private float skala = 40;
private PointF kozepVilag = new PointF(0, 0);
private List<PointF> pontok = new List<PointF>();
private float szog = 0;
private float lukt = 0;
private bool beallit = false;

private void Form1_Load(object sender, EventArgs e)
{
    cmbFuggveny.Items.AddRange(new object[] { "sin(x)", "x²", "1/x", "sin(x)/x", "√x" });
    cmbFuggveny.SelectedIndex = 0;
    tbNagyit.Minimum = 10;
    tbNagyit.Maximum = 120;
    tbNagyit.Value = 40;
    tmrForgat.Interval = 20;
    tmrForgat.Start();
}

private PointF Kepernyore(double x, double y)
{
    return new PointF(rpAbra.Width / 2f + (float)((x - kozepVilag.X) * skala), rpAbra.Height / 2f - (float)((y - kozepVilag.Y) * skala));
}

private PointF Vilagba(Point p)
{
    return new PointF((p.X - rpAbra.Width / 2f) / skala + kozepVilag.X, -(p.Y - rpAbra.Height / 2f) / skala + kozepVilag.Y);
}

private double F(double x)
{
    switch (cmbFuggveny.SelectedIndex)
    {
        case 1: return x * x;
        case 2: return 1 / x;
        case 3: return x == 0 ? 1 : Math.Sin(x) / x;
        case 4: return Math.Sqrt(x);
        default: return Math.Sin(x);
    }
}

private void rpAbra_Paint(object sender, PaintEventArgs e)
{
    Graphics g = e.Graphics;
    g.Clear(Color.White);
    g.SmoothingMode = SmoothingMode.AntiAlias;

    if (rpAbra.Width < 10 || rpAbra.Height < 10) { return; }

    // rács egységenként
    float bal = Vilagba(new Point(0, 0)).X, jobb = Vilagba(new Point(rpAbra.Width, 0)).X;
    float also = Vilagba(new Point(0, rpAbra.Height)).Y, felso = Vilagba(new Point(0, 0)).Y;

    using (Pen racs = new Pen(Color.Gainsboro))
    {
        for (int x = (int)Math.Floor(bal); x <= jobb; x++) { PointF a = Kepernyore(x, 0); g.DrawLine(racs, a.X, 0, a.X, rpAbra.Height); }
        for (int y = (int)Math.Floor(also); y <= felso; y++) { PointF a = Kepernyore(0, y); g.DrawLine(racs, 0, a.Y, rpAbra.Width, a.Y); }
    }

    PointF origo = Kepernyore(0, 0);
    g.DrawLine(Pens.Black, 0, origo.Y, rpAbra.Width, origo.Y);
    g.DrawLine(Pens.Black, origo.X, 0, origo.X, rpAbra.Height);

    // a függvény: megszakítható töröttvonal
    List<PointF> szakasz = new List<PointF>();

    using (Pen toll = new Pen(Color.SteelBlue, 2))
    {
        for (int px = 0; px <= rpAbra.Width; px += 2)
        {
            double x = Vilagba(new Point(px, 0)).X;
            double y = F(x);

            bool ok = !double.IsNaN(y) && !double.IsInfinity(y);
            PointF k = ok ? Kepernyore(x, y) : PointF.Empty;

            if (ok && Math.Abs(k.Y) < 10000)
            {
                szakasz.Add(k);
            }
            else
            {
                if (szakasz.Count > 1) { g.DrawLines(toll, szakasz.ToArray()); }

                szakasz.Clear();
            }
        }

        if (szakasz.Count > 1) { g.DrawLines(toll, szakasz.ToArray()); }
    }

    // a kattintott pontok (világ-koordinátában tárolva)
    foreach (PointF v in pontok)
    {
        PointF k = Kepernyore(v.X, v.Y);

        g.FillEllipse(Brushes.Crimson, k.X - 4, k.Y - 4, 8, 8);
        g.DrawString("(" + v.X.ToString("0.00") + "; " + v.Y.ToString("0.00") + ")", this.Font, Brushes.Black, k.X + 6, k.Y - 18);
    }
}

private void rpAbra_MouseMove(object sender, MouseEventArgs e)
{
    PointF v = Vilagba(e.Location);

    tsslEger.Text = "Kliens: " + e.X + ", " + e.Y;
    tsslVilag.Text = "Világ: " + v.X.ToString("0.00") + "; " + v.Y.ToString("0.00");
}

private void rpAbra_MouseClick(object sender, MouseEventArgs e)
{
    pontok.Add(Vilagba(e.Location));
    rpAbra.Invalidate();
}

private void Valtozas(object sender, EventArgs e)
{
    if (beallit) { return; }

    skala = tbNagyit.Value;
    kozepVilag = new PointF((float)nudKozepX.Value, (float)nudKozepY.Value);
    rpAbra.Invalidate();
}

private void btnAlap_Click(object sender, EventArgs e)
{
    beallit = true;
    tbNagyit.Value = 40;
    nudKozepX.Value = 0;
    nudKozepY.Value = 0;
    beallit = false;
    Valtozas(this, EventArgs.Empty);
}

private PointF[] Csillag(float kulso, float belso)
{
    PointF[] p = new PointF[10];

    for (int i = 0; i < 10; i++)
    {
        double radian = (-90 + i * 36) * Math.PI / 180;
        float r = i % 2 == 0 ? kulso : belso;
        p[i] = new PointF((float)(r * Math.Cos(radian)), (float)(r * Math.Sin(radian)));
    }

    return p;
}

private void rpCsillag_Paint(object sender, PaintEventArgs e)
{
    Graphics g = e.Graphics;
    g.Clear(Color.White);
    g.SmoothingMode = SmoothingMode.AntiAlias;

    GraphicsState alap = g.Save();

    g.TranslateTransform(rpCsillag.Width / 2f, rpCsillag.Height / 2f);
    g.RotateTransform(szog);

    if (chkNagyit.Checked)
    {
        float s = 1.15f + 0.15f * (float)Math.Sin(lukt);
        g.ScaleTransform(s, s);
    }

    PointF[] cs = Csillag(80, 35);

    using (Brush arany = new SolidBrush(Color.Gold))
    using (Pen keret = new Pen(Color.DarkGoldenrod, 2))
    {
        g.FillPolygon(arany, cs);
        g.DrawPolygon(keret, cs);
        g.FillEllipse(Brushes.White, -6, -6, 12, 12);
    }

    g.Restore(alap);   // a szöveg már forgatás nélkül
    g.DrawString("Szög: " + szog.ToString("0") + "°", this.Font, Brushes.Black, 8, 8);
}

private void tmrForgat_Tick(object sender, EventArgs e)
{
    szog = (szog + 2) % 360;
    lukt += 0.1f;
    rpCsillag.Invalidate();
}