The StarPoints function generates the points needed to draw a star and returns them in an array.

// Return PointFs to define a star.
private PointF[] StarPoints(int num_points, Rectangle bounds)
{
    // Make room for the points.
    PointF[] pts = new PointF[num_points];

    double rx = bounds.Width / 2;
    double ry = bounds.Height / 2;
    double cx = bounds.X + rx;
    double cy = bounds.Y + ry;

    // Start at the top.
    double theta = -Math.PI / 2;
    double dtheta = 4 * Math.PI / num_points;
    for (int i = 0; i < num_points; i++)
    {
        pts[i] = new PointF(
            (float)(cx + rx * Math.Cos(theta)),
            (float)(cy + ry * Math.Sin(theta)));
        theta += dtheta;
    }

    return pts;
}

The function allocates room for the points and then uses a loop to generate them. The variable theta determines the direction of each point from the center of the star. If the code were drawing a regular polygon with num_points sides, then the difference between adjacent theta values would be 2 * Pi / num_points. In this function, dtheta is twice that so the lines drawing the star skip polygon points much as you probably do when you draw a five-pointed star.

(Note that this only works for stars with an odd number of points.)

The program uses this function as shown in the following code.

// Draw a star.
private void Form1_Paint(object sender, PaintEventArgs e)
{
    e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;

    PointF[] pts = StarPoints(5, this.ClientRectangle);
    e.Graphics.DrawPolygon(Pens.Blue, pts);
}