Determining Intersection of Two Line Segments in the Same Plane

Determining whether two line segments in the same plane intersect requires implementing specific computational geometry algorithms. A common approach involves using cross-product calculations to check the relative orientation of points. The algorithm typically checks if the endpoints of each segment lie on opposite sides of the other segment using vector cross products. First, calculate the orientation of point pairs using the determinant method: for segments (p1,p2) and (p3,p4), compute orientations like (p2-p1)×(p3-p1) and (p2-p1)×(p4-p1). If these orientations differ in sign for both segments, they intersect properly. Special cases include when segments share endpoints or are collinear - these require additional checks using bounding box comparisons and point-on-segment tests. The implementation should handle all edge cases: segments touching at endpoints, overlapping collinear segments, or completely disjoint segments. This method provides a robust solution with O(1) time complexity, making it suitable for real-time applications in computer graphics and spatial computations.