How to check if two given line segments intersect? | GeeksforGeeks

Given two line segments (p1, q1) and (p2, q2), find if the given line segments intersect with each other.

1. General Case:
- (p1, q1, p2) and (p1, q1, q2) have different orientations and
- (p2, q2, p1) and (p2, q2, q1) have different orientations

2. Special Case 
- (p1, q1, p2), (p1, q1, q2), (p2, q2, p1), and (p2, q2, q1) are all collinear and
- the x-projections of (p1, q1) and (p2, q2) intersect
- the y-projections of (p1, q1) and (p2, q2) intersect

bool onSegment(Point p, Point q, Point r)

{

    if (q.x <= max(p.x, r.x) && q.x >= min(p.x, r.x) &&

        q.y <= max(p.y, r.y) && q.y >= min(p.y, r.y))

       return true;

 

    return false;

}

 

// To find orientation of ordered triplet (p, q, r).

// The function returns following values

// 0 --> p, q and r are colinear

// 1 --> Clockwise

// 2 --> Counterclockwise

int orientation(Point p, Point q, Point r)

{

    // See 10th slides from following link for derivation of the formula

    // http://www.dcs.gla.ac.uk/~pat/52233/slides/Geometry1x1.pdf

    int val = (q.y - p.y) * (r.x - q.x) -

              (q.x - p.x) * (r.y - q.y);

 

    if (val == 0) return 0;  // colinear

 

    return (val > 0)? 1: 2; // clock or counterclock wise

}

// The main function that returns true if line segment 'p1q1'

// and 'p2q2' intersect.

bool doIntersect(Point p1, Point q1, Point p2, Point q2)

{

    // Find the four orientations needed for general and

    // special cases

    int o1 = orientation(p1, q1, p2);

    int o2 = orientation(p1, q1, q2);

    int o3 = orientation(p2, q2, p1);

    int o4 = orientation(p2, q2, q1);

 

    // General case

    if (o1 != o2 && o3 != o4)

        return true;

 

    // Special Cases

    // p1, q1 and p2 are colinear and p2 lies on segment p1q1

    if (o1 == 0 && onSegment(p1, p2, q1)) return true;

 

    // p1, q1 and p2 are colinear and q2 lies on segment p1q1

    if (o2 == 0 && onSegment(p1, q2, q1)) return true;

 

    // p2, q2 and p1 are colinear and p1 lies on segment p2q2

    if (o3 == 0 && onSegment(p2, p1, q2)) return true;

 

     // p2, q2 and q1 are colinear and q1 lies on segment p2q2

    if (o4 == 0 && onSegment(p2, q1, q2)) return true;

 

    return false; // Doesn't fall in any of the above cases

}

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