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What's wrong with my polygon area calculator code

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Mert Ayduman
Mert Ayduman 2016-10-26
回答： John D'Errico 2016-10-26
Hi, I wrote this code. It essentially calculates area of a polygon when given coordinates by shoelace formula. But it gives me wrong answer. Couldn't figure out why.
function AreaOfPolygon = gaussarea (xymatrice)
[r,c]=size(xymatrice);
x=xymatrice(:,1);
y=xymatrice(:,2);
calculation=0;
x1=xymatrice(1,1);
y1=xymatrice(1,2);
xLast=xymatrice(r,1);
yLast=xymatrice(r,2);
for i=1:r
if i==1
calculation=calculation+(x1*(y(i+1)-yLast));
elseif i==r
calculation=calculation+(xLast*(y1-y(i-1)));
else
calculation=calculation+(x(i)*y(i+1)-y(i-1));
end
end
AreaOfPolygon=abs(calculation)/2
end

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John D'Errico
John D'Errico 2016-10-26
It seems to work for me. A simple case:
x = [0 0 1 1 0];
y = [0 1 1 0 0];
xymatrice = [x',y'];
AreaOfPolygon
AreaOfPolygon =
1
polyarea(x,y)
ans =
1
When I ran your code, it yields 1 as the result, which is indeed the area of that square.
So perhaps you can show an example where you think there is a problem. It may be a case where you have a complex polygon that is self intersecting. In that case
xymatrice = rand(10,2);
AreaOfPolygon =
1.0281
polyarea(xymatrice(:,1),xymatrice(:,2))
ans =
0.060961
So in this rather nasty case the two give different results.
plot(x,y,'o-')
But in that case, the "area" is a complicated thing.

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