How to detect if a line intersects with itself?

Question

John 2014-5-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/131598-how-to-detect-if-a-line-intersects-with-itself

回答： George Papazafeiropoulos 2014-5-29

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Given a coordinate matrix:

A = [1 1; 1 2; 2 2; 2 1; 3 1];

And a tour order:

tour_order = [2; 1; 4; 3; 5; 2];

Which, when plotted, produces the following:

How do you detect that the line produced intersects with itself, and return where it does (i.e in this case it occurs by the lines 4-3 and 5-2)?

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Answer 1

George Papazafeiropoulos 2014-5-29

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https://ww2.mathworks.cn/matlabcentral/answers/131598-how-to-detect-if-a-line-intersects-with-itself#answer_138714

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% initial data
A = [1 1; 1 2; 2 2; 2 1; 3 1];
tour_order = [2; 1; 4; 3; 5; 2];
% engine
sizeA=size(A,1);
meanA=mean(A); % point inbetween the others
vecs=A-meanA(ones(sizeA,1),:); % vectors connecting points with point inbetween
vec1=vecs(1,:);
vec1=vec1(ones(sizeA,1),:);
cosines1=sum(vecs.*vec1,2)./(hypot(vecs(:,1),vecs(:,2)).*hypot(vec1(:,1),vec1(:,2)));
vec2=vecs(1,:);
vec2=[vec2(2),-vec2(1)];
vec2=vec2(ones(sizeA,1),:);
cosines2=sum(vecs.*vec2,2)./(hypot(vecs(:,1),vecs(:,2)).*hypot(vec2(:,1),vec2(:,2)));
ind1=find(cosines2>0);
ind2=find(cosines2<0);
[~,order1]=sort(cosines1(ind1),'descend');
[~,order2]=sort(cosines1(ind2));
full_order=[1;ind1(order1);ind2(order2)];
dmax=polyarea(A(full_order,1),A(full_order,2));
d=polyarea(A(:,1),A(:,2));
% result
if d<dmax
    disp('lines intersect')
end