To detect where two line segments intersect, follow these steps:
1. Orientation: Calculate the orientation of the points using a formula. If three points are collinear, their orientation is 0; if they form a clockwise or counterclockwise turn, the result is positive or negative.
2. Intersection Check: The segments intersect if the endpoints of one segment are on opposite sides of the other segment. You need to check the orientation for each combination of endpoints.
3. Special Case: If points are collinear, check if the points lie within the segment’s bounds. This method helps detect whether two line segments intersect and where.