在给定坡度的直线上找到给定距离的点-yiteyi-C++库

给定二维点p（x）的坐标 ₀ Y ₀ ).找出距离L的点，使这些点连接形成的线的斜率为M。

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例如：

Input : p = (2, 1)        L = sqrt(2)        M = 1Output :3, 2        1, 0Explanation:The two points are sqrt(2) distance away from the source and have the required slopem = 1.Input : p = (1, 0)        L = 5        M = 0Output : 6, 0        -4, 0

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

我们需要在一条斜率为M的直线上找到两个距离给定点L的点。下面的帖子介绍了这个想法。使用中点查找矩形的角点

根据输入斜率，问题可分为三类。

如果斜率为零，我们只需要调整源点的x坐标
如果斜率为无穷大，则需要调整y坐标
对于坡度的其他值，我们可以使用以下方程式来找到这些点

$Given that the point (x, y) is at distance I away from (x_0, y_0) ewline ewline (y-y_0)^{2} + (x-x_0)^{2}= l^{2} ewline ewline Also as the line that passes through (x, y) and (x0, y0) satisfies ewline ewline frac{y-y_0}{x-x_0}= m ewline ewline Rearranging we get ewline y=y_0+m*(x-x_0) ewline ewline Putting the values in first equation ewline ewline m^2.(x-x_0)^2+(x-x_0)^2=l^2 ewline ewline Hence, we have ewline ewline x=x_0pm l.sqrt{frac{1}{1+m^2}} ewline ewline y=y_0 pm m.l.sqrt{frac{1}{1+m^2}}$

现在使用上述公式，我们可以找到所需的点。

C++

                         // C++ program to find the points on a line of                       
                         // slope M at distance L                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // structure to represent a co-ordinate                       
                         // point                       
                         struct                                     Point {                       
           
                                                 float                                     x, y;                       
                                                 Point()                       
                                                 {                       
                                                 x = y = 0;                       
                                                 }                       
                                                 Point(                                     float                                     a,                                     float                                     b)                       
                                                 {                       
                                                 x = a, y = b;                       
                                                 }                       
                         };                       
           
                         // Function to print pair of points at                       
                         // distance 'l' and having a slope 'm'                       
                         // from the source                       
                         void                                     printPoints(Point source,                                     float                                     l,                       
                                                 int                                     m)                       
                         {                       
                                                 // m is the slope of line, and the                       
                                                 // required Point lies distance l                       
                                                 // away from the source Point                       
                                                 Point a, b;                       
           
                                                 // slope is 0                       
                                                 if                                     (m == 0) {                       
                                                 a.x = source.x + l;                       
                                                 a.y = source.y;                       
           
                                                 b.x = source.x - l;                       
                                                 b.y = source.y;                       
                                                 }                       
           
                                                 // if slope is infinite                       
                                                 else                                     if                                     (m == std::numeric_limits<                                     float                                     >                       
                                                 ::max()) {                       
                                                 a.x = source.x;                       
                                                 a.y = source.y + l;                       
           
                                                 b.x = source.x;                       
                                                 b.y = source.y - l;                       
                                                 }                       
                                                 else                                     {                       
                                                 float                                     dx = (l /                                     sqrt                                     (1 + (m * m)));                       
                                                 float                                     dy = m * dx;                       
                                                 a.x = source.x + dx;                       
                                                 a.y = source.y + dy;                       
                                                 b.x = source.x - dx;                       
                                                 b.y = source.y - dy;                       
                                                 }                       
           
                                                 // print the first Point                       
                                                 cout << a.x <<                                     ", "                                     << a.y << endl;                       
           
                                                 // print the second Point                       
                                                 cout << b.x <<                                     ", "                                     << b.y << endl;                       
                         }                       
           
                         // driver function                       
                         int                                     main()                       
                         {                       
                                                 Point p(2, 1), q(1, 0);                       
                                                 printPoints(p,                                     sqrt                                     (2), 1);                       
                                                 cout << endl;                       
                                                 printPoints(q, 5, 0);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the points on                       
                         // a line of slope M at distance L                       
                         class                                     GFG{                       
           
                         // Class to represent a co-ordinate                       
                         // point                       
                         static                                     class                                     Point                       
                         {                       
                                                 float                                     x, y;                       
                                                 Point()                       
                                                 {                       
                                                 x = y =                                     0                                     ;                       
                                                 }                       
                                                 Point(                                     float                                     a,                                     float                                     b)                       
                                                 {                       
                                                 x = a;                       
                                                 y = b;                       
                                                 }                       
                         };                       
           
                         // Function to print pair of points at                       
                         // distance 'l' and having a slope 'm'                       
                         // from the source                       
                         static                                     void                                     printPoints(Point source,                       
                                                 float                                     l,                                     int                                     m)                       
                         {                       
                                   
                                                 // m is the slope of line, and the                       
                                                 // required Point lies distance l                       
                                                 // away from the source Point                       
                                                 Point a =                                     new                                     Point();                       
                                                 Point b =                                     new                                     Point();                       
                                   
                                                 // Slope is 0                       
                                                 if                                     (m ==                                     0                                     )                       
                                                 {                       
                                                 a.x = source.x + l;                       
                                                 a.y = source.y;                       
           
                                                 b.x = source.x - l;                       
                                                 b.y = source.y;                       
                                                 }                       
           
                                                 // If slope is infinite                       
                                                 else                                     if                                     (Double.isInfinite(m))                       
                                                 {                       
                                                 a.x = source.x;                       
                                                 a.y = source.y + l;                       
           
                                                 b.x = source.x;                       
                                                 b.y = source.y - l;                       
                                                 }                       
                                                 else                       
                                                 {                       
                                                 float                                     dx = (                                     float                                     )(l / Math.sqrt(                                     1                                     + (m * m)));                       
                                                 float                                     dy = m * dx;                       
                                                 a.x = source.x + dx;                       
                                                 a.y = source.y + dy;                       
                                                 b.x = source.x - dx;                       
                                                 b.y = source.y - dy;                       
                                                 }                       
           
                                                 // Print the first Point                       
                                                 System.out.println(a.x +                                     ", "                                     + a.y);                       
           
                                                 // Print the second Point                       
                                                 System.out.println(b.x +                                     ", "                                     + b.y);                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     main(String[] args)                       
                         {                       
                                                 Point p =                                     new                                     Point(                                     2                                     ,                                     1                                     ),                       
                                                 q =                                     new                                     Point(                                     1                                     ,                                     0                                     );                       
                                                 printPoints(p, (                                     float                                     )Math.sqrt(                                     2                                     ),                                     1                                     );                       
                                   
                                                 System.out.println();                       
                                   
                                                 printPoints(q,                                     5                                     ,                                     0                                     );                       
                         }                       
                         }                       
           
                         // This code is contributed by Rajnis09                       

C#

                         // C# program to find the points on                       
                         // a line of slope M at distance L                       
                         using                                     System;                       
           
                         class                                     GFG{                       
           
                         // Class to represent a co-ordinate                       
                         // point                       
                         public                                     class                                     Point                       
                         {                       
                                                 public                                     float                                     x, y;                       
                                   
                                                 public                                     Point()                       
                                                 {                       
                                                 x = y = 0;                       
                                                 }                       
                                   
                                                 public                                     Point(                                     float                                     a,                                     float                                     b)                       
                                                 {                       
                                                 x = a;                       
                                                 y = b;                       
                                                 }                       
                         };                       
           
                         // Function to print pair of points at                       
                         // distance 'l' and having a slope 'm'                       
                         // from the source                       
                         static                                     void                                     printPoints(Point source,                       
                                                 float                                     l,                                     int                                     m)                       
                         {                       
                                   
                                                 // m is the slope of line, and the                       
                                                 // required Point lies distance l                       
                                                 // away from the source Point                       
                                                 Point a =                                     new                                     Point();                       
                                                 Point b =                                     new                                     Point();                       
                                   
                                                 // Slope is 0                       
                                                 if                                     (m == 0)                       
                                                 {                       
                                                 a.x = source.x + l;                       
                                                 a.y = source.y;                       
           
                                                 b.x = source.x - l;                       
                                                 b.y = source.y;                       
                                                 }                       
           
                                                 // If slope is infinite                       
                                                 else                                     if                                     (Double.IsInfinity(m))                       
                                                 {                       
                                                 a.x = source.x;                       
                                                 a.y = source.y + l;                       
           
                                                 b.x = source.x;                       
                                                 b.y = source.y - l;                       
                                                 }                       
                                                 else                       
                                                 {                       
                                                 float                                     dx = (                                     float                                     )(l / Math.Sqrt(                       
                                                 1 + (m * m)));                       
                                                 float                                     dy = m * dx;                       
                                                 a.x = source.x + dx;                       
                                                 a.y = source.y + dy;                       
                                                 b.x = source.x - dx;                       
                                                 b.y = source.y - dy;                       
                                                 }                       
           
                                                 // Print the first Point                       
                                                 Console.WriteLine(a.x +                                     ", "                                     + a.y);                       
           
                                                 // Print the second Point                       
                                                 Console.WriteLine(b.x +                                     ", "                                     + b.y);                       
                         }                       
           
                         // Driver code                       
                         public                                     static                                     void                                     Main(String[] args)                       
                         {                       
                                                 Point p =                                     new                                     Point(2, 1),                       
                                                 q =                                     new                                     Point(1, 0);                       
                                   
                                                 printPoints(p, (                                     float                                     )Math.Sqrt(2), 1);                       
                                   
                                                 Console.WriteLine();                       
                                   
                                                 printPoints(q, 5, 0);                       
                         }                       
                         }                       
           
                         // This code is contributed by Amit Katiyar                       

输出：

3, 21, 06, 0-4, 0

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