Generate Random Point in a Circle in C++

Suppose we have the radius and x-y positions of the center of a circle, we have to write a function called randPoint() which generates a uniform random point in the circle. So there will be some important points that we have to keep in mind −

• Input and output values are in floating-point.
• Radius and x-y position of the center of the circle is passed into the class constructor.
• A point on the circumference of the circle is considered to be in the circle.
• The randPoint() returns x-position and y-position of the random point, in that order.

So if the input is like [10, 5,-7.5], then it may generate some random points like [11.15792,-8.54781],[2.49851,-16.27854],[11.16325,-12.45479].

To solve this, we will follow these steps −

• Define a method called uniform(). This will work as follows −
• return random_number/MAX RANDOM
• Through the initializer initialize the rad, and center coordinate
• The randPoint will work as follows −
• theta = 2*Pi*uniform()
• r := square root of uniform()
• return a pair like (center_x + r*radius*cos(theta), center_y + r*radius*sin(theta))

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<auto> v){
   cout << "[";
   for(int i = 0; i<v.size(); i++){
      cout << v[i] << ", ";
   }
   cout << "]"<<endl;
}
class Solution {
   public:
   const double PI = 3.14159265358979732384626433832795;
   double m_radius, m_x_center, m_y_center;
   double uniform() {
      return (double)rand() / RAND_MAX;
   }
   Solution(double radius, double x_center, double y_center) {
      srand(time(NULL));
      m_radius = radius; m_x_center = x_center; m_y_center = y_center;
   }
   vector<double> randPoint() {
      double theta = 2 * 3.14159265358979323846264 * uniform();
      double r = sqrt(uniform());
      return vector<double>{
         m_x_center + r * m_radius * cos(theta),
         m_y_center + r * m_radius * sin(theta)
      };
   }
};
main(){
   Solution ob(10, 5, 7);
   print_vector(ob.randPoint());
   print_vector(ob.randPoint());
   print_vector(ob.randPoint());
}

Input

Pass 10, 5, 7 into constructor
Call randPoint() three times

Output

[1.5441, 9.14912, ]
[-1.00029, 13.9072, ]
[10.2384, 6.49618, ]