# How to calculate the area percentage of the polygons?

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SUSHMA MB
on 29 Jun 2017

Commented: Image Analyst
on 30 Jun 2017

I have x_limit and y_limit as [69.5,70.5] and [21.2,21.8] inside which their i have plotted many polygons (the coordinates of those polygons are attached with this text). Now i want to calculate the percentage of area occupied by the polygons inside the particular x_limit and y_limit.

Thank you

##### 0 Comments

### Accepted Answer

Image Analyst
on 30 Jun 2017

Edited: Image Analyst
on 30 Jun 2017

Try this, using polyarea(). Note though that I am not deducting area for any overlapping portions. In other words, I assume no polygons overlap when computing area fraction:

clc; % Clear the command window.

close all; % Close all figures (except those of imtool.)

clear; % Erase all existing variables. Or clearvars if you want.

workspace; % Make sure the workspace panel is showing.

format long g;

format compact;

fontSize = 15;

s = load('polygons_coordinates.mat')

output = s.output;

x1 = 69.5

x2 = 70.5;

y1 = 21.2;

y2 = 21.8;

boxArea = (x2-x1) * (y2-y1)

numPolygons = length(output);

colors = hsv(numPolygons);

totalArea = 0;

for k = 1 : length(output)

thisPolygon = output{k};

x = thisPolygon(:, 1);

y = thisPolygon(:, 2);

thisArea = polyarea(x, y);

totalArea = totalArea + thisArea;

patch(x, y, colors(k, :));

hold on;

end

hold off;

grid on;

areaFraction = totalArea / boxArea

caption = sprintf('%d total polygons. Area Fraction = %f', ...

numPolygons, areaFraction);

title(caption, 'FontSize', fontSize);

xlabel('X', 'FontSize', fontSize);

ylabel('Y', 'FontSize', fontSize);

##### 2 Comments

Image Analyst
on 30 Jun 2017

### More Answers (2)

John BG
on 29 Jun 2017

Edited: John BG
on 30 Jun 2017

Hi Sushma

All polygons in polygons_coordinates.mat are within the rectangle [x_limit y_limit]

load('polygons_coordinates','.mat','output')

O=output

xlim=[69.5 70.5];ylim=[21.2 21.8];

[s1 s2]=size(O);

figure(1);hold all

kout=[]

for k=1:1:s2

L=O{k};

Lx=L(:,1);Ly=L(:,2);

plot(Lx,Ly)

if sum(Lx<xlim(1)') || sum(Lx>xlim(2)') || sum(Lx<xlim(1)') || sum(Lx>xlim(2)')

kout=[kout k];

end

end

% the fence

plot([xlim(1) xlim(2) xlim(2) xlim(1) xlim(1)],[ylim(1) ylim(1) ylim(2) ylim(2) ylim(1)],'r','LineWidth',1.5)

Apc=0

for k=1:1:kout

% for each polygon with at least one vertex outside fence find partial percentage area

% add up

Apc=Apc+A0

end

Apc

kout contains the index to the cell of the polygon that has at least 1 vertex outside the rectangle [x_limit y_limit].

kout is empty.

##### 0 Comments

Jan
on 30 Jun 2017

Edited: Jan
on 30 Jun 2017

If the overlap matters and you have the Mapping toolbox, you can start with the rectangle as polygone, then subtract all polygones by polybool iteratively:

[Rectx, Recty] = polybool('subtraction', Rectx, Recty, x, y);

Finally the area of the remaining polygone can be dertmined by polyarea.

I cannot post some working code, because I do not have the Mapping Toolbox.

##### 1 Comment

Image Analyst
on 30 Jun 2017

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