Remove overlapping areas of 663 rectangles

As in the first image (Figure 1), I am trying to remove the overlaps of 663 intersecting rectangles, and have the outmost lines visible. The second image (Figure 2) presents an example with two intersecting rectangle. I have attached an EXCEL file containing the coordinates of all the rectangles. I've stuck with this problem, please help me.

Figure 1

Figure 2

[KSSV]

There are many rectangles overlapping..you want to consider only two rectangles? OR all the overlapping rectangles?

[Wen Fang]

Thank you for your comment. I want to consider all the overlapping rectangles.

[KSSV]

If you can tell what is the final purpose....there might be another simple approach rather then this.

Are you looking for something like this?

[Wen Fang]

You are totally right. But I want to have the sides of the polygons visible after removing the overlaps. The following is a simple example with three intersecting rectangles.

Answer 1

[Bruno Luong]

data = xlsread('Rectangle points.xlsx');

data = reshape(data,[],2,4);
data = permute(data,[2 3 1]);

n = size(data,3);
p = arrayfun(@(k) polyshape(data(1,:,k),data(2,:,k)), 1:n);
q = p(1);
for k=2:n
    q = union(q,p(k));
end

plot(q)
axis equal

[Wen Fang]

Bingo! Thank you so much for helping me solve this problem. It helps me a lot. By the way, is there any way to calculate the area of the final ploygons filled with color?

[KSSV]

+1...I was thinking it in a complex way.

[Bruno Luong]

>> q.area

ans =

     2.8940e+05

Please read doc of POLYSHAPE before asking.

[KSSV]

@ Wen Fang I am curious to know what this data corresponds to and what is the application? Kind of maze or something?

[Wen Fang]

@Bruno Luong I am sorry, but I don't have POLYSHAPE function in my version of MATLAB(R2015b). I have added a copy of this function to my MATLAB. Thank you again for your kind help.

@KSSV Also give special thanks to you=. Actually this data corresponds to the fracture distribution of a outcrop, something relates to my major.

[Bruno Luong]

For your convenient Online doc of polyshape.

[Wen Fang]

@ Bruno Luong Thank you so much for your previous kind help. Now this problem become harder. What if the problem becomes a 3D problem? That is to say, every rectangle becomes a cuboid. We still know the 8 coordpoints of every cuboid (plz see attachment). Is there any way to remove the intersections? Please help me.

[Bruno Luong]

Sorry I do not know any built-in data structure that can store a volume in 3D by plannar faces, beside convex hul (but in your case it is not convex at all), let alone doing operation on it.

[Wen Fang]

@ Bruno Luong Thank you for your reply. Seems like this is an impossible task.