Check if given four points form a Square

In a 2d plane, four points are given. This algorithm will check whether four points are forming a square or not.

Checking for a square we have to match these conditions −

• All four sides formed by given points are same.
• All two connecting sides are right-angled.

Input and Output

Input:
Four points {(20, 10), (10, 20), (20, 20), (10, 10)}
Output:
Points are forming a square.

Algorithm

isFormingSquare(p1, p2, p3, p4)

In this procedure, we will use a method squareDist(p1, p2), it will return squared distance of two given points.

Input: Four points.

Output: True when given points are forming a square.

Begin
   dist12 := squareDist(p1, p2)
   dist13 := squareDist(p1, p3)
   dist14 := squareDist(p1, p4)

   if dist12 = dist13 and 2*dist12 = dist14, then
      dist := squareDist(p2, p4)
      return true when dist = squareDist(p3, p4) and dist = dist12
   if dist13 = dist14 and 2*dist13 = dist12, then
      dist := squareDist(p2, p3)
      return true when dist = squareDist(p2, p4) and dist = dist13
   if dist12 = dist14 and 2*dist12 = dist13, then
      dist := squareDist(p2, p3)
      return true when dist = squareDist(p3, p4) and dist = dist12
   return false
End

Example

#include<iostream>
using namespace std;

struct Point {
   int x, y;
};

int squareDist(Point p, Point q) {
   return (p.x - q.x)*(p.x - q.x) + (p.y - q.y)*(p.y - q.y);
}

bool isSquare(Point p1, Point p2, Point p3, Point p4) {    //check four points are forming square or not
   int dist12 = squareDist(p1, p2);     // distance from p1 to p2
   int dist13 = squareDist(p1, p3);     // distance from p1 to p3
   int dist14 = squareDist(p1, p4);     // distance from p1 to p4

   //when length of p1-p2 and p1-p3 are same, and square of (p1-p4) = 2*(p1-p2)
   if (dist12 == dist13 && 2*dist12 == dist14) {
      int dist = squareDist(p2, p4);
      return (dist == squareDist(p3, p4) && dist == dist12);
   }

   //same condition for all other combinations
   if (dist13 == dist14 && 2*dist13 == dist12) {
      int dist = squareDist(p2, p3);
      return (dist == squareDist(p2, p4) && dist == dist13);
   }

   if (dist12 == dist14 && 2*dist12 == dist13) {
      int dist = squareDist(p2, p3);
      return (dist == squareDist(p3, p4) && dist == dist12);
  }
  return false;
}

int main() {
   Point p1 = {20, 10}, p2 = {10, 20}, p3 = {20, 20}, p4 = {10, 10};
   if(isSquare(p1, p2, p3, p4))
      cout << "Points are forming a square.";
   else
      cout << "Points are not forming a square";
}

Output

Points are forming a square.