C++ Program to Apply Above-Below-on Test to Find the Position of a Point with respect to a Line

This is a C++ Program to check whether point lies above, below or on the line. For any point t (xt, yt) on the plane, its position with respect to the line L connecting p and q is found by calculating the scalar s:
s = A xt + B yt + C
If s < 0, t lies in the clockwise halfplane of L; if s > 0, t lies on the counter-clockwise halfplane; if s = 0, t lies on L.
For example, the equation of the line connecting points (2, 2) and (4, 5) is -3x + 2y + 2 = 0. The point (6, 3) lies in the clockwise halfplane of this line, because (-3)(6) + (2)(3) + 2 = -10. Conversely, the point (0, 5) lies in the other halfplane as (-3)(0) +(2)(5) +2 = 12.

Here is source code of the C++ Program to Apply Above-Below-on Test to Find the Position of a Point with respect to a Line. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. #include<time.h>
  2. #include<stdlib.h>
  3. #include<iostream>
  4. #include<math.h>
  5.  
  6. using namespace std;
  7. const int LOW = 0;
  8. const int HIGH = 10;
  9. int main(int argc, char **argv)
  10. {
  11.     time_t seconds;
  12.     time(&seconds);
  13.     srand((unsigned int) seconds);
  14.  
  15.     int x1, x2, y1, y2;
  16.     x1 = rand() % (HIGH - LOW + 1) + LOW;
  17.     x2 = rand() % (HIGH - LOW + 1) + LOW;
  18.     y1 = rand() % (HIGH - LOW + 1) + LOW;
  19.     y2 = rand() % (HIGH - LOW + 1) + LOW;
  20.  
  21.     cout << "The Equation of the 1st line is : (" << (y2 - y1) << ")x+(" << (x1
  22.             - x2) << ")y+(" << (x2 * y1 - x1 * y2) << ") = 0\n";
  23.  
  24.     int x, y;
  25.     cout << "\nEnter the point:";
  26.     cin >> x;
  27.     cin >> y;
  28.  
  29.     int s = (y2 - y1) * x + (x1 - x2) * y + (x2 * y1 - x1 * y2);
  30.     if (s < 0)
  31.         cout << "The point lies below the line or left side of the line";
  32.     else if (s > 0)
  33.         cout << "The point lies above the line or right side of the line";
  34.     else
  35.         cout << "The point lies on the line";
  36.     return 0;
  37. }

Output:

$ g++ PointWRTLine.cpp
$ a.out
 
The Equation of the 1st line is : (3)x+(0)y+(-3) = 0
 
Enter the point:1 4
The point lies on the line
 
The Equation of the 1st line is : (5)x+(-1)y+(-25) = 0
 
Enter the point:1 1
The point lies below the line or left side of the line
 
The Equation of the 1st line is : (-6)x+(8)y+(-24) = 0
 
Enter the point:19 21
The point lies above the line or right side of the line
------------------
(program exited with code: 0)
Press return to continue

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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