Check if a line touches or intersects a circle
Given coordinate of the center and radius > 1 of a circle and the equation of a line. The task is to check if the given line collide with the circle or not. There are three possibilities :
- Line intersect the circle.
- Line touches the circle.
- Line is outside the circle.
Note: General equation of a line is a*x + b*y + c = 0, so only constant a, b, c are given in the input.
Examples :
Input : radius = 5, center = (0, 0),
a = 1, b = -1, c = 0.
Output : Intersect
Input : radius = 5, center = (0, 0),
a = 5, b = 0, c = 0.
Output : Touch
Input : radius = 5, center = (0, 0),
a = 1, b = 1, c = -16.
Output : Outside
The idea is to compare the perpendicular distance between center of circle and line with the radius of the circle.
Algorithm:
1. Find the perpendicular (say p) between center of circle and given line.
2. Compare this distance p with radius r.
……a) If p > r, then line lie outside the circle.
……b) If p = r, then line touches the circle.
……c) If p < r, then line intersect the circle.
How to find the perpendicular distance?
Distance of a line from a point can be computed using below formula:
Refer Wiki for details of above formula.
C++
// CPP program to check if a line touches or// intersects or outside a circle.#include <bits/stdc++.h>using namespace std;void checkCollision(int a, int b, int c, int x, int y, int radius){ // Finding the distance of line from center. int dist = (abs(a * x + b * y + c)) / sqrt(a * a + b * b); // Checking if the distance is less than, // greater than or equal to radius. if (radius == dist) cout << "Touch" << endl; else if (radius > dist) cout << "Intersect" << endl; else cout << "Outside" << endl;}// Driven Programint main(){ int radius = 5; int x = 0, y = 0; int a = 3, b = 4, c = 25; checkCollision(a, b, c, x, y, radius); return 0;} |
Java
// Java program to check if a line touches or// intersects or outside a circle.import java.io.*;class GFG { static void checkCollision(int a, int b, int c, int x, int y, int radius) { // Finding the distance of line from center. double dist = (Math.abs(a * x + b * y + c)) / Math.sqrt(a * a + b * b); // Checking if the distance is less than, // greater than or equal to radius. if (radius == dist) System.out.println ( "Touch" ); else if (radius > dist) System.out.println( "Intersect") ; else System.out.println( "Outside") ; } // Driven Program public static void main (String[] args) { int radius = 5; int x = 0, y = 0; int a = 3, b = 4, c = 25; checkCollision(a, b, c, x, y, radius); }}// This article is contributed by vt_m. |
Python3
# python program to check if a line# touches or intersects or outside# a circle.import mathdef checkCollision(a, b, c, x, y, radius): # Finding the distance of line # from center. dist = ((abs(a * x + b * y + c)) / math.sqrt(a * a + b * b)) # Checking if the distance is less # than, greater than or equal to radius. if (radius == dist): print("Touch") elif (radius > dist): print("Intersect") else: print("Outside")# Driven Programradius = 5x = 0y = 0a = 3b = 4c = 25checkCollision(a, b, c, x, y, radius)# This code is contributed by Sam007 |
C#
// C# program to check if a line touches or// intersects or outside a circle.using System;class GFG { static void checkCollision(int a, int b, int c, int x, int y, int radius) { // Finding the distance of line from center. double dist = (Math.Abs(a * x + b * y + c)) / Math.Sqrt(a * a + b * b); // Checking if the distance is less than, // greater than or equal to radius. if (radius == dist) Console.WriteLine ("Touch"); else if (radius > dist) Console.WriteLine("Intersect"); else Console.WriteLine("Outside"); } // Driven Program public static void Main () { int radius = 5; int x = 0, y = 0; int a = 3, b = 4, c = 25; checkCollision(a, b, c, x, y, radius); }}// This article is contributed by vt_m. |
PHP
<?php// PHP program to check if a line // touches or intersects or outside// a circle.function checkCollision($a, $b, $c, $x, $y, $radius){ // Finding the distance // of line from center. $dist = (abs($a * $x + $b * $y + $c)) / sqrt($a * $a + $b * $b); // Checking if the distance is less than, // greater than or equal to radius. if ($radius == $dist) echo "Touch"; else if ($radius > $dist) echo "Intersect"; else echo "Outside" ;}// Driver Code$radius = 5;$x = 0;$y = 0;$a = 3;$b = 4;$c = 25;checkCollision($a, $b, $c, $x, $y, $radius);// This code is contributed by Sam007?> |
Javascript
<script>// JavaScript program to check if a line touches or// intersects or outside a circle.function checkCollision(a, b, c, x, y, radius) { // Finding the distance of line from center. let dist = (Math.abs(a * x + b * y + c)) / Math.sqrt(a * a + b * b); // Checking if the distance is less than, // greater than or equal to radius. if (radius == dist) document.write ( "Touch" ); else if (radius > dist) document.write( "Intersect") ; else document.write( "Outside") ; }// Driver Code let radius = 5; let x = 0, y = 0; let a = 3, b = 4, c = 25; checkCollision(a, b, c, x, y, radius);// This code is contributed by susmitakundugoaldanga.</script> |
Output :
Touch
Time Complexity : O(1)
Auxiliary Space : O(1)
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