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++
#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;} |
Java
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. |
Python3
# 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 Codeif __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 |
C#
// C# program to Check whether a given // point lies inside a rectangle or notusing 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. |
PHP
<?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 - $y2)) / 2.0);}/* A function to check whether point P(x, y) lies inside the rectangleformed by A(x1, y1), B(x2, y2), C(x3, y3)and D(x4, y4) */function check($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.?> |
Javascript
<script>/* 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 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) */function check(x1, y1, x2, y2, x3, y3, x4, y4, x, y) { /* Calculate area of rectangle ABCD */ let A = area(x1, y1, x2, y2, x3, y3) + area(x1, y1, x4, y4, x3, y3); /* Calculate area of triangle PAB */ let A1 = area(x, y, x1, y1, x2, y2); /* Calculate area of triangle PBC */ let A2 = area(x, y, x2, y2, x3, y3); /* Calculate area of triangle PCD */ let A3 = area(x, y, x3, y3, x4, y4); /* Calculate area of triangle PAD */ let 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 */ /* 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)) document.write("yes"); else document.write("no"); // This code is contributed by Mayank Tyagi</script> |
Output:
no
Time complexity: O(1)
Auxiliary Space: O(1)
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