3.5 Additional Key Applications
3.5.1 Intersection of Line Segments
In a graphics context, lines can represent light rays, but the edges of objects are usually line segments, not fully infinite lines. This means that two lines may intersect, but line segments on those lines may not. Determining whether two segments intersect is key, for instance, in deciding whether two-dimensional objects collide or not. Looking deeper into this problem does highlight a few more useful techniques in the associated vector geometry.
To set up the situation, suppose we have two lines 
and 
with segments on each. The first segment has end points 
and 
while the segment on the second line has end points 
and 
. Once we form vectors 
and , we can describe each line. has equation , and line has equation .
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