How to plot a large number of rectangles from a matrix

I have thousands of files of survey data. My ultimate goal is find a way of grouping these together by geographical region and concatenating those that are similar. This is a difficult concept for me but what Ive decided might be the easiest is to first find there geographical limits, graph a rectangle of each using the NE and SW corner, find the area, then determine if the surveys are in the same region using the amount of overlap from each rectangle. For instance, if the area of one survey rectanlge over laps another by 70 percent then they could be considered the same region and the files should be concatenated before being processed. Hopefully that makes sense and if there is an easier way of doing this please let me know.

To start im trying to create these rectangles. The first thing I did was set up where the files are and how they should be read. Next I found the max and min lat and long. I created four points, minlong maxlat, minlong minlat, maxlon minlat, maxlon maxlat. This should be enough to create a rectangle right? The first issue im running into is how to get every file to add these four values to one matrix, Im getting confused on the format of it all, how should the matrix be setup to be read as ordered points and individual rectangles? Right now I have two columns with 12 total rows from 3 files, everything was read correctly but how I do then plot each of these as individual rectangles to find the area? Im pretty lost but the little bit of code Ive created is below. Thanks for any and all help!

clear
P = 'C:/Users/lastname/OneDrive/Desktop/Single Beam Bathy/SN06222'; 
Q = 'C:/Users/lastname/OneDrive/Desktop/Single Beam Bathy/SN06222/Corrected CSV'; 
S = dir(fullfile(P,'*.csv'));
% S = natsortfiles(S); 
N = numel(S);
C = cell(N,2);

for k= 1:numel(S)
    F1 = fullfile(S(k).folder,S(k).name);
    M = readmatrix(F1);  
    
    lat = M(:,1);
    lon = M(:,2);

    [minLat, maxLat] = bounds(lat);
    [minLon, maxLon] = bounds(lon);

    C{k,1} = [maxLat; maxLat; minLat; minLat];
    C{k,2} = [maxLon; minLon; maxLon; minLon];
    c = cell2mat(C);
end

Answer 1

[Matt J]

I don't really see why you need to find bounding rectangles to do what you describe. You could just represent the regions as polyshapes,

N=numel(S);
p(N)=polyshape();

for k= 1:numel(S)
    F1 = fullfile(S(k).folder,S(k).name);
    p(k) = polyshape(readmatrix(F1));  
end

plot(p)

You can also find the overlap area of two of the regions using polyshape methods,

overlap(j,k) = area( intersect( p(j),p(k) ) )

[Bradley]

What i am having an issue with (and the reason I found the geographical limits) is that each survey has between 50-100k points and often overlaps or has the same vertices. With polyshape I suspect it will plot some really crazy shape that includes all the different lines. What im really trying to find is whether the survey is unique (a region that has only been surveyed once) or if it a region that has been surveyed many times. I figured by creating a rectangle for each then it should be easier and faster to calculate which surveys should be concatenated. Hopefully im making sense, im still new to matlab and trying to learn as much as I can. Thanks again for your help. Do you know of a way to find overlap in patch objects?

[Matt J]

You can still have rectangular polyshapes,

for k= 1:numel(S)
    F1 = fullfile(S(k).folder,S(k).name);
    M = readmatrix(F1);  
    
    lat = M(:,1);
    lon = M(:,2);
    [minLat, maxLat] = bounds(lat);
    [minLon, maxLon] = bounds(lon);
    
    p(k)=polyshape([maxLat, maxLat, minLat, minLat; ...
                    maxLon, minLon, maxLon, minLon]')
end


plot(p)

[Bradley]

Thanks again for the help, I had to brute force the polyshape as it wanted a 2 column matrix with at least 3 rows. My updated code is below, what does p(j) do in the overlap function above? Thanks!

for k= 1:numel(S)
    F1 = fullfile(S(k).folder,S(k).name);
    M = readmatrix(F1);  
    
    lat = M(:,1);
    lon = M(:,2);
    [minLat, maxLat] = bounds(lat);
    [minLon, maxLon] = bounds(lon);

    C = [maxLon maxLon minLon minLon; maxLat minLat minLat maxLat];
    c = C.';

    p(k)=polyshape(c);
end
plot(p)

I used these lines to create a matrix of overlap

polyvec = p;
plot(polyvec)
TF = overlaps(polyvec);

Also, is there any logic behind the color schemes? I have ~10 suverys plotted using this method and some have similar or the same colors while others have unique colors. Is there a way to change the colors based on how many surveys overlap each other? Thanks again for the help.

[Matt J]

The polyshape colors and alphas are under your control through the handles returned by plot(), e.g.,

p1 = polyshape([0 0 1 1],[1 0 0 1]);
p2 = polyshape([0.75 1.25 1.25 0.75],[0.25 0.25 0.75 0.75]);
p3 = polyshape([1.25 1.25 1.75 1.75],[0.75 1.25 1.25 0.75]);
polyvec = [p1 p2 p3];
H=plot(polyvec);

H(1).FaceColor='r'; H(1).FaceAlpha=0.8;
H(2).FaceColor='g'; H(2).FaceAlpha=0.2;
H(3).FaceColor='b';