Intersecting rectangle when bottom-left and top-right corners of two rectangles are given

Given coordinates of 4 points, bottom-left and top-right corners of two rectangles. The task is to find the coordinates of the intersecting rectangle formed by the given two rectangles.

Examples:

Input:
rec1: bottom-left(0, 0), top-right(10, 8),
rec2: bottom-left(2, 3), top-right(7, 9)
Output: (2, 3) (7, 8) (2, 8) (7, 3)

Input:
rec1: bottom-left(0, 0), top-right(3, 3),
rec2: bottom-left(1, 1), top-right(2, 2)
Output: (1, 1) (2, 2) (1, 2) (2, 1)



Approach :
As two given points are diagonals of a rectangle. so, x1 < x2, y1 < y2. similarly x3 < x4, y3 < y4.
so, bottom-left and top-right points of intersection rectangle can be found by using formula.

x5 = max(x1, x3);
y5 = max(y1, y3);
x6 = min(x2, x4);
y6 = min(y2, y4);  

In case of no intersection, x5 and y5 will always exceed x6 and y5 respectively. The other two points of the rectangle can be found by using simple geometry.

Below is the implementation of the above approach:

C++

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// CPP program to find intersection
// rectangle of given two rectangles.
#include <bits/stdc++.h>
using namespace std;
  
// function to find intersection rectangle of given two rectangles.
void FindPoints(int x1, int y1, int x2, int y2,
                int x3, int y3, int x4, int y4)
{
    // gives bottom-left point
    // of intersection rectangle
    int x5 = max(x1, x3);
    int y5 = max(y1, y3);
  
    // gives top-right point
    // of intersection rectangle
    int x6 = min(x2, x4);
    int y6 = min(y2, y4);
  
    // no intersection
    if (x5 > x6 || y5 > y6) {
        cout << "No intersection";
        return;
    }
  
    cout << "(" << x5 << ", " << y5 << ") ";
  
    cout << "(" << x6 << ", " << y6 << ") ";
  
    // gives top-left point
    // of intersection rectangle
    int x7 = x5;
    int y7 = y6;
  
    cout << "(" << x7 << ", " << y7 << ") ";
  
    // gives bottom-right point
    // of intersection rectangle
    int x8 = x6;
    int y8 = y5;
  
    cout << "(" << x8 << ", " << y8 << ") ";
}
  
// Driver code
int main()
{
    // bottom-left and top-right
    // corners of first rectangle
    int x1 = 0, y1 = 0, x2 = 10, y2 = 8;
  
    // bottom-left and top-right
    // corners of first rectangle
    int x3 = 2, y3 = 3, x4 = 7, y4 = 9;
  
    // function call
    FindPoints(x1, y1, x2, y2, x3, y3, x4, y4);
  
    return 0;
}

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Java

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// Java program to find intersection
// rectangle of given two rectangles.
class GFG
{
  
// function to find intersection 
// rectangle of given two rectangles.
static void FindPoints(int x1, int y1, 
                       int x2, int y2,
                       int x3, int y3, 
                       int x4, int y4)
{
    // gives bottom-left point
    // of intersection rectangle
    int x5 = Math.max(x1, x3);
    int y5 = Math.max(y1, y3);
  
    // gives top-right point
    // of intersection rectangle
    int x6 = Math.min(x2, x4);
    int y6 = Math.min(y2, y4);
  
    // no intersection
    if (x5 > x6 || y5 > y6) 
    {
        System.out.println("No intersection");
        return;
    }
  
    System.out.print("(" + x5 + ", " +
                           y5 + ") ");
  
    System.out.print("(" + x6 + ", "
                           y6 + ") ");
  
    // gives top-left point
    // of intersection rectangle
    int x7 = x5;
    int y7 = y6;
  
    System.out.print("(" + x7 + ", "
                           y7 + ") ");
  
    // gives bottom-right point
    // of intersection rectangle
    int x8 = x6;
    int y8 = y5;
  
    System.out.print("(" + x8 + ", "
                           y8 + ") ");
}
  
// Driver code
public static void main(String args[])
{
    // bottom-left and top-right
    // corners of first rectangle
    int x1 = 0, y1 = 0
        x2 = 10, y2 = 8;
  
    // bottom-left and top-right
    // corners of first rectangle
    int x3 = 2, y3 = 3
        x4 = 7, y4 = 9;
  
    // function call
    FindPoints(x1, y1, x2, y2, 
               x3, y3, x4, y4);
}
}
  
// This code is contributed
// by Arnab Kundu

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Python 3

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# Python 3 program to find intersection
# rectangle of given two rectangles.
  
# function to find intersection
# rectangle of given two rectangles.
def FindPoints(x1, y1, x2, y2, 
               x3, y3, x4, y4):
  
    # gives bottom-left point
    # of intersection rectangle
    x5 = max(x1, x3)
    y5 = max(y1, y3)
  
    # gives top-right point
    # of intersection rectangle
    x6 = min(x2, x4)
    y6 = min(y2, y4)
  
    # no intersection
    if (x5 > x6 or y5 > y6) :
        print("No intersection")
        return
  
    print( "(", x5, ", ", y5, ") ", end = " ")
  
    print( "(", x6, ", ", y6, ") ", end = " ")
  
    # gives top-left point
    # of intersection rectangle
    x7 = x5
    y7 = y6
  
    print( "(", x7, ", ", y7, ") ", end = " ")
  
    # gives bottom-right point
    # of intersection rectangle
    x8 = x6
    y8 = y5
  
    print( "(", x8, ", ", y8, ") ")
  
# Driver code
if __name__ == "__main__":
      
    # bottom-left and top-right
    # corners of first rectangle
    x1 = 0
    y1 = 0
    x2 = 10
    y2 = 8
  
    # bottom-left and top-right
    # corners of first rectangle
    x3 = 2
    y3 = 3
    x4 = 7
    y4 = 9
  
    # function call
    FindPoints(x1, y1, x2, y2, x3, y3, x4, y4)
  
# This code is contributed 
# by ChitraNayal

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C#

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// C# program to find intersection
// rectangle of given two rectangles.
using System;
  
class GFG
{
  
// function to find intersection 
// rectangle of given two rectangles.
static void FindPoints(int x1, int y1, 
                       int x2, int y2,
                       int x3, int y3, 
                       int x4, int y4)
{
    // gives bottom-left point
    // of intersection rectangle
    int x5 = Math.Max(x1, x3);
    int y5 = Math.Max(y1, y3);
  
    // gives top-right point
    // of intersection rectangle
    int x6 = Math.Min(x2, x4);
    int y6 = Math.Min(y2, y4);
  
    // no intersection
    if (x5 > x6 || y5 > y6) 
    {
        Console.WriteLine("No intersection");
        return;
    }
  
    Console.Write("(" + x5 + ", " +
                        y5 + ") ");
  
    Console.Write("(" + x6 + ", "
                        y6 + ") ");
  
    // gives top-left point
    // of intersection rectangle
    int x7 = x5;
    int y7 = y6;
  
    Console.Write("(" + x7 + ", "
                        y7 + ") ");
  
    // gives bottom-right point
    // of intersection rectangle
    int x8 = x6;
    int y8 = y5;
  
    Console.Write("(" + x8 + ", "
                        y8 + ") ");
}
  
// Driver code
public static void Main()
{
    // bottom-left and top-right
    // corners of first rectangle
    int x1 = 0, y1 = 0, 
        x2 = 10, y2 = 8;
  
    // bottom-left and top-right
    // corners of first rectangle
    int x3 = 2, y3 = 3, 
        x4 = 7, y4 = 9;
  
    // function call
    FindPoints(x1, y1, x2, y2, 
               x3, y3, x4, y4);
}
}
  
// This code is contributed
// by Akanksha Rai

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PHP

$x6 || $y5 > $y6)
{
echo “No intersection”;
return;
}

echo “(” . $x5 . “, ” . $y5 . “) “;

echo “(” . $x6 . “, ” . $y6 . “) “;

// gives top-left point
// of intersection rectangle
$x7 = $x5;
$y7 = $y6;

echo “(” . $x7 . “, ” . $y7 . “) “;

// gives bottom-right point
// of intersection rectangle
$x8 = $x6;
$y8 = $y5;

echo “(” . $x8 . “, ” . $y8 . “) “;
}



// Driver code

// bottom-left and top-right
// corners of first rectangle
$x1 = 0; $y1 = 0; $x2 = 10; $y2 = 8;

// bottom-left and top-right
// corners of first rectangle
$x3 = 2; $y3 = 3; $x4 = 7; $y4 = 9;

// function call
FindPoints($x1, $y1, $x2, $y2,
$x3, $y3, $x4, $y4);

// This code is contributed
// by Akanksha Rai
?>

Output:

(2, 3) (7, 8) (2, 8) (7, 3)

Time Complexity: O(1)



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