Computational Geometry is the branch of computer science that studies algorithms for solving geometric problems.The input to a problem in this area is typically is a set of geometric objects such as a set of points, a set of line segments, or the vertices of a polygon in counter-clockwise order.
To determine whether a set of n line-segments contains any intersections, we review a technique called sweeping.
Before we discuss sweeping, let us use the following:
Two consecutive segments turn left or right if their cartesian product (p2-p0)*(p1-p0) is positive or negative.
Two line segments intersect each other if each segment straddles the line containing the other.
segments-intersect (p1, p2, p3, p4)
We determine if line segments straddle by finding the directions of the four line segments and checking that there are pairs that are opposite. We also check that if any of the directions are zero, then we check that the opposite end is colinear with a segment.
Now we look at the sweeping technique that describes whether any two line segments in a set of segments intersect.
In sweeping, an imaginary vertical sweep line passes through the given set of geometric objects, usually from the left to the right.  This technique provides a way of ordering the geometric objects by placing them in a dynamic data structure. We further assume that no input segment is vertical and that no three input segments intersect at a single point.
The first assumption tells us that any segment crossing a vertical sweep line intersects it at only one point.
Where the line segments intersect the sweeping line, the intersection points are comparable and are taken in the order of the increasing y coordinates. Where the segments intersect, this order is reversed. Any sweep line that passes through the shaded region has e and f intersect, they reverse their orders.