How do I calculate where do 2 line segments intersect?

Question

I've implemented line segment intersection formula from GeeksForGeeks .It works great, but I also need to know the point of intersection of these 2 line segments. How can I modify the code to do that? (C++)

First comes the Point class (just a 2d Vector really)

#include <iostream> 
using namespace std; 

struct Point 
{ 
int x; 
int y; 
}; 

This function checks if 2 points are on the same segment.

// Given three colinear points p, q, r, the function checks if 
// point q lies on line segment 'pr' 
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; 
} 

This one find the rotation of ordered triplet.

// 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 https://www.geeksforgeeks.org/orientation-3-ordered-points/ 
// for details of below formula. 
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. 

And finally functions that checks for intersection. But where did it occur?

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 q2 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 
} 

Answer 1

You just need to implement one of the equations found in this wiki .

In the following code i chose to implement the first equation

// your previous code 

Point CalcIntersection(Point p1, Point q1, Point p2, Point q2){
   struct Point pInt;
   if(doIntersect(p1, q1, p2, q2)){
   pInt.x= ((p1.x * q1.y - p1.y * q1.x)*(p2.x-q2.x) - (p2.x * q2.y - p2.y * q2.x)*(p1.x-q1.x)) / ((p1.x-q1.x) * (p2.y-q2.y) -(p1.y-q1.y) * (p2.x-q2.x));

   pInt.y = ((p1.x * q1.y - p1.y * q1.x)*(p2.y-q2.y) - (p2.x * q2.y - p2.y * q2.x)*(p1.y-q1.y)) / ((p1.x-q1.x) * (p2.y-q2.y) -(p1.y-q1.y) * (p2.x-q2.x));

}
 return pInt;
}

Rq: i think your x and y should be a float not an int