I need a fast algorithm to determine if two line segments intersect.
Any help would be greatly appreciated.
From the FAQ:Quote:>I need a fast algorithm to determine if two line segments intersect.
>Any help would be greatly appreciated.
Subject: 8) How do I find intersections of 2 2D line segments?
This problem can be extremely easy or extremely difficult depends
on your applications. If all you want is the intersection point,
the following should work:
Let A,B,C,D be 2-space position vectors. Then the directed line
segments AB & CD are given by:
AB=A+r(B-A), r in [0,1]
CD=C+s(D-C), s in [0,1]
If AB & CD intersect, then
YA+r(YB-YA)=YC+s(YD-YC) for some r,s in [0,1]
Solving the above for r and s yields
r = ----------------------------- (eqn 1)
s = ----------------------------- (eqn 2)
Let I be the position vector of the intersection point, then
By examining the values of r & s, you can also determine some
other limiting conditions:
If 0<=r<=1 & 0<=s<=1, intersection exists
r<0 or r>1 or s<0 or s>1 line segments do not intersect
If the denominator in eqn 1 is zero, AB & CD are parallel
If the numerator in eqn 1 is also zero, AB & CD are coincident
If the intersection point of the 2 lines are needed (lines in this
context mean infinite lines) regardless whether the two line
segments intersect, then
If r>1, I is located on extension of AB
If r<0, I is located on extension of BA
If s>1, I is located on extension of CD
If s<0, I is located on extension of DC
Also note that the denominators of eqn 1 & 2 are identical.
[O'Rourke] pp. 249-51
[Gems III] pp. 199-202 "Faster Line Segment Intersection,"
this question goes for anyone who is familiar with and has tried to
implement the sweep line algorithm to find all intersections between a
group of sections. my problem is: supose my sweep line moves from left
to right. how do i sort vertical sections in the status data structure.
(the definition of the Status sorting function does not cover the cse of
thanks in advance