Vercidium

Vector3 GetPoint()
{
    Vector3 v = Vector3.Zero;
    
    // Generate a point
    ...

    // Calculate the global angle of the point around the axis
    var a = Math.Atan2(v.X, v.Z);

Vercidium

var v = GetPoint();

// Add some variance to each star
v += NextV3(-0.5, 0.5);

// Shift stars vertically as they get closer to the center of the galaxy
var s = beamHeight / v.Magnitude;
v.Y = Next(-s, s);

Vercidium

Vector3 GetPoint()
{
    Vector3 v;
    double armDivisor = Math.PI / armCount;

    while (true)
    {
        // Generate a random normalised point with a weighting
        // towards the center controlled by the gravity variable
        v = NextV3(-1, 1).Normalized() * Math.Pow(Next(0, 1.0), gravity);