通过程序查找通过2个点的线-yiteyi-C++库

给定坐标平面上的两点P和Q，求出通过这两点的直线的方程。这种转换在许多几何算法中非常有用，比如线的相交，求环中心一个三角形，找到因森特一个三角形和更多…

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例如：

Input : P(3, 2)        Q(2, 6)Output : 4x + 1y = 14Input : P(0, 1)        Q(2, 4)Output : 3x + -2y = -2

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

设给定两点为P（x） _1. Y _1. )和Q（x） _2. Y _2. )现在，我们找到由这些点构成的直线方程。任何线条都可以表示为， ax+by=c 让两点满足给定的直线。所以我们有，斧头 _1. +由 _1. =c 斧头 _2. +由 _2. =c

我们可以设置以下值，使所有方程都成立，

a = y₂ - y₁b = x₁ - x₂c = ax₁ + by₁

首先直接求出斜率，然后求出直线的截距，就可以得到它们。或者，也可以通过以下简单观察巧妙得出：

推导：

ax₁ + by₁ = c ...(i)ax₂ + by₂ = c ...(ii)Equating (i) and (ii),ax₁ + by₁ = ax₂ + by₂=> a(x₁ - x₂) = b(y₂ - y₁)Thus, for equating LHS and RHS, we can simply have,a = (y₂ - y₁)ANDb = (x₁ - x₂)so that we have,(y₂ - y₁)(x₁ - x₂) = (x₁ - x₂)(y₂ - y₁)ANDPutting these values in (i), we get,c = ax₁ + by₁

因此，我们现在有a，b和c的值，这意味着我们有坐标平面上的线。

C++

                         // C++ Implementation to find the line passing                       
                         // through two points                       
                         #include <iostream>                       
                         using                                     namespace                                     std;                       
           
                         // This pair is used to store the X and Y                       
                         // coordinate of a point respectively                       
                         #define pdd pair<double, double>                       
           
                         // Function to find the line given two points                       
                         void                                     lineFromPoints(pdd P, pdd Q)                       
                         {                       
                                                 double                                     a = Q.second - P.second;                       
                                                 double                                     b = P.first - Q.first;                       
                                                 double                                     c = a * (P.first) + b * (P.second);                       
           
                                                 if                                     (b < 0) {                       
                                                 cout <<                                     "The line passing through points P and Q "                       
                                                 "is: "                       
                                                 << a <<                                     "x - "                                     << b <<                                     "y = "                                     << c << endl;                       
                                                 }                       
                                                 else                                     {                       
                                                 cout <<                                     "The line passing through points P and Q "                       
                                                 "is: "                       
                                                 << a <<                                     "x + "                                     << b <<                                     "y = "                                     << c << endl;                       
                                                 }                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 pdd P = make_pair(3, 2);                       
                                                 pdd Q = make_pair(2, 6);                       
                                                 lineFromPoints(P, Q);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Implementation to find the line passing                       
                         // through two points                       
                         class                                     GFG {                       
           
                                                 // This pair is used to store the X and Y                       
                                                 // coordinate of a point respectively                       
                                                 static                                     class                                     Pair {                       
                                                 int                                     first, second;                       
           
                                                 public                                     Pair(                                     int                                     first,                                     int                                     second)                       
                                                 {                       
                                                 this                                     .first = first;                       
                                                 this                                     .second = second;                       
                                                 }                       
                                                 }                       
           
                                                 // Function to find the line given two points                       
                                                 static                                     void                                     lineFromPoints(Pair P, Pair Q)                       
                                                 {                       
                                                 int                                     a = Q.second - P.second;                       
                                                 int                                     b = P.first - Q.first;                       
                                                 int                                     c = a * (P.first) + b * (P.second);                       
           
                                                 if                                     (b <                                     0                                     ) {                       
                                                 System.out.println(                       
                                                 "The line passing through points P and Q is: "                       
                                                 + a +                                     "x - "                                     + b +                                     "y = "                                     + c);                       
                                                 }                       
                                                 else                                     {                       
                                                 System.out.println(                       
                                                 "The line passing through points P and Q is: "                       
                                                 + a +                                     "x + "                                     + b +                                     "y = "                                     + c);                       
                                                 }                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 Pair P =                                     new                                     Pair(                                     3                                     ,                                     2                                     );                       
                                                 Pair Q =                                     new                                     Pair(                                     2                                     ,                                     6                                     );                       
                                                 lineFromPoints(P, Q);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Princi Singh                       

Python3

                         # Python3 Implementation to find the line passing                       
                         # through two points                       
           
                         # This pair is used to store the X and Y                       
                         # coordinate of a point respectively                       
                         # define pdd pair<double, double>                       
           
                         # Function to find the line given two points                       
           
           
                         def                                     lineFromPoints(P, Q):                       
           
                                                 a                                     =                                     Q[                                     1                                     ]                                     -                                     P[                                     1                                     ]                       
                                                 b                                     =                                     P[                                     0                                     ]                                     -                                     Q[                                     0                                     ]                       
                                                 c                                     =                                     a                                     *                                     (P[                                     0                                     ])                                     +                                     b                                     *                                     (P[                                     1                                     ])                       
           
                                                 if                                     (b <                                     0                                     ):                       
                                                 print                                     (                                     "The line passing through points P and Q is:"                                     ,                       
                                                 a,                                     "x - "                                     , b,                                     "y = "                                     , c,                                     ""                                     )                       
                                                 else                                     :                       
                                                 print                                     (                                     "The line passing through points P and Q is: "                                     ,                       
                                                 a,                                     "x + "                                     , b,                                     "y = "                                     , c,                                     ""                                     )                       
           
           
                         # Driver code                       
                         if                                     __name__                                     =                                     =                                     '__main__'                                     :                       
                                                 P                                     =                                     [                                     3                                     ,                                     2                                     ]                       
                                                 Q                                     =                                     [                                     2                                     ,                                     6                                     ]                       
                                                 lineFromPoints(P, Q)                       
           
                         # This code is contributed by ash264                       

C#

                         // C# Implementation to find the line passing                       
                         // through two points                       
                         using                                     System;                       
           
                         class                                     GFG {                       
           
                                                 // This pair is used to store the X and Y                       
                                                 // coordinate of a point respectively                       
                                                 public                                     class                                     Pair {                       
                                                 public                                     int                                     first, second;                       
           
                                                 public                                     Pair(                                     int                                     first,                                     int                                     second)                       
                                                 {                       
                                                 this                                     .first = first;                       
                                                 this                                     .second = second;                       
                                                 }                       
                                                 }                       
           
                                                 // Function to find the line given two points                       
                                                 static                                     void                                     lineFromPoints(Pair P, Pair Q)                       
                                                 {                       
                                                 int                                     a = Q.second - P.second;                       
                                                 int                                     b = P.first - Q.first;                       
                                                 int                                     c = a * (P.first) + b * (P.second);                       
           
                                                 if                                     (b < 0) {                       
                                                 Console.WriteLine(                       
                                                 "The line passing through points P and Q is: "                       
                                                 + a +                                     "x - "                                     + b +                                     "y = "                                     + c);                       
                                                 }                       
                                                 else                                     {                       
                                                 Console.WriteLine(                       
                                                 "The line passing through points P and Q is: "                       
                                                 + a +                                     "x + "                                     + b +                                     "y = "                                     + c);                       
                                                 }                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main(String[] args)                       
                                                 {                       
                                                 Pair P =                                     new                                     Pair(3, 2);                       
                                                 Pair Q =                                     new                                     Pair(2, 6);                       
                                                 lineFromPoints(P, Q);                       
                                                 }                       
                         }                       
           
                         // This code has been contributed by 29AjayKumar                       

Javascript

                         <script>                       
           
                         // Javascript implementation to find the                       
                         // line passing through two points                       
           
                         // Function to find the line given two points                       
                         function                                     lineFromPoints(P, Q)                       
                         {                       
                                                 var                                     a = Q[1] - P[1]                       
                                                 var                                     b = P[0] - Q[0]                       
                                                 var                                     c = a*(P[0]) + b*(P[1])                       
           
                                                 if                                     (b < 0)                       
                                                 document.write(                                     "The line passing through "                                     +                       
                                                 "points P and Q is:  "                                     + a +                       
                                                 "x - "                                     + b +                                     "y = "                                     + c +                                     "<br>"                                     )                       
                                                 else                       
                                                 document.write(                                     "The line passing through "                                     +                       
                                                 "points P and Q is:  "                                     + a +                       
                                                 "x + "                                     + b +                                     "y = "                                     + c +                                     "<br>"                                     )                       
                         }                       
           
                         // Driver code                       
                         var                                     P = [ 3, 2 ]                       
                         var                                     Q = [ 2, 6 ]                       
           
                         lineFromPoints(P, Q)                       
           
                         // This code is contributed by akshitsaxenaa09                       
           
                         </script>                       

输出：

The line passing through points P and Q is: 4x + 1y = 14

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