Generating RGB Color Map – Photoshop

I’m not sure exactly what it’s called, but I’m trying to generate an RGB color map like what you see when creating a custom color in MS Paint (or Photoshop or any other countless applications).

The code I currently found and am using:

private final static int COLORS_WIDTH = 256;
private final static int COLORS_HEIGHT = 256;

_colorPixmap = new Pixmap(256, 256, Format.RGB888);

for (int x = 0; x < COLORS_WIDTH; ++x)
{
    for (int y = 0; y < COLORS_HEIGHT; ++y)
    {
        float h = x / (float) COLORS_WIDTH;
        float s = (COLORS_HEIGHT - y) / (float) COLORS_HEIGHT;
        float l = 0.5f;
        Color color = HSLtoRGB(h, s, l);

        _colorPixmap.setColor(color);
        _colorPixmap.drawPixel(x, y);
    }
}

Generates this:

http://i.imgur.com/9sHrfJR.png

Which is great, however, I absolutely require to have black/white as selectable colors too, but this RGB map doesn’t have it.

I’m not good with color stuff (hue, saturation, brightness) and can’t seem to tweak the code to get what I’m looking for.

Any help / suggestions or do I need a different approach?

Thanks!