在Java中找到平行四边形的所有可能坐标

平行四边形是指具有两对平行边的四边形，其中对边长度相等，对角线度量相等。

In this article we are going to find all possible coordinates of a Parallelogram.

Basically, we will find all the possible coordinates from the given three coordinates to make a parallelogram of a non-zero area. Here the three given coordinates are not fixed points and can change.

因此，如果给出三个坐标，我们可以断言只有这三个坐标可以构建一个平行四边形。

As per diagram given above, the opposite sides of a parallelogram are equal in length i.e., AD = BC and AB = CD, we can calculate the coordinates of the missing point (D) as

AD = BC

(Dx - Ax, Dy - Ay) = (Cx - Bx, Cy - By)

Dx = Ax + Cx - Bx

Dy = Ay + Cy - By

让我们开始吧！

展示给你一些实例

Instance-1

假设这三个点是 −

{a1 = 3, a2 = 2}, {b1 = 1, b2 = 0}, {c1 = 4, c2 = 2}

After finding all possible coordinates of a Parallelogram, result will be −

The (x, y) coordinates are −

0, 0

6, 4

2, 0

Instance-2

假设这三个点是 −

{a1 = 7, a2 = 2}, {b1 = 3, b2 = 0}, {c1 =0, c2 = 1}

After finding all possible coordinates of a Parallelogram, result will be −

The (x,y) coordinates are −

10, 1

4, 3

-4, -1

Algorithm

Step 1 − Declare the three coordinates of parallelogram.

Step 2 − Find the other possible coordinates using the formula.

Step 3 − Print the result.

Multiple Approaches

我们以不同的方法提供了解决方案。

• 通过使用静态输入值

• 通过用户定义的方法

让我们逐个查看程序及其输出。

方法一：通过使用静态输入值

在这种方法中，我们将把这三个点作为静态输入，并应用公式来打印结果。

Example

public class Main{

   // main method
   public static void main(String[] args){

      //Declare the three coordinates of parallelogram
      int a1 = 3, a2 = 2;
      int b1 = 1, b2 = 0;
      int c1 = 4, c2 = 2;
       
      //find the other possible coordinates and printing it
      System.out.println("The (x,y) coordinates are: ");
      System.out.println(a1 + b1 - c1 + ", " + (a2 + b2 - c2));
      System.out.println(a1 + c1 - b1 + ", " + (a2 + c2 - b2));
      System.out.println(c1 + b1 - a1 + ", " + (c2 + b2 - a2));
   }
}

Output

The (x,y) coordinates are: 
0, 0
6, 4
2, 0

Approach-2: By Using User Defined Method

In this approach, first we will initialise a user defined method and we will take the three points as input and apply the formula to print the result.

Example

public class Main {
	
   // main method
   public static void main(String[] s){
      //Declare the three coordinates of parallelogram 
      int a1 = 7, a2 = 2; 
      int b1 = 3, b2 = 0; 
      int c1 = 0, c2 = 1; 
      //calling user defined function
      func(a1, a2, b1, b2, c1, c2);
   }
      
   //user defined function
   static void func(int a1, int a2, int b1, int b2, int c1, int c2){
      //find the other possible coordinates and printing it
      System.out.println("The (x,y) coordinates are: ");
      System.out.println(a1 + b1 - c1 + ", " + (a2 + b2 - c2));
      System.out.println(a1 + c1 - b1 + ", " + (a2 + c2 - b2));
      System.out.println(c1 + b1 - a1 + ", " + (c2 + b2 - a2));
   }
}

Output

The (x,y) coordinates are: 
10, 1
4, 3
-4, -1

在这篇文章中，我们探讨了如何通过使用不同的方法在Java中找到平行四边形的所有可能坐标。

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