Random Gaussian Number Generator

From Second Life Wiki
Jump to: navigation, search

Port of the Random Gaussian algorithm found on http://www.taygeta.com/random/gaussian.html.

float randGauss(float mean, float stdev){
    float x, y, r2;
    do{//Generate a point in a unit circle that is not zero.
        x = llFrand(2.) - 1;
        y = llFrand(2.) - 1;
        r2 = x * x + y * y;
    } while (r2 > 1.0 || r2 == 0);
 
    //Box-Muller transformation
    return mean + x * stdev * llSqrt( -2 * llLog(r2) / r2);
}
vector randGaussPair(vector center, float stdev){//2D
    //returns a random point on the x/y plain with a specified standard deviation from center.
    float r2;
    vector p;
    do{//Generate a point in a unit circle that is not zero.
        p = <llFrand(2.) - 1, llFrand(2.) - 1, 0>;
        r2 = p * p;//dot product
    } while (r2 > 1.0 || r2 == 0);
 
    //Box-Muller transformation
    return center + (p * (stdev * llSqrt( -2 * llLog(r2) / r2)));
}

Box-Muller Transformation

The Box-Muller transformation is used to adjust the magnitude of the vector, remapping it to a standard deviation.

3D

Is this correct? Or does Box-Muller need to be adjusted?

vector randGaussPoint(vector center, float stdev){//3D
    //returns a random point with a specified standard deviation from center?
    float r2;
    vector p;
    do{//Generate a point in a unit sphere that is not zero.
        p = <llFrand(2.) - 1, llFrand(2.) - 1, llFrand(2.) - 1>;
        r2 = p * p;//dot product
    } while (r2 > 1.0 || r2 == 0);
 
    //Box-Muller transformation
    return center + (p * (stdev * llSqrt( -2 * llLog(r2) / r2)));
}