Java: Check if a point (x, y) is in a triangle or not

Last update on May 13 2025 12:58:59 (UTC/GMT +8 hours)

Check Point Inside Triangle

Write a Java program to check if a point (x, y) is in a triangle or not. A triangle is formed by three points.

Input:
x1,y1,x2,y2,x3,y3,xp,yp separated by a single space.

Sample Solution:

Java Code:

// Importing the necessary Java utility package
import java.util.*;

// Main class named "Main"
public class Main { 
    // Method to calculate the outer product of vectors (x1, y1) and (x2, y2) with respect to point (x, y)
    private double outer_product(double x, double y, double x1, double y1, double x2, double y2){
        // Shifting vectors to be relative to the point (x, y)
        x1 = x1 - x;
        y1 = y1 - y;
        x2 = x2 - x;
        y2 = y2 - y;

        // Calculating the cross product (outer product) of the two vectors
        double s = x1 * y2 - y1 * x2;
        return s;
    } 

    // Method to input coordinates and determine if a point is inside a triangle
    public void point(){
        // Creating a Scanner object for input
        Scanner sc = new Scanner(System.in);

        // Arrays to store coordinates of the triangle vertices (x, y)
        double [] x = new double[3];
        double [] y = new double[3];

        // Prompting the user to input the coordinates of the three vertices of the triangle
        System.out.println("Input (x1, y1)");            
        x[0] = sc.nextDouble();
        y[0] = sc.nextDouble();

        System.out.println("Input (x2, y2)");            
        x[1] = sc.nextDouble();
        y[1] = sc.nextDouble();

        System.out.println("Input (x3, y3)");            
        x[2] = sc.nextDouble();
        y[2] = sc.nextDouble();

        // Prompting the user to input the coordinates of the point (xp, yp)
        System.out.println("Input (xp, yp)");            
        double xp = sc.nextDouble();
        double yp = sc.nextDouble();

        // Array to store the results of the outer product calculations for each edge of the triangle
        boolean [] ans = new boolean[3];

        // Calculating the outer product for each edge and determining if the point is inside the triangle
        for(int i=0; i < 3; i++){
            ans[i] = outer_product(xp, yp, x[i], y[i], x[(i+1)%3], y[(i+1)%3]) > 0.0;
        }

        // Checking if all outer products have the same sign, indicating the point is inside the triangle
        if(ans[0] == ans[1] && ans[1] == ans[2]){
            // The point is inside the triangle
            // Additional processing, if needed, can be added here
        }
        else{
            // The point is outside the triangle
            System.out.println("The point is outside the triangle.");
        }
    }

    // Main method to create an object of the class and invoke the point method
    public static void main(String[] args) {
        Main obj = new Main();
        obj.point();
    }
}

Sample Output:

Input (x1, y1)
2
6
Input (x2, y2)
3
5
Input (x3, y3)
4
6
Input (xp, yp)
5
6
The point is outside the triangle.

Flowchart:

Flowchart: Java exercises: Check if a point (x, y) is in a triangle or not.

For more Practice: Solve these Related Problems:

Write a Java program to determine if a point lies strictly inside, on the edge, or outside a given triangle.
Write a Java program to check if a point is inside a triangle using barycentric coordinates.
Write a Java program to determine whether multiple points lie within a triangle defined by three vertices.
Write a Java program to check point inclusion in a triangle using the area comparison method.

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