c# - Calculate random points (pixel) within a circle (image)

I have an image that contains a circles at a specific location, and of a specific diameter. What I need to do is to be able to calculate random points within the circle, and then manipulate the pixels said points correlate to. I have the following code already:

private Point CalculatePoint()
{
    var angle = _random.NextDouble() * ( Math.PI * 2 );
    var x = _originX + ( _radius * Math.Cos( angle ) );
    var y = _originY + ( _radius * Math.Sin( angle ) );
    return new Point( ( int )x, ( int )y );
}

And that works fine for finding all the points at the circumference of the circle, but I need all points from anywhere in the circle. If this doesn't make sense let me know and I will do my best to clarify.

Answer

If you want a simple solution just randomize the radius too:

private Point CalculatePoint()
{
    var angle = _random.NextDouble() * Math.PI * 2;
    var radius = _random.NextDouble() * _radius;
    var x = _originX + radius * Math.Cos(angle);
    var y = _originY + radius * Math.Sin(angle);
    return new Point((int)x,(int)y);
}

That however results in your points being more concentrated towards the center of the circle:

In order to get an uniform distribution make the following change to the algorithm:

var radius = Math.Sqrt(_random.NextDouble()) * _radius;

Which will give the following result:

For more information check the following link: MathWorld - Disk Point Picking.

And finally here's a simple JsFiddle demonstration comparing both version of the algorithm.