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Find N random points within a Circle

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  • Last Updated : 22 Jun, 2022
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Given four integers N, R, X, and Y such that it represents a circle of radius R with [X, Y] as coordinates of the center. The task is to find N random points inside or on the circle. 
Examples:

Input: R = 12, X = 3, Y = 3, N = 5 
Output: (7.05, -3.36) (5.21, -7.49) (7.53, 0.19) (-2.37, 12.05) (1.45, 11.80)
Input: R = 5, X = 1, Y = 1, N = 3 
Output: (4.75, 1.03) (2.57, 5.21) (-1.98, -0.76)

Approach: To find a random point in or on a circle we need two components, an angle(theta) and distance(D) from the center. After that Now, the point (xi, yi) can be expressed as:

xi = X + D * cos(theta)
yi = Y + D * sin(theta)

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
#define PI 3.141592653589
 
// Return a random double between 0 & 1
double uniform()
{
    return (double)rand() / RAND_MAX;
}
 
// Function to find the N random points on
// the given circle
vector<pair<double, double> > randPoint(
    int r, int x, int y, int n)
{
    // Result vector
    vector<pair<double, double> > res;
 
    for (int i = 0; i < n; i++) {
 
        // Get Angle in radians
        double theta = 2 * PI * uniform();
 
        // Get length from center
        double len = sqrt(uniform()) * r;
 
        // Add point to results.
        res.push_back({ x + len * cos(theta),
                        y + len * sin(theta) });
    }
 
    // Return the N points
    return res;
}
 
// Function to display the content of
// the vector A
void printVector(
    vector<pair<double, double> > A)
{
 
    // Iterate over A
    for (pair<double, double> P : A) {
 
        // Print the N random points stored
        printf("(%.2lf, %.2lf)\n",
               P.first, P.second);
    }
}
 
// Driver Code
int main()
{
    // Given dimensions
    int R = 12;
    int X = 3;
    int Y = 3;
    int N = 5;
 
    // Function Call
    printVector(randPoint(R, X, Y, N));
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
     
static final double PI = 3.141592653589;
static class pair
{
    double first, second;
 
    public pair(double first,
                double second)
    {
        super();
        this.first = first;
        this.second = second;
    }
}
 
// Return a random double between 0 & 1
static double uniform(){return Math.random();}
 
// Function to find the N random points on
// the given circle
static Vector<pair> randPoint(int r, int x,
                              int y, int n)
{
     
    // Result vector
    Vector<pair> res = new Vector<pair>();
 
    for(int i = 0; i < n; i++)
    {
         
        // Get Angle in radians
        double theta = 2 * PI * uniform();
 
        // Get length from center
        double len = Math.sqrt(uniform()) * r;
 
        // Add point to results.
        res.add(new pair(x + len * Math.cos(theta),
                         y + len * Math.sin(theta)));
    }
     
    // Return the N points
    return res;
}
 
// Function to display the content of
// the vector A
static void printVector(Vector<pair> A)
{
 
    // Iterate over A
    for(pair P : A)
    {
         
        // Print the N random points stored
        System.out.printf("(%.2f, %.2f)\n",
                          P.first, P.second);
    }
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given dimensions
    int R = 12;
    int X = 3;
    int Y = 3;
    int N = 5;
 
    // Function call
    printVector(randPoint(R, X, Y, N));
}
}
 
// This code is contributed by Rajput-Ji

Python3




# Python program for the above approach
import math
import random
PI = 3.141592653589;
 
class pair:
 
    def __init__(self, first, second):
        self.first = first;
        self.second = second;
 
# Return a random between 0 & 1
def uniform():
    return random.random();
 
# Function to find the N random points on
# the given circle
def randPoint(r, x, y, n):
   
    # Result vector
    res = list();
 
    for i in range(n):
        # Get Angle in radians
        theta = 2 * PI * uniform();
 
        # Get length from center
        len = math.sqrt(uniform()) * r;
 
        # Add point to results.
        res.append(pair((x + len * math.cos(theta)), (y + len * math.sin(theta))));
 
    # Return the N points
    return res;
 
# Function to display the content of
# the vector A
def printVector(A):
 
    # Iterate over A
    for P in A:
        # Print the N random points stored
        print("({0:.2f}".format(P.first),", ","{0:.2f})".format(P.second));
 
# Driver Code
if __name__ == '__main__':
    # Given dimensions
    R = 12;
    X = 3;
    Y = 3;
    N = 5;
 
    # Function call
    printVector(randPoint(R, X, Y, N));
 
# This code is contributed by 29AjayKumar

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG
{
     
static readonly double PI = 3.141592653589;
class pair
{
    public double first, second;
 
    public pair(double first,
                double second)
    {
        this.first = first;
        this.second = second;
    }
}
 
// Return a random double between 0 & 1
static double uniform()
{
    return new Random().NextDouble();
}
 
// Function to find the N random points on
// the given circle
static List<pair> randPoint(int r, int x,
                              int y, int n)
{
     
    // Result vector
    List<pair> res = new List<pair>();
    for(int i = 0; i < n; i++)
    {
         
        // Get Angle in radians
        double theta = 2 * PI * uniform();
 
        // Get length from center
        double len = Math.Sqrt(uniform()) * r;
 
        // Add point to results.
        res.Add(new pair(x + len * Math.Cos(theta),
                         y + len * Math.Sin(theta)));
    }
     
    // Return the N points
    return res;
}
 
// Function to display the content of
// the vector A
static void printList(List<pair> A)
{
 
    // Iterate over A
    foreach(pair P in A)
    {
         
        // Print the N random points stored
        Console.Write("({0:F2}, {1:F2})\n",
                          P.first, P.second);
    }
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given dimensions
    int R = 12;
    int X = 3;
    int Y = 3;
    int N = 5;
 
    // Function call
    printList(randPoint(R, X, Y, N));
}
}
 
// This code is contributed by 29AjayKumar

Javascript




// JavaScript program for the above approach
 
// Return a random double between 0 & 1
function uniform()
{
    return Math.random();
}
 
// Function to find the N random points on
// the given circle
function randPoint(r, x, y, n)
{
    // Result vector
    let res = new Array();
 
    for (let i = 0; i < n; i++) {
 
        // Get Angle in radians
        let theta = 2 * Math.PI * uniform();
 
        // Get length from center
        let len = Math.sqrt(uniform()) * r;
 
        // Add point to results.
        res.push([x + len * Math.cos(theta), y + len * Math.sin(theta)]);
    }
 
    // Return the N points
    return res;
}
 
// Function to display the content of
// the vector A
function printVector(A)
{
    // Iterate over A
    for (let i = 0; i < A.length; i++) {      
        // Print the N random points stored
        console.log("(" + A[i][0].toFixed(2) + ", " + A[i][1].toFixed(2) + ")");
    }
}
 
// Driver Code
// Given dimensions
let R = 12;
let X = 3;
let Y = 3;
let N = 5;
 
// Function Call
printVector(randPoint(R, X, Y, N));
 
// The code is contributed by gautam goel (gautamgoel962)

Output: 

(7.05, -3.36)
(5.21, -7.49)
(7.53, 0.19)
(-2.37, 12.05)
(1.45, 11.80)

Time Complexity: O(N) 
Space Complexity: O(N)
 


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