4. 判斷 2 線段是否有相交

using System.Xml.XPath;

namespace Q4
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Load(object sender, EventArgs e)
        {

        }

        int x0 = -1, x1, y0, y1;
        int x2 = -1, x3, y2, y3;

        private void panel1_Paint(object sender, PaintEventArgs e)
        {
            var ml = 20;
            var mt = 20;

            //e.Graphics.DrawLine(new Pen(Brushes.Black), ml, midY, panel1.Width - ml, midY);
            //e.Graphics.DrawLine(new Pen(Brushes.Black), midX, mt, midX, panel1.Height - mt);
            e.Graphics.TranslateTransform(10, 10);
            e.Graphics.ScaleTransform(8, 8);
            var pen = new Pen(Brushes.Black);
            pen.Width = .2f;
            e.Graphics.DrawLine(pen, ax(-40), ay(0), ax(40), ay(0));
            e.Graphics.DrawLine(pen, ax(0), ay(-30), ax(0), ay(30));

            for (int y = -3; y <= 3; y++)
            {
                e.Graphics.FillEllipse(Brushes.Black, ax(-.5f), ay(.5f + (y) * 10), 1f, 1f);
            }

            for (int x = -4; x <= 4; x++)
            {
                e.Graphics.FillEllipse(Brushes.Black, ax(-.5f + x * 10), ay(.5f), 1f, 1f);
            }
            e.Graphics.DrawString("(-40,0)", new Font(FontFamily.GenericSansSerif, 1f), Brushes.Black, ax(-.5f + -40), ay(1f));
            e.Graphics.DrawString("(40,0)", new Font(FontFamily.GenericSansSerif, 1f), Brushes.Black, ax(-.5f + 40), ay(1f));
            e.Graphics.DrawString("(0,30)", new Font(FontFamily.GenericSansSerif, 1f), Brushes.Black, ax(1f), ay(-30f + .5f));
            e.Graphics.DrawString("(0,-30)", new Font(FontFamily.GenericSansSerif, 1f), Brushes.Black, ax(1f), ay(29f + .5f));

            if (x0 == -1) return;
            MessageBox.Show(x0 + " " + x1 + " / " + y0 + " / " + y1);
            e.Graphics.DrawLine(pen, ax(x0), ay(y0), ax(x1), ay(y1));
            e.Graphics.DrawLine(pen, ax(x2), ay(y2), ax(x3), ay(y3));

            // ax+by=c
            // dx+ey=f
            //N: (ce-bf)/(ae-bd)
            //O: (cd-af)/(bd-ae)

            // ax+by=c
            // (y-y0)*(x1-x0) = (x-x0)*(y1-y0)
            // -(y1-y0)*x + (x1-x0)*y = -(y1-y0)*x0+(x1-x0)*y0
            
            double a = -(y1 - y0);
            double b = x1 - x0;
            double c = -(y1 - y0) * x0 + (x1 - x0) * y0;

            double d = -(y3 - y2);
            double ee = x3 - x2;
            double f = -(y3 - y2) * x2 + (x3 - x2) * y2;

            double N = (c * ee - b * f) / (a * ee - b * d);
            double O = (c * d - a * f) / (b * d - a * ee);

            textBox6.Text = "";
            bool inst =  (O >= y0 && O <= y1|| O >= y2 && O <= y3) ||
                 (N >= x2 && N <= x3 || N >= x0 && N <= x1);
            textBox5.Text = inst ? "有相交" : "未相交";
            //if (inst)
                textBox6.Text = $"{N:0.##},{O:0.##}";
        }
        float ax(float x)
        {
            return x + 40;
        }

        float ay(float y)
        {
            return -y + 30;
        }

        private void button2_Click(object sender, EventArgs e)
        {
            x0 = -1;
            panel1.Refresh();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            var l10 = textBox1.Text.Split(",").Select(int.Parse).ToList();
            var l11 = textBox2.Text.Split(",").Select(int.Parse).ToList();
            var l20 = textBox3.Text.Split(",").Select(int.Parse).ToList();
            var l21 = textBox4.Text.Split(",").Select(int.Parse).ToList();
            x0 = l10[0];
            y0 = l10[1];
            x1 = l11[0];
            y1 = l11[1];

            x2 = l20[0];
            y2 = l20[1];
            x3 = l21[0];
            y3 = l21[1];
            panel1.Refresh();
        }

        private void textBox6_TextChanged(object sender, EventArgs e)
        {

        }
    }
}