C# graphics flickering

First don't use CreateGraphics() unless you absolutely have to. Bind an event handler to OnPaint and call Invalidate() when you want to refresh the surface.

If you don't want it to flicker you'll need to double buffer your drawing surface. The easiest way to do this is to set your form's DoubleBuffered property to True.

I would highly recommend if you plan on extending this to do your drawing to the PictureBox control. PictureBox is double-buffered by default and allows you to control your drawing region much more simply.

In code:

public partial class Form1 : Form
    {
    int xFirst, yFirst;
    Bitmap bm = new Bitmap(1000, 1000);
    Graphics bmG;
    Pen pen = new Pen(Color.Black, 1);
    bool draw = false;

    public Form1()
    {
        InitializeComponent();
    }

    private void Form1_Load(object sender, EventArgs e)
    {
        bmG = Graphics.FromImage(bm);
        bmG.Clear(Color.White);
    }

    private void Form1_MouseDown(object sender, MouseEventArgs e)
    {
        xFirst = e.X;
        yFirst = e.Y;
        draw = true;
    }

    private void Form1_MouseUp(object sender, MouseEventArgs e)
    {
        bmG.DrawLine(pen, xFirst, yFirst, e.X, e.Y);
        draw = false;
        Invalidate();
    }

    private void Form1_MouseMove(object sender, MouseEventArgs e)
    {
        if (draw)
        {
            Invalidate();
        }
    }

    private void Form1_Paint(object sender, PaintEventArgs e)
    {
        if (draw) {
            e.Graphics.DrawImage(bm, 0, 0);
            e.Graphics.DrawLine(pen, xFirst, yFirst, e.X, e.Y);
        } else {
            e.Graphics.DrawImage(bm, 0, 0);
        }
    }
}

Edit:

Another issue, you are creating a private Pen member. Pens (and Brushes, as well as many GDI+ objects) represent handles to unmanaged objects that need to be disposed otherwise your program will leak. Either wrap them in using statements (the preferred and exception-safe way) or explicitly dispose of them in the form's Dispose method.

Alternatively in System.Drawing you can access some pre-built Pens and Brushes that don't need to be (and shouldn't be) disposed. Use them like:

    private void Form1_Paint(object sender, PaintEventArgs e)
    {
        if (draw) {
            e.Graphics.DrawImage(bm, 0, 0);
            e.Graphics.DrawLine(Pens.Black, xFirst, yFirst, e.X, e.Y);
        } else {
            e.Graphics.DrawImage(bm, 0, 0);
        }
    }

The reason it is flickering is that you are drawing the background (which is immediately displayed on screen, wiping away the line) and then superimpose the line. Thus the line keeps disappearing and appearing, giving a flickering display.

The best solution to this is called Double Buffering. What you do is draw the whole image to an "offscreen" bitmap, and only show it on the screen when it is completed. Because you only ever display the completed image, there is no flickering effect. You should just be able to set this.DoubleBuffered = true to get WinForms to do all the hard work for you.

NB: You shouldn't really be drawing outside of your paint handler - ideally, you should Invalidate() the area that needs redrawing, and then your paint handler will redraw just that area (with any overlaid lines etc as needed).

Fixed and working code.

public partial class Form1 : Form
{
    int x1, y1, x2, y2;
    bool drag = false;

    Bitmap bm = new Bitmap(1000, 1000);
    Graphics bmg;


    public Form1()
    {
        InitializeComponent();
    }

    private void Form1_Load(object sender, EventArgs e)
    {
        bmg = Graphics.FromImage(bm);
    }

    private void pictureBox_MouseDown(object sender, MouseEventArgs e)
    {
        drag = true;
        x1 = e.X;
        y1 = e.Y;
    }

    private void pictureBox_MouseUp(object sender, MouseEventArgs e)
    {
        drag = false;

        bmg.DrawLine(Pens.Black, x1, y1, e.X, e.Y);
        pictureBox.Invalidate();
    }

    private void pictureBox_MouseMove(object sender, MouseEventArgs e)
    {
        if (drag)
        {
            x2 = e.X;
            y2 = e.Y;
            pictureBox.Invalidate();
        }
    }

    private void pictureBox_Paint(object sender, PaintEventArgs e)
    {
        if (drag) {
            e.Graphics.DrawImage(bm, 0, 0);
            e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);            
        }
        else {
            e.Graphics.DrawImage(bm, 0, 0);
        }
    }
}