在Java中找到平行四邊形的所有可能座標

平行四邊形是指具有兩對平行邊的四邊形，其中對邊長度相等，對角線度量相等。

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，如果給出三個座標，我們可以斷言只有這三個座標可以建構一個平行四邊形。

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

讓我們開始吧！

展示給你一些實例

Instance-1

假設這三個點是 −

{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

假設這三個點是 −

{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

我們以不同的方法提供了解決方案。

• 透過使用靜態輸入值

• #透過使用者定義的方法

#讓我們逐一查看程式及其輸出。

方法一：透過使用靜態輸入值

在這個方法中，我們將把這三個點當作靜態輸入，並應用公式來列印結果。

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

在這篇文章中，我們探討如何透過使用不同的方法在Java中找到平行四邊形的所有可能座標。

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