intersectionOfLines.cpp

 // intersection of two lines 
#include <bits/stdc++.h> 
using namespace std; 
  
// This pair is used to store the X and Y 
// coordinates of a point respectively 
#define pdd pair<double, double> 
  
// Function used to display X and Y coordinates 
// of a point 
void displayPoint(pdd P) 
{ 
    cout << "(" << P.first << ", " << P.second 
         << ")" << endl; 
} 
  
pdd lineLineIntersection(pdd A, pdd B, pdd C, pdd D) 
{ 
    // Line AB represented as a1x + b1y = c1 
    double a1 = B.second - A.second; 
    double b1 = A.first - B.first; 
    double c1 = a1*(A.first) + b1*(A.second); 
  
    // Line CD represented as a2x + b2y = c2 
    double a2 = D.second - C.second; 
    double b2 = C.first - D.first; 
    double c2 = a2*(C.first)+ b2*(C.second); 
  
    double determinant = a1*b2 - a2*b1; 
  
    if (determinant == 0) 
    { 
        // The lines are parallel. This is simplified 
        // by returning a pair of FLT_MAX 
        return make_pair(FLT_MAX, FLT_MAX); 
    } 
    else
    { 
        double x = (b2*c1 - b1*c2)/determinant; 
        double y = (a1*c2 - a2*c1)/determinant; 
        return make_pair(x, y); 
    } 
} 
  
// Driver code 
int main() 
{ 
    pdd A = make_pair(1, 1); 
    pdd B = make_pair(4, 4); 
    pdd C = make_pair(1, 8); 
    pdd D = make_pair(2, 4); 
  
    pdd intersection = lineLineIntersection(A, B, C, D); 
  
    if (intersection.first == FLT_MAX && 
        intersection.second==FLT_MAX) 
    { 
        cout << "The given lines AB and CD are parallel.\n"; 
    } 
  
    else
    { 
        // NOTE: Further check can be applied in case 
        // of line segments. Here, we have considered AB 
        // and CD as lines 
        cout << "The intersection of the given lines AB "
                "and CD is: "; 
        displayPoint(intersection); 
    } 
  
    return 0; 
}