Check whether a given point lies inside a rectangle or not

Given four points of a rectangle, and one more point P. Write a function to check whether P lies within the given rectangle or not.

Examples:

Input : R = [(10, 10), (10, -10), 
             (-10, -10), (-10, 10)]
        P = (0, 0)
Output : yes
Illustration : 


Input : R = [(10, 10), (10, -10),
             (-10, -10), (-10, 10)],
        P = (20, 20)
Output : no
Illustration :
 

Prerequisite: Check whether a given point lies inside a triangle or not



Approach : Let the coordinates of four corners be A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). And coordinates of the given point P be (x, y)

1) Calculate area of the given rectangle, i.e., area of the rectangle ABCD as area of triangle ABC + area of triangle ACD.
Area A = [ x1(y2 – y3) + x2(y3 – y1) + x3(y1-y2)]/2 + [ x1(y4 – y3) + x4(y3 – y1) + x3(y1-y4)]/2
2) Calculate area of the triangle PAB as A1.
3) Calculate area of the triangle PBC as A2.
4) Calculate area of the triangle PCD as A3.
5) Calculate area of the triangle PAD as A4.
6) If P lies inside the triangle, then A1 + A2 + A3 + A4 must be equal to A.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

#include <bits/stdc++.h>
using namespace std;
  
/* A utility function to calculate area of 
   triangle formed by (x1, y1), (x2, y2) and
  (x3, y3) */
float area(int x1, int y1, int x2, int y2,
                            int x3, int y3)
{
    return abs((x1 * (y2 - y3) + x2 * (y3 - y1) + 
                x3 * (y1 - y2)) / 2.0);
}
  
/* A function to check whether point P(x, y) 
   lies inside the rectangle formed by A(x1, y1), 
   B(x2, y2), C(x3, y3) and D(x4, y4) */
bool check(int x1, int y1, int x2, int y2, int x3, 
             int y3, int x4, int y4, int x, int y)
{
    /* Calculate area of rectangle ABCD */
    float A = area(x1, y1, x2, y2, x3, y3) + 
              area(x1, y1, x4, y4, x3, y3);
  
    /* Calculate area of triangle PAB */
    float A1 = area(x, y, x1, y1, x2, y2);
  
    /* Calculate area of triangle PBC */
    float A2 = area(x, y, x2, y2, x3, y3);
  
    /* Calculate area of triangle PCD */
    float A3 = area(x, y, x3, y3, x4, y4);
  
    /* Calculate area of triangle PAD */
    float A4 = area(x, y, x1, y1, x4, y4);
  
    /* Check if sum of A1, A2, A3 and A4 
       is same as A */
    return (A == A1 + A2 + A3 + A4);
}
  
/* Driver program to test above function */
int main()
{
    /* Let us check whether the point P(10, 15)
      lies inside the rectangle formed by A(0, 10),
      B(10, 0) C(0, -10) D(-10, 0) */
    if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
        cout << "yes";
    else
        cout << "no";
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

class GFG
{
    /* A utility function to calculate area of 
    triangle formed by (x1, y1), (x2, y2) and
    (x3, y3) */
    static float area(int x1, int y1, int x2, 
                        int y2, int x3, int y3)
    {
        return (float)Math.abs((x1 * (y2 - y3) + 
        x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
    }
          
    /* A function to check whether point P(x, y) 
    lies inside the rectangle formed by A(x1, y1), 
    B(x2, y2), C(x3, y3) and D(x4, y4) */
    static boolean check(int x1, int y1, int x2, int y2,
    int x3, int y3, int x4, int y4, int x, int y)
    {
          
        /* Calculate area of rectangle ABCD */
        float A = area(x1, y1, x2, y2, x3, y3)+ 
                area(x1, y1, x4, y4, x3, y3);
      
        /* Calculate area of triangle PAB */
        float A1 = area(x, y, x1, y1, x2, y2);
      
        /* Calculate area of triangle PBC */
        float A2 = area(x, y, x2, y2, x3, y3);
      
        /* Calculate area of triangle PCD */
        float A3 = area(x, y, x3, y3, x4, y4);
      
        /* Calculate area of triangle PAD */
        float A4 = area(x, y, x1, y1, x4, y4);
      
        /* Check if sum of A1, A2, A3 and A4 
        is same as A */
        return (A == A1 + A2 + A3 + A4);
    }
      
    // Driver code
    public static void main (String[] args)
    {
          
        /* Let us check whether the point P(10, 15)
        lies inside the rectangle formed by A(0, 10),
        B(10, 0) C(0, -10) D(-10, 0) */
        if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
            System.out.print("yes");
        else
            System.out.print("no");
    }
}
  
// This code is contributed by Anant Agarwal.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# A utility function to calculate 
# area of triangle formed by (x1, y1), 
# (x2, y2) and (x3, y3) 
def area(x1, y1, x2, y2, x3, y3):
      
    return abs((x1 * (y2 - y3) + 
                x2 * (y3 - y1) + 
                x3 * (y1 - y2)) / 2.0)
  
# A function to check whether point 
# P(x, y) lies inside the rectangle 
# formed by A(x1, y1), B(x2, y2), 
# C(x3, y3) and D(x4, y4) 
def check(x1, y1, x2, y2, x3, 
          y3, x4, y4, x, y):
                
    # Calculate area of rectangle ABCD 
    A = (area(x1, y1, x2, y2, x3, y3) +
         area(x1, y1, x4, y4, x3, y3))
  
    # Calculate area of triangle PAB 
    A1 = area(x, y, x1, y1, x2, y2)
  
    # Calculate area of triangle PBC 
    A2 = area(x, y, x2, y2, x3, y3)
  
    # Calculate area of triangle PCD 
    A3 = area(x, y, x3, y3, x4, y4)
  
    # Calculate area of triangle PAD 
    A4 = area(x, y, x1, y1, x4, y4);
  
    # Check if sum of A1, A2, A3 
    # and A4 is same as A 
    return (A == A1 + A2 + A3 + A4)
  
# Driver Code
if __name__ == '__main__':
      
    # Let us check whether the point 
    # P(10, 15) lies inside the 
    # rectangle formed by A(0, 10),
    # B(10, 0) C(0, -10) D(-10, 0) 
    if (check(0, 10, 10, 0, 0, -10
                    -10, 0, 10, 15)):
        print("yes")
    else:
        print("no")
  
# This code is contributed by
# Surendra_Gangwar

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to Check whether a given 
// point lies inside a rectangle or not
using System;
  
class GFG {
      
    // A utility function to calculate area
    // of triangle formed by (x1, y1), 
    // (x2, y2) and (x3, y3)
    static float area(int x1, int y1, int x2, 
                      int y2, int x3, int y3)
    {
        return (float)Math.Abs((x1 * (y2 - y3) + 
                                x2 * (y3 - y1) + 
                                x3 * (y1 - y2)) / 2.0);
    }
          
    // A function to check whether point P(x, y) 
    // lies inside the rectangle formed by A(x1, y1), 
    // B(x2, y2), C(x3, y3) and D(x4, y4) 
    static bool check(int x1, int y1, int x2,
                      int y2, int x3, int y3, 
                   int x4, int y4, int x, int y)
    {
          
        // Calculate area of rectangle ABCD 
        float A = area(x1, y1, x2, y2, x3, y3) + 
                  area(x1, y1, x4, y4, x3, y3);
      
        // Calculate area of triangle PAB 
        float A1 = area(x, y, x1, y1, x2, y2);
      
        // Calculate area of triangle PBC 
        float A2 = area(x, y, x2, y2, x3, y3);
      
        // Calculate area of triangle PCD 
        float A3 = area(x, y, x3, y3, x4, y4);
      
        // Calculate area of triangle PAD
        float A4 = area(x, y, x1, y1, x4, y4);
      
        // Check if sum of A1, A2, A3  
        // and A4is same as A 
        return (A == A1 + A2 + A3 + A4);
    }
      
    // Driver code
    public static void Main ()
    {
          
        // Let us check whether the point 
        // P(10, 15) lies inside the rectangle
        // formed by A(0, 10), B(10, 0), 
        // C(0, -10), D(-10, 0)
        if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
            Console.Write("yes");
        else
            Console.Write("no");
    }
}
  
// This code is contributed by Nitin Mittal.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to check whether a 
// given point lies inside a 
// rectangle or not
  
// A utility function to 
// calculate area of 
// triangle formed by 
// (x1, y1), (x2, y2) 
// and (x3, y3)
function area($x1, $y1, $x2
              $y2, $x3, $y3)
{
    return abs(($x1 * ($y2 - $y3) + 
                $x2 * ($y3 - $y1) + 
                $x3 * ($y1 - $y2)) / 2.0);
}
  
/* A function to check 
whether point P(x, y) 
lies inside the rectangle
formed by A(x1, y1), 
B(x2, y2), C(x3, y3)
and D(x4, y4) */
function check($x1, $y1, $x2, $y2, $x3
               $y3, $x4, $y4, $x, $y)
{
    // Calculate area of rectangle ABCD 
    $A = area($x1, $y1, $x2, $y2, $x3, $y3) + 
         area($x1, $y1, $x4, $y4, $x3, $y3);
  
    // Calculate area of triangle PAB 
    $A1 = area($x, $y, $x1, $y1, $x2, $y2);
  
    // Calculate area of triangle PBC 
    $A2 = area($x, $y, $x2, $y2, $x3, $y3);
  
    // Calculate area of triangle PCD
    $A3 = area($x, $y, $x3, $y3, $x4, $y4);
  
    // Calculate area of triangle PAD 
    $A4 = area($x, $y, $x1, $y1, $x4, $y4);
  
    // Check if sum of A1, A2, 
    // A3 and A4  is same as A 
    return ($A == $A1 + $A2 + $A3 + $A4);
}
  
// Driver Code
  
// Let us check whether 
// the point P(10, 15)
// lies inside the rectangle
// formed by A(0, 10),
// B(10, 0) C(0, -10) 
// D(-10, 0) 
if (check(0, 10, 10, 0, 0, -10,
               -10, 0, 10, 15))
    echo "yes";
      
else
    echo "no";
      
// This code is contributed by vt_m.
?>

chevron_right



Output:

no

This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up



Article Tags :
Practice Tags :


3


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.