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++
// 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; } |
C
// C program to find intersection // rectangle of given two rectangles. #include <stdio.h> int min( int a, int b) { int min = a; if (min > b) min = b; return min; } int max( int a, int b) { int max = a; if (max < b) max = b; return max; } // 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) { printf ( "No intersection" ); return ; } printf ( "(%d, %d) " ,x5,y5); printf ( "(%d, %d) " ,x6,y6); // gives top-left point // of intersection rectangle int x7 = x5; int y7 = y6; printf ( "(%d, %d) " ,x7,y7); // gives bottom-right point // of intersection rectangle int x8 = x6; int y8 = y5; printf ( "(%d, %d) " ,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; } // This code is contributed by kothavvsaakash. |
Java
// 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 |
Python3
# 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 |
C#
// 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 |
PHP
<?php // PHP program to find intersection // rectangle of given two rectangles. // function to find intersection rectangle // of given two rectangles. function 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 || $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 ?> |
Javascript
<script> // Javascript program to find intersection // rectangle of given two rectangles. // Function to find intersection // rectangle of given two rectangles. function FindPoints(x1, y1, x2, y2, x3, y3, x4, y4) { // Gives bottom-left point // of intersection rectangle var x5 = Math.max(x1, x3); var y5 = Math.max(y1, y3); // Gives top-right point // of intersection rectangle var x6 = Math.min(x2, x4); var y6 = Math.min(y2, y4); // No intersection if (x5 > x6 || y5 > y6) { document.write( "No intersection" ); return ; } document.write( "(" + x5 + ", " + y5 + ") " ); document.write( "(" + x6 + ", " + y6 + ") " ); // Gives top-left point // of intersection rectangle var x7 = x5; var y7 = y6; document.write( "(" + x7 + ", " + y7 + ") " ); // Gives bottom-right point // of intersection rectangle var x8 = x6; var y8 = y5; document.write( "(" + x8 + ", " + y8 + ") " ); } // Driver Code // bottom-left and top-right // corners of first rectangle var x1 = 0, y1 = 0, x2 = 10, y2 = 8; // bottom-left and top-right // corners of first rectangle var x3 = 2, y3 = 3, x4 = 7, y4 = 9; // Function call FindPoints(x1, y1, x2, y2, x3, y3, x4, y4); // This code is contributed by kirti </script> |
(2, 3) (7, 8) (2, 8) (7, 3)
Time Complexity: O(1)
Auxiliary Space: O(1)
Please Login to comment...