检查直线是否与圆接触或相交-yiteyi-C++库

给定圆心和半径大于1的坐标以及直线方程。任务是检查给定的直线是否与圆碰撞。有三种可能性：

null

直线与圆相交。
线与圆接触。
线在圆圈外。

Check if a line touches or intersects a circle

注：直线的一般方程为a*x+b*y+c=0，因此输入中只给出常数a、b、c。 例如：

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

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

这个想法是比较圆心和直线之间的垂直距离与圆的半径。算法： 1.求圆心和给定直线之间的垂线（比如p）。 2.将距离p与半径r进行比较。 ……a）如果p>r，则直线位于圆外。 ……b）如果p=r，则直线与圆接触。 ……c）如果p 如何求垂直距离？ 直线与点之间的距离可以使用以下公式计算： $frac{ax_{0}+by_{0}+c}{sqrt{a^{2}+b^{2}}}$ 参考维基有关上述公式的详细信息。

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 Program                       
                         int                                     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                                     math                       
                                   
                         def                                     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 Program                       
                         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                       

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>                       

输出：

Touch

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