution is to be increased upto 5 or 6 or more and the quantity of random number generation is kept around 500 simulations and we need to track the output for such 500 simulations...

I was figuring out this solution for last 2 days sir...

even though I am new to this platform...

would be able to do it because of you...

Thank you so much

will appreciate if you help in further simulation...

i think a for loop will help in getting those 500 simulations for N=5 or 6 or more...

[Matt J]

C={centreG1,centreG2,centreG3,centreG4,centreG5,centreG6};
radiioverall={30,30,30,30,30,30}
p=cellfun(@polycircle,C,radiioverall);

rect=polyshape([-125,29875;-125,30125;125,30125;125,29875]);

Area=area(intersection(union(p),rect))

function p=polycircle(center,R)
p=translate( nsidedpoly(1e4,'Radius',R), center);
end

[Matt J]

intersection is unrecognised function is the error

Should be

Area=area(intersect(union(p),rect))

also if N is 2 or more then how the solution can be designed...?

That seems like a very different matter. I would post that as a new question (after Accept-clicking this solution).

[Rohan Shinde]

Okay it worked... :-)

intersect is the function

Now how do we turn this situation for 2 or more than 2 times the circles are created by the normal distribution function and then number of circles will increase by N then how to solve and such simulation to be run for 500 times...

[Rohan Shinde]

yes i would create another qeustion and share that link with you in a minute...

[Rohan Shinde]

https://in.mathworks.com/matlabcentral/answers/1665914-evaluate-the-intersection-area-between-the-circles-and-the-rectangle-with-increasing-number-of-circl?s_tid=srchtitle

@Matt J

[Rohan Shinde]

@Matt J how to plot {area(intersect(union(p),rect))} this area???

and also kindly check the above link for another question i have uploaded...

[Rohan Shinde]

solved the plotting issue myself...

plot(intersect(union(p),rect))

Answer 2

[Steven Lord]

A different approach, one that doesn't involve cell arrays or cellfun:

center = randi(10, 6, 2); % 6 circle centers
radius = randi(5, 6, 1); % 6 circle radii

% Iterate backwards so the first assignment to C allocates
% the right number of elements
for whichCircle = size(center, 1):-1:1
    % Approximate each circle with a 1000-sided polyshape
    C(whichCircle) = nsidedpoly(1e3, ...
        'Center', center(whichCircle, :), ...
        'Radius', radius(whichCircle));
end
plot(C)
axis equal

A = area(union(C))

A = 162.1206

[Rohan Shinde]

the circles are inclusive in the rectangle sir...

[Steven Lord]

This sample code focused on creating some sample circles. You can take it and adapt it to suit your additional requirements.

[Rohan Shinde]

yes i have competed the solution but another problem need to be sorted...

here is the link, kindly suggest the solution...

https://in.mathworks.com/matlabcentral/answers/1665914-evaluate-the-intersection-area-between-the-circles-and-the-rectangle-with-increasing-number-of-circl?s_tid=srchtitle