Given N vertices of the polygon, the task is to find the centroid of the polygon
Examples:
Input: ar = {{0, 0}, {0, 8}, {8, 8}, {8, 0}}
Output: {Cx, Cy} = {4, 4}
Input: ar = {{1, 2}, {3, -4}, {6, -7}}
Output: {Cx, Cy} = {3.33, -3}
Approach:
The centroid of a non-self-intersecting closed polygon defined by n vertices (x0, y0), (x1, y1), …, (xn-1, yn-1) is the point (Cx, Cy), where:
Below is the implementation of the above approach:
C++
// C++ program to implement the // above approach#include <bits/stdc++.h>using namespace std;pair<double, double> find_Centroid(vector<pair<double, double> >& v){ pair<double, double> ans = { 0, 0 }; int n = v.size(); double signedArea = 0; // For all vertices for (int i = 0; i < v.size(); i++) { double x0 = v[i].first, y0 = v[i].second; double x1 = v[(i + 1) % n].first, y1 = v[(i + 1) % n].second; // Calculate value of A // using shoelace formula double A = (x0 * y1) - (x1 * y0); signedArea += A; // Calculating coordinates of // centroid of polygon ans.first += (x0 + x1) * A; ans.second += (y0 + y1) * A; } signedArea *= 0.5; ans.first = (ans.first) / (6 * signedArea); ans.second = (ans.second) / (6 * signedArea); return ans;}// Driver codeint main(){ // Coordinate of the vertices vector<pair<double, double> > vp = { { 1, 2 }, { 3, -4 }, { 6, -7 } }; pair<double, double> ans = find_Centroid(vp); cout << setprecision(12) << ans.first << " " << ans.second << '\n'; return 0;} |
Java
// Java implementation of the approach class GFG { static double[] find_Centroid(double v[][]) { double []ans = new double[2]; int n = v.length; double signedArea = 0; // For all vertices for (int i = 0; i < n; i++) { double x0 = v[i][0], y0 = v[i][1]; double x1 = v[(i + 1) % n][0], y1 = v[(i + 1) % n][1]; // Calculate value of A // using shoelace formula double A = (x0 * y1) - (x1 * y0); signedArea += A; // Calculating coordinates of // centroid of polygon ans[0] += (x0 + x1) * A; ans[1] += (y0 + y1) * A; } signedArea *= 0.5; ans[0] = (ans[0]) / (6 * signedArea); ans[1]= (ans[1]) / (6 * signedArea); return ans; } // Driver code public static void main (String[] args) { // Coordinate of the vertices double vp[][] = { { 1, 2 }, { 3, -4 }, { 6, -7 } }; double []ans = find_Centroid(vp); System.out.println(ans[0] + " " + ans[1]); } }// This code is contributed by AnkitRai01 |
Python3
# Python3 program to implement the# above approachdef find_Centroid(v): ans = [0, 0] n = len(v) signedArea = 0 # For all vertices for i in range(len(v)): x0 = v[i][0] y0 = v[i][1] x1 = v[(i + 1) % n][0] y1 =v[(i + 1) % n][1] # Calculate value of A # using shoelace formula A = (x0 * y1) - (x1 * y0) signedArea += A # Calculating coordinates of # centroid of polygon ans[0] += (x0 + x1) * A ans[1] += (y0 + y1) * A signedArea *= 0.5 ans[0] = (ans[0]) / (6 * signedArea) ans[1] = (ans[1]) / (6 * signedArea) return ans# Driver code# Coordinate of the verticesvp = [ [ 1, 2 ], [ 3, -4 ], [ 6, -7 ] ]ans = find_Centroid(vp)print(round(ans[0], 12), ans[1])# This code is contributed by Mohit Kumar |
C#
// C# implementation of the approach using System;class GFG { static double[] find_Centroid(double [,]v) { double []ans = new double[2]; int n = v.GetLength(0); double signedArea = 0; // For all vertices for (int i = 0; i < n; i++) { double x0 = v[i, 0], y0 = v[i, 1]; double x1 = v[(i + 1) % n, 0], y1 = v[(i + 1) % n, 1]; // Calculate value of A // using shoelace formula double A = (x0 * y1) - (x1 * y0); signedArea += A; // Calculating coordinates of // centroid of polygon ans[0] += (x0 + x1) * A; ans[1] += (y0 + y1) * A; } signedArea *= 0.5; ans[0] = (ans[0]) / (6 * signedArea); ans[1]= (ans[1]) / (6 * signedArea); return ans; } // Driver code public static void Main (String[] args) { // Coordinate of the vertices double [,]vp = { { 1, 2 }, { 3, -4 }, { 6, -7 } }; double []ans = find_Centroid(vp); Console.WriteLine(ans[0] + " " + ans[1]); } }// This code is contributed by PrinciRaj1992 |
Javascript
<script> // Javascript implementation of the approach function find_Centroid(v) { let ans = new Array(2); ans.fill(0); let n = v.length; let signedArea = 0; // For all vertices for (let i = 0; i < n; i++) { let x0 = v[i][0], y0 = v[i][1]; let x1 = v[(i + 1) % n][0], y1 = v[(i + 1) % n][1]; // Calculate value of A // using shoelace formula let A = (x0 * y1) - (x1 * y0); signedArea += A; // Calculating coordinates of // centroid of polygon ans[0] += (x0 + x1) * A; ans[1] += (y0 + y1) * A; } signedArea *= 0.5; ans[0] = (ans[0]) / (6 * signedArea); ans[1]= (ans[1]) / (6 * signedArea); return ans; } // Coordinate of the vertices let vp = [ [ 1, 2 ], [ 3, -4 ], [ 6, -7 ] ]; let ans = find_Centroid(vp); document.write(ans[0].toFixed(11) + " " + ans[1]); // This code is contributed by divyeshrabadiya07.</script> |
Output:
3.33333333333 -3
Time Complexity: O(n)
Auxiliary Space: O(1)
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