B样条（B-Spline）是常用的曲线拟合与插值算法之一。

这里给出在 Form 的 图像 Picturebox 组件上，按鼠标点击点绘制 （三次）B样条曲线的代码。

2022-12-05 修改了代码。

1 文本格式

using System;
using System.Data;
using System.Linq;
using System.Text;
using System.Drawing;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace Legalsoft.Truffer.Algorithm;
{
    public partial class Form1 : Form
    {
        public double[] splinex = new double[1001];
        public double[] spliney = new double[1001];
        public point[] pt = new point[6];
        public int no_of_points = 0;

        /// <summary>
        /// Prints a dot at the place whrere the mouseup event occurs
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void pictureBox1_MouseUp(object sender, MouseEventArgs e)
        {
            Graphics g = pictureBox1.CreateGraphics();
            Color cl = Color.DarkBlue;
            g.DrawLine(new Pen(cl, 2), e.X-3, e.Y, e.X + 3, e.Y);
            g.DrawLine(new Pen(cl, 2), e.X, e.Y-3, e.X, e.Y + 3);
            g.DrawString(no_of_points+"", new Font("宋体",12), new SolidBrush(Color.Red), e.X, e.Y);

        }

        /// <summary>
        /// At each mousedown event the the no of points is calculated
        /// if the value is more than 3 then the curve is drawn
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void pictureBox1_MouseDown(object sender, MouseEventArgs e)
        {
           if (no_of_points > 3)
            {
                pt[0] = pt[1];
                pt[1] = pt[2];
                pt[2] = pt[3];
                pt[3].X = e.X;
                pt[3].Y = e.Y;

                double temp = Math.Sqrt(Math.Pow(pt[2].X - pt[1].X, 2F) + Math.Pow(pt[2].Y - pt[1].Y, 2F));
                int interpol = System.Convert.ToInt32(temp);
                bspline(pt[0], pt[1], pt[2], pt[3], interpol);

                int width = 2;
                Graphics g = pictureBox1.CreateGraphics();
                Color cl = Color.Blue;
                int x, y;
                for (int i = 0; i <= interpol - 1; i++)
                {
                    x = System.Convert.ToInt32(splinex[i]);
                    y = System.Convert.ToInt32(spliney[i]);
                    g.DrawLine(new Pen(cl, width), x - 1, y, x + 1, y);
                    g.DrawLine(new Pen(cl, width), x, y - 1, x, y + 1);
                }
            }
            else
            {
                pt[no_of_points].X = e.X;
                pt[no_of_points].Y = e.Y;
            }
            no_of_points++;
        }

        /// <summary>
        /// calculating the values using the algorithm 
        /// </summary>
        /// <param name="p1"></param>
        /// <param name="p2"></param>
        /// <param name="p3"></param>
        /// <param name="p4"></param>
        /// <param name="divisions"></param>
        public void bspline(point p1, point p2, point p3, point p4, int divisions)
        {
            double[] a = new double[5];
            double[] b = new double[5];
            a[0] = (-p1.X + 3 * p2.X - 3 * p3.X + p4.X) / 6.0;
            a[1] = (3 * p1.X - 6 * p2.X + 3 * p3.X) / 6.0;
            a[2] = (-3 * p1.X + 3 * p3.X) / 6.0;
            a[3] = (p1.X + 4 * p2.X + p3.X) / 6.0;
            b[0] = (-p1.Y + 3 * p2.Y - 3 * p3.Y + p4.Y) / 6.0;
            b[1] = (3 * p1.Y - 6 * p2.Y + 3 * p3.Y) / 6.0;
            b[2] = (-3 * p1.Y + 3 * p3.Y) / 6.0;
            b[3] = (p1.Y + 4 * p2.Y + p3.Y) / 6.0;

            splinex[0] = a[3];
            spliney[0] = b[3];

            for (int i = 1; i <= divisions - 1; i++)
            {
                double t = System.Convert.ToSingle(i) / System.Convert.ToSingle(divisions);
                splinex[i] = (a[2] + t * (a[1] + t * a[0])) * t + a[3];
                spliney[i] = (b[2] + t * (b[1] + t * b[0])) * t + b[3];
            }
        }
    }
}
 

2 代码格式

using System;
using System.Data;
using System.Linq;
using System.Text;
using System.Drawing;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace Legalsoft.Truffer.Algorithm;
{
    public partial class Form1 : Form
    {
        public double[] splinex = new double[1001];
        public double[] spliney = new double[1001];
        public point[] pt = new point[6];
        public int no_of_points = 0;

        /// <summary>
        /// Prints a dot at the place whrere the mouseup event occurs
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void pictureBox1_MouseUp(object sender, MouseEventArgs e)
        {
            Graphics g = pictureBox1.CreateGraphics();
            Color cl = Color.DarkBlue;
            g.DrawLine(new Pen(cl, 2), e.X-3, e.Y, e.X + 3, e.Y);
            g.DrawLine(new Pen(cl, 2), e.X, e.Y-3, e.X, e.Y + 3);
            g.DrawString(no_of_points+"", new Font("宋体",12), new SolidBrush(Color.Red), e.X, e.Y);

        }

        /// <summary>
        /// At each mousedown event the the no of points is calculated
        /// if the value is more than 3 then the curve is drawn
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void pictureBox1_MouseDown(object sender, MouseEventArgs e)
        {
           if (no_of_points > 3)
            {
                pt[0] = pt[1];
                pt[1] = pt[2];
                pt[2] = pt[3];
                pt[3].X = e.X;
                pt[3].Y = e.Y;

                double temp = Math.Sqrt(Math.Pow(pt[2].X - pt[1].X, 2F) + Math.Pow(pt[2].Y - pt[1].Y, 2F));
                int interpol = System.Convert.ToInt32(temp);
                bspline(pt[0], pt[1], pt[2], pt[3], interpol);

                int width = 2;
                Graphics g = pictureBox1.CreateGraphics();
                Color cl = Color.Blue;
                int x, y;
                for (int i = 0; i <= interpol - 1; i++)
                {
                    x = System.Convert.ToInt32(splinex[i]);
                    y = System.Convert.ToInt32(spliney[i]);
                    g.DrawLine(new Pen(cl, width), x - 1, y, x + 1, y);
                    g.DrawLine(new Pen(cl, width), x, y - 1, x, y + 1);
                }
            }
            else
            {
                pt[no_of_points].X = e.X;
                pt[no_of_points].Y = e.Y;
            }
            no_of_points++;
        }

        /// <summary>
        /// calculating the values using the algorithm 
        /// </summary>
        /// <param name="p1"></param>
        /// <param name="p2"></param>
        /// <param name="p3"></param>
        /// <param name="p4"></param>
        /// <param name="divisions"></param>
        public void bspline(point p1, point p2, point p3, point p4, int divisions)
        {
            double[] a = new double[5];
            double[] b = new double[5];
            a[0] = (-p1.X + 3 * p2.X - 3 * p3.X + p4.X) / 6.0;
            a[1] = (3 * p1.X - 6 * p2.X + 3 * p3.X) / 6.0;
            a[2] = (-3 * p1.X + 3 * p3.X) / 6.0;
            a[3] = (p1.X + 4 * p2.X + p3.X) / 6.0;
            b[0] = (-p1.Y + 3 * p2.Y - 3 * p3.Y + p4.Y) / 6.0;
            b[1] = (3 * p1.Y - 6 * p2.Y + 3 * p3.Y) / 6.0;
            b[2] = (-3 * p1.Y + 3 * p3.Y) / 6.0;
            b[3] = (p1.Y + 4 * p2.Y + p3.Y) / 6.0;

            splinex[0] = a[3];
            spliney[0] = b[3];

            for (int i = 1; i <= divisions - 1; i++)
            {
                double t = System.Convert.ToSingle(i) / System.Convert.ToSingle(divisions);
                splinex[i] = (a[2] + t * (a[1] + t * a[0])) * t + a[3];
                spliney[i] = (b[2] + t * (b[1] + t * b[0])) * t + b[3];
            }
        }
    }
}