Java Program to Check Orientation of 3 Given Ordered Points

In the previous article, we have discussed about Java Program to Count Integral Points Inside a Triangle

In this article we are going to see how to check orientation of 3 ordered points using Java programming language.

Java Program to Check Orientation of 3 Given Ordered Points

Before Jumping into the program directly let’s see how to check orientation of 3 ordered points.

Explanation:

Lets take 3 points P(x1,y1) , Q(x2,y2), R(x3,y3)

Now,

Slope of line segment (P,Q) = S1 = (y2 - y1)/(x2 - x1)

Slope of line segment (Q,R) = S2 = (y3 - y2)/(x3 - x2)

If S1 > S2, then orientation is clockwise

If S1 < S2, then orientation is counter-clockwise

Using above values of S1 and S2, it is clear that, the orientation depends on sign of below expression:

Value = (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1)

If value = 0, then orientation is co-linear
If value > 0, then orientation is clockwise
If value < 0, then orientation is counter-clockwise

Example:

P = (1,2)
Q = (3,4)
R = (5,6)

Value = (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1) = 0

Since value = 0, hence orientation is co-linear.

Let’s see different ways to check orientation of 3 given ordered points.

By Using Static Input Value
By Using User Input Value

Method-1: Java Program to Check Orientation of 3 Given Ordered Points By Using Static Value

Approach:

Declare an double variable say ‘x1’ and assign the value to it, which holds the x coordinate of point P
Declare an double variable say ‘y1’ and assign the value to it, which holds the y coordinate of point P
Declare an double variable say ‘x2’ and assign the value to it, which holds the x coordinate of point Q
Declare an double variable say ‘y2’ and assign the value to it, which holds the y coordinate of point Q
Declare an double variable say ‘x3’ and assign the value to it, which holds the x coordinate of point R
Declare an double variable say ‘y3’ and assign the value to it, which holds the y coordinate of point R
Find the orientation using the formula (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1)
If value = 0, then orientation is co-linear OR If value > 0, then orientation is clockwise OR If value < 0, then orientation is counter-clockwise.
Print the result.

Program:

import java.util.*;
public class Main
{
   public static void main(String[] args)
   {
       //coordinates declared
      double x1 = 1;
      double y1 = 2;
      double x2 = 3;
      double y2 = 4;
      double x3 = 5;
      double y3 = 6;
        // relation between the slopes of PQ, QR
        double value = (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1);
        // checking condition for orientation
        if(value == 0)
            System.out.println("Point P,Q,R are co-linear");
        else if(value > 0)
            System.out.println("Point P,Q,R are clockwise");
        else
            System.out.println("Point P,Q,R are counter-clockwise");
   }
}

Output:

Point P,Q,R are co-linear

Method-2: Java Program to Check Orientation of 3 Given Ordered Points By Using User Input Value

Approach:

Declare an double variable say ‘x1’ which holds the x coordinate of point P
Declare an double variable say ‘y1’ which holds the y coordinate of point P
Declare an double variable say ‘x2’ which holds the x coordinate of point Q
Declare an double variable say ‘y2’ which holds the y coordinate of point Q
Declare an double variable say ‘x3’ which holds the x coordinate of point R
Declare an double variable say ‘y3’ which holds the y coordinate of point R
Then we will take the value of “x1”, “y1”, “x2”, “y2”, “x3”, “y3” as user input using scanner class.
Find the orientation using the formula (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1)
If value = 0, then orientation is co-linear OR If value > 0, then orientation is clockwise OR If value < 0, then orientation is counter-clockwise.
Print the result.

Program:

import java.util.*;
public class Main
{
   public static void main(String[] args)
   {
       //Scanner class objectv created
      Scanner s = new Scanner(System.in);
      //Taking input of points
      System.out.println("Enter the x coordinate of point P: ");
      double x1 = s.nextDouble();
      System.out.println("Enter the y coordinate of point P: ");
      double y1 = s.nextDouble();
      System.out.println("Enter the x coordinate of point Q: ");
      double x2 = s.nextDouble();
      System.out.println("Enter the y coordinate of point Q: ");
      double y2 = s.nextDouble();
      System.out.println("Enter the x coordinate of point R: ");
      double x3 = s.nextDouble();
      System.out.println("Enter the y coordinate of point R: ");
      double y3 = s.nextDouble();

        // relation between the slopes of PQ, QR
        double value = (y2 - y1)*(x3 - x2) - (y3 - y2)*(x2 - x1);
        // checking condition for orientation
        if(value == 0)
            System.out.println("Point P,Q,R are co-linear");
        else if(value > 0)
            System.out.println("Point P,Q,R are clockwise");
        else
            System.out.println("Point P,Q,R are counter-clockwise");
   }
}

Output:

Enter the x coordinate of point P: 
0
Enter the y coordinate of point P: 
0
Enter the x coordinate of point Q: 
4
Enter the y coordinate of point Q: 
4
Enter the x coordinate of point R: 
1
Enter the y coordinate of point R: 
2
Point P,Q,R are counter-clockwise

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