Do not understand Curve intersections code

Question

NA 2019-10-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/483796-do-not-understand-curve-intersections-code

评论： darova 2019-10-7

在 MATLAB Online 中打开

I used Curve intersections code and it gives the answer

https://ww2.mathworks.cn/matlabcentral/fileexchange/22441-curve-intersections

But the problem is that I do not understand some part of the code and the algorithm.

For examle what this line do

hF = @le; % line 50
C1 = feval(hF,D(bsxfun(@times,dx1,y2)-bsxfun(@times,dy1,x2),S1),0); % line 63
C2 = feval(hF,D((bsxfun(@times,y1,dx2)-bsxfun(@times,x1,dy2))',S2'),0)'; % line 65
function u = D(x,y)
        u = bsxfun(@minus,x(:,1:end-1),y).*bsxfun(@minus,x(:,2:end),y);
end

what is 'signed distances'

 %...Determine 'signed distances'   
    S1 = dx1.*y1(1:end-1) - dy1.*x1(1:end-1);
    S2 = dx2.*y2(1:end-1) - dy2.*x2(1:end-1);

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Answer 1

darova 2019-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/483796-do-not-understand-curve-intersections-code#answer_394994

在 MATLAB Online 中打开

Intersections just loops through all segments of curves and find all intersections

Many of segments have intersections, but intersection point has to be on these segments

Here are equations need to be solved to find intersection point

Try to find x,y and see if this solution has something in common with this

function u = D(x,y)
        u = bsxfun(@minus,x(:,1:end-1),y).*bsxfun(@minus,x(:,2:end),y);
end

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darova 2019-10-7

在 MATLAB Online 中打开

Look here: Intersections

Piece of explanation from there:

% In principle, we have to perform this computation on every pair of line
% segments in the input data.  This can be quite a large number of pairs so
% we will reduce it by doing a simple preliminary check to eliminate line
% segment pairs that could not possibly cross.  The check is to look at the
% smallest enclosing rectangles (with sides parallel to the axes) for each
% line segment pair and see if they overlap.
% ...