matlab - How to find all lines in a set that coincide in a single point? -

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suppose given set of lines, how can partition set number of clusters, such lines in each cluster coincide in single point?

if number of lines n reasonable, can use o(n^3) algorithm: ever pair of lines (in form a*x+b*y+c=0) check whether intersect - exclude pairs of parallel , not-coincident lines determinant

|a1 b1|         = 0  |a2 b2|

for every intersecting pair if line shares same intersecting point, determinant:

|a1 b1 c1| |a2 b2 c2| = 0  |a3 b3 c3|

if n large cubic algorithm using, calculate intersection points (upto o(n^2) of them) , add these points map structure (hashtable, example). check matching points. don't forget numerical errors issue.


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