c++ random point in circle - where did I go wrong?

Question

class Solution {
private:
double c_radius;
double xcenter;
double ycenter;

public:
    Solution(double radius, double x_center, double y_center) {
    c_radius = radius;
    xcenter = x_center;
    ycenter = y_center;  
}

vector<double> randPoint() {
    double randomradius= (sqrt((double)rand()) / RAND_MAX) * c_radius;
    double randomangle= ((double)rand() / RAND_MAX) * 360.0;
    double yp= sin(randomangle)*randomradius;
    double xp= cos(randomangle)*randomradius;
    std::vector<double> point= {xp+xcenter, yp+ycenter};
    return point; 
}
};

Hi everyone, I was doing a Leet Code question about finding a random point within a circle. It all goes well until following test: Inputs: [[0.01,-73839.1,-3289891.3]

It is essentially generating a random point within a circle however my result seems to be rounded off and I am not sure why.

My Output after generating point:

[null,[-73839.10**000**,-3289891.30**000**],[-73839.10**000**,-3289891.30000],[-73839.10000,-3289891.30000],[-73839.10000,-3289891.30000],[-73839.10000,-3289891.30000]...

Expected Output

[null,[-73839.10**006**,-3289891.30**228**],[-73839.10**541**,-3289891.30660],[-73839.10634,-3289891.30124],[-73839.10256,-3289891.30684],[-73839.09825,-3289891.29962]...

Now my question is where is the error? Is there a fault in my math? The results are close but not close enough. I cannot seem to pinpoint where this error occurs. Any help is greatly appreciated.

Answer 1

With your current approach you will not get uniform distribution (even when radians are fixed). Points will be focused in a center.

Task description says points distribution suppose to be uniform, but I have doubts if proper statistical test for it is written.

Instead making this complicated, just randomly pick coordinates in square containing a circle and keep generating this point until it fits inside a circle.

class Solution {
    std::mt19937 gen;
    std::uniform_real_distribution<> dis;
    double xc;
    double yc;
    double r2;

public:
    Solution(double radius, double x_center, double y_center) 
        : dis{-radius, radius}
        , xc{x_center}
        , yc{y_center}
        , r2{radius * radius}
    {
    }
    
    std::vector<double> randPoint() {
        double dx, dy;
        do {
            dx = dis(gen);
            dy = dis(gen);
        } while (dx*dx + dy*dy > r2);
        return {xc + dx, yc + dy};
    }
};