How to Find the Area of any Polygon Using Triangulation in Java?

Polygons are basic shapes in geometry and can have many sides. Finding the Area of a Polygon is a complex task, So to perform this complex task we have a method called Triangulation. Triangulation is a method of dividing a polygon into triangles and then finding the area of each triangle to get the total area of the polygon. In this article, we’ll check the methods of how to find the area of any polygon using triangulation in Java.

Methods to Find Area of Polygon

There are a couple of methods to find the area of a Polygon as mentioned below:

1. Break the polygon into triangles
2. Using the shoelace formula

1. Break the Polygon into Triangles

We can divide the polygon into smaller triangles and then find the area of each triangle. The triangulation algorithm can be implemented using different methods, such as the Delaunay triangulation method, the ear clipping method, etc.

Implementation of the above approach:

Java

// Java Program to implement
// Break the polygon into triangles
import java.util.Scanner;

// Main Class
public class GFG {
    public static void main(String[] args)
    {

        // number of sides of the polygon
        int n = 4;

        // x-coordinates of the vertices of the polygon
        int[] xCoords = { 0, 1, 0, 1 };

        // y-coordinates of the vertices of the polygon
        int[] yCoords = { 0, 0, 2, 2 };

        // initialize the area
        double area = 0.0;

        // the three vertices of the triangle
        for (int i = 0; i < n - 2; i++) {
            // first vertex is always the same
            int v1 = 0;

            // second vertex moves from 1 to n-2
            int v2 = i + 1;
            // third vertex moves from 2 to n-1
            // calculate the area of the triangle using
            // Shoelace formula
            int v3 = i + 2;

            // add the area of the triangle to the total
            // area
            double triangleArea = Math.abs(
                0.5
                * (xCoords[v1] * (yCoords[v2] - yCoords[v3])
                   + xCoords[v2]
                         * (yCoords[v3] - yCoords[v1])
                   + xCoords[v3]
                         * (yCoords[v1] - yCoords[v2])));

            area += triangleArea;
        }

        // print the final result
        System.out.println("Area of Polygon: " + area);
    }
}

Output

Area of Polygon: 2.0

In this code, n is the number of sides of the polygon, and xCoords and yCoords are the arrays containing the x and y coordinates of the vertices of the polygon, respectively. The main method calculates the area of the polygon by triangulating it into smaller triangles and summing the areas of each triangle. The formula for calculating the area of a triangle is 0.5 * base * height.

Time complexity: O(n)
Space Complexity: O(n)

2. Using the Shoelace Formula

The shoelace formula is a mathematical formula that can be used to find the area of a polygon. It works by adding the areas of the triangles formed by connecting the vertices of the polygon to a common point.

Implementation of the above approach:

Java

// Java Program to implement
// Using shoelace formula
import java.io.*;

// Main Class
class GFG {
    public static void main(String[] args)
    {
        // number of vertices in the polygon
        int n = 4;

        // array to store x coordinates of the vertices
        int[] xCoords = { 0, 1, 1, 0 };

        // array to store y coordinates of the vertices
        int[] yCoords = { 0, 0, 2, 2 };

        // variable to store the area of the polygon
        double area = 0.0;

        // loop to calculate the area of the polygon
        for (int i = 0; i < n - 1; i++) {
            // add the area of the current triangle
            area += xCoords[i] * yCoords[i + 1]
                    - xCoords[i + 1] * yCoords[i];
        }

        // add the area of the last triangle
        area += xCoords[n - 1] * yCoords[0]
                - xCoords[0] * yCoords[n - 1];

        // divide the total area by 2 to get the final
        // answer
        area = Math.abs(0.5 * area);

        // print the area of the polygon
        System.out.println("Area of Polygon: " + area);
    }
}

Output

Area of Polygon: 2.0

In this code, n is the number of sides of the polygon, and xCoords and yCoords are the arrays containing the x and y coordinates of the vertices of the polygon, respectively. The main method calculates the area of the polygon using the Shoelace formula by summing the areas of each triangular component formed by the vertices and the origin. The formula is 0.5 * (sum of (x_i * y_i+1 – x_i+1 * y_i)) where x_i and y_i are the x and y coordinates of the ith vertex.

Time Complexity: O(n)
Space Complexity: O(n)