intersection area of 3 or more rectangles

hi all, I have multiple rectangles defined by rectangle()- function. I now want to find the intersection area of 3 rectangles (I know that for 2 rectangles rectint works). Alternatively it might be an option to find the intersection area of the intersection (rectangle 1, rectangle 2) with the rectangle 3.

Is there a funtion or simple solution for this problem?

Thanks!

Answer 1

[Adam Danz]

This approach is inspired by the even-odd rule for determining if a point is inside a polygon. If the max left-edge value is smaller than the min right-edge value and if the max bottom-edge value is smaller than the min top-edge value, then all rectangles overlap. This only works when rectangle edges are parallel to the axes (ie, not rotated beyond 90 deg intervals).

Input:

r: an array of handles of rectangle objects. Add as many as you'd like.

Output:

rectDim: 1x4 vector; contains the [left, bottom, width, height] of the overlapping rectangle. If there isn't an overlapp of all rectangles, it will be all NaN values.

Variations:

If you'd rather work with [left, bottom, right, top] values directly rather than working with rectangle objects, create an nx4 matrix of those values for n rectangles, name it LBRT and remove the first two sections of code.

If you'd rather work with [left, bottom, width, height] values directly rather than working with rectangle objects, create an nx4 matrix of those values for n rectangles and convert to bounds using the LBRT conversion in the second section of code.

% Generate n rectangels with random positions and sizes and 
% store their handles in vector 'r'.
cla()
hold on
r(1) = rectangle('position',rand(1,4).*[1,1,2,2],'EdgeColor','g','LineWidth',3); 
r(2) = rectangle('position',rand(1,4).*[1,1,2,2],'EdgeColor','m','LineWidth',3); 
r(3) = rectangle('position',rand(1,4).*[1,1,2,2],'Edgecolor','b','LineWidth',3); 
% r(n) = rectangel(....)  add as many as you want! 

%% Find overlap of all rectangles
% Convert nx4 matrix [left,bottom,width,height] -> [left,bottom,right,top]
LBRT = vertcat(r.Position); 
LBRT(:,3) = sum(LBRT(:,[1,3]),2);
LBRT(:,4) = sum(LBRT(:,[2,4]),2); 

% Test Left|Right edge intersections
[~,LRidx] = sort([LBRT(:,1);LBRT(:,3)]);
LRtest = max(LRidx(1:numel(LRidx)/2)) < min(LRidx(numel(LRidx)/2+1:end));

% Test Bottom|Top edge intersections
[~,BTidx] = sort([LBRT(:,2);LBRT(:,4)]);
BTtest = max(BTidx(1:numel(BTidx)/2)) < min(BTidx(numel(BTidx)/2+1:end));

if LRtest && BTtest
    % All rectangles overlap. The overlap is defined by the max left side, 
    % min right side, same with bottom/top. Fill in overlap.
    overlapPos = [max(LBRT(:,1)), max(LBRT(:,2)), min(LBRT(:,3)), min(LBRT(:,4))];
    rectDim = [overlapPos(1:2), overlapPos(3:4)-overlapPos(1:2)];
    rectangle('Position', rectDim, 'FaceColor',[.0 0 0 .3])
else
    rectDim = nan(1,4);
end

[Tobias Eißler]

Thanks @Adam Danz, it ssems like this is what I have been looking for! still have to try it if it works for my problem :D

[Adam Danz]

I tried with 3, 4 and 5 rectangles and it works just as in the GIF image. It should work with any number of rectangles, I believe.

[Tobias Eißler]

yeah it works perfectly, thanks a lot!

Answer 2

[darova]

Try polyxpoly with for loop

[Adam Danz]

I didn't know about polyxpoly, thanks @darova! But it's immediately clear to me how that would be applied to finding the internal intersection of n rectanlges.

[Tobias Eißler]

thanks @darova, I am still quite new to MATLAB so I am not really sure how i would use it. So I think I will try @Adam Danz solution

Answer 3

[Matt J]

If you put your rectangles in the form of a polyshape vector (I'll call it polyvec), then it is very easy:

Area = area(intersect(polyvec))