三阶贝塞尔曲线 C# 代码

以下是一个简单的三阶贝塞尔曲线的 C# 代码示例：

using System;
using System.Drawing;
using System.Windows.Forms;

public class BezierCurveForm : Form
{
    private Point[] controlPoints;

    public BezierCurveForm()
    {
        controlPoints = new Point[4];
        controlPoints[0] = new Point(50, 100);
        controlPoints[1] = new Point(150, 50);
        controlPoints[2] = new Point(250, 150);
        controlPoints[3] = new Point(350, 100);

        this.ClientSize = new Size(400, 200);
        this.Paint += new PaintEventHandler(BezierCurveForm_Paint);
    }

    private void BezierCurveForm_Paint(object sender, PaintEventArgs e)
    {
        Graphics g = e.Graphics;
        Pen pen = new Pen(Color.Black, 2);

        // 绘制控制点
        for (int i = 0; i < controlPoints.Length; i++)
        {
            g.FillEllipse(Brushes.Red, controlPoints[i].X - 3, controlPoints[i].Y - 3, 6, 6);
        }

        // 绘制贝塞尔曲线
        for (double t = 0; t <= 1; t += 0.01)
        {
            Point p = CalculateBezierPoint(t, controlPoints);
            g.FillEllipse(Brushes.Blue, p.X - 1, p.Y - 1, 2, 2);
        }

        // 绘制控制线
        g.DrawLine(pen, controlPoints[0], controlPoints[1]);
        g.DrawLine(pen, controlPoints[1], controlPoints[2]);
        g.DrawLine(pen, controlPoints[2], controlPoints[3]);
    }

    private Point CalculateBezierPoint(double t, Point[] controlPoints)
    {
        double u = 1 - t;
        double tt = t * t;
        double uu = u * u;
        double uuu = uu * u;
        double ttt = tt * t;

        double x = uuu * controlPoints[0].X; // (1-t)^3 * P0
        x += 3 * uu * t * controlPoints[1].X; // 3 * (1-t)^2 * t * P1
        x += 3 * u * tt * controlPoints[2].X; // 3 * (1-t) * t^2 * P2
        x += ttt * controlPoints[3].X; // t^3 * P3

        double y = uuu * controlPoints[0].Y; // (1-t)^3 * P0
        y += 3 * uu * t * controlPoints[1].Y; // 3 * (1-t)^2 * t * P1
        y += 3 * u * tt * controlPoints[2].Y; // 3 * (1-t) * t^2 * P2
        y += ttt * controlPoints[3].Y; // t^3 * P3

        return new Point((int)Math.Round(x), (int)Math.Round(y));
    }

    public static void Main()
    {
        Application.Run(new BezierCurveForm());
    }
}

这段代码创建了一个简单的窗体应用程序，绘制了一个三阶贝塞尔曲线，并显示了控制点和控制线。你可以根据需要修改控制点的坐标，以获得不同形状的贝塞尔曲线。运行程序后，你会看到绘制的贝塞尔曲线在窗体中显示出来。