c# - Visual Studio，在用户点击按钮时绘制 Lorenz 混沌

Question

所以去年我用 C 语言为我的类(class)编写了一个程序，该程序使用 Lorenz 方程和 Runge Kutta 方法求解微分方程来演示混沌。

我最近决定重新审视这个问题并制作一个能够绘制出粒子轨迹的程序。我让它成功工作，但现在想扩展它，以便用户可以输入参数，例如粒子的起始位置和其他参数(在我的例子中是 a、b 和 r)。目前我在程序运行后立即绘制轨迹，但我想延迟此操作，直到用户将他们的参数输入某些文本框然后按下按钮。为此，我想我应该创建一个新类并将我当前的代码放入其中，然后在 btn1_Click 方法下的主 .cs 文件中调用它。但是，我在这方面遇到了很大的麻烦，主要是因为我真的不知道该怎么做。到目前为止，在我的最佳尝试中，我对涉及“createGraphics()”的行有一个错误，即类文件中没有它的定义。我在类顶部的使用部分的顶部有所有相同的引用，就像在主文件中一样工作正常。

此外，如果有人可以给我任何关于我的代码的反馈(即任何不好的做法或我使事情过于复杂的地方)或任何让它变得更好的建议，我将非常感激，如果您需要更多信息由我来帮助，那么我会尽力回答!

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

namespace Lorenz_chaos
{
public partial class Form1 : Form
{
    public Form1()
    {
        InitializeComponent();
    }
        private void Form1_Paint(object sender, PaintEventArgs e)
    {
        double a = 10, b = (8 / 3), r = 28;     //standard values for lorenz model

        /*m defines the number of iterations of the for loop so the number of lines drawn
        good idea to keep m inversely proportional to dt (the time interval). A smaller dt will
        mean smaller lines so smoother overall drawing m=50000 and dt=0.0005 is a good starting point
        that demonstrates chaos well*/
        double m = 500000, dt = 0.00005;

        //EVOLUTION VALUE FOR RUNGE_KUTTA METHOD
        //values for first particle
        double y11, y12, y13;
        double y21, y22, y23;
        double y31, y32, y33;
        double y41, y42, y43;
        double y51, y52, y53;
        double xi, yi, xf, yf;           //coordinates for drawing particle 1 trajectory

        double f10, f11, f12, f13;      //function values to be calculated, 
        double f20, f21, f22, f23;      //for fxy (x>1) these are intermediate fn calculations at different
        double f30, f31, f32, f33;      //times in Runga Kutta

        //values for second particle
        double z11, z12, z13;
        double z21, z22, z23;
        double z31, z32, z33;
        double z41, z42, z43;
        double z51, z52, z53;
        double ai, bi, af, bf;          //coordinates for drawing particle 2 trajectory (these are badly named...)

        double g10, g11, g12, g13;      //equivalent of f values for particle 2 
        double g20, g21, g22, g23;
        double g30, g31, g32, g33;

        //OTHER NEEDED QUANTITIES
        int i;          //for loop iteration integer
        int k1 = 20;    //scaling factors to make drawing fill form
        int k2 = 9;
        int y0 = 450;   //offset values to centre drawing on form
        int x0 = 550;
        int start = 10;   //starting position for calculations
        double diff = 0.01;//initial displacement between two particles

        //starting positions for particles            
        y11 = start;//particle 1
        y12 = start;
        y13 = start;

        z11 = start + diff;//particle 2
        z12 = start + diff;
        z13 = start + diff;

        //initial coords for particles at t=0
        xi = (y11) * k1 + x0;
        yi = (y12) * k2 + y0;
        ai = (z11) * k1 + x0;
        bi = (z12) * k2 + y0;

        for (i = 1; i <= m; i++)
        {
            f10 = a * (y12 - y11);
            f20 = r * y11 - y12 - y11 * y13;
            f30 = y11 * y12 - b * y13;

            y21 = y11 + f10 * dt / 2;               //finding y1 y2 y3 at the first
            y22 = y12 + f20 * dt / 2;               //fraction of dt
            y23 = y13 + f30 * dt / 2;

            f11 = a * (y22 - y21);
            f21 = r * y21 - y22 - y21 * y23;
            f31 = y21 * y22 - b * y23;

            y31 = y11 + f11 * dt / 2;               //finding y1 y2 y3 at the second
            y32 = y12 + f21 * dt / 2;               //fraction of dt
            y33 = y13 + f31 * dt / 2;

            f12 = a * (y32 - y31);
            f22 = r * y31 - y32 - y31 * y33;
            f32 = y31 * y32 - b * y33;

            y41 = y11 + f12 * dt;               //finding y1 y2 y3 at the third
            y42 = y12 + f22 * dt;               //fraction of dt
            y43 = y13 + f32 * dt;

            f13 = a * (y42 - y41);
            f23 = r * y41 - y42 - y41 * y43;
            f33 = y41 * y42 - b * y43;

            y51 = y11 + (f10 + 2 * f11 + 2 * f12 + f13) * dt / 6; //final y values at y(t+dt)
            y52 = y12 + (f20 + 2 * f21 + 2 * f22 + f23) * dt / 6; //then to be repesated in for loop for all steps
            y53 = y13 + (f30 + 2 * f31 + 2 * f32 + f33) * dt / 6;

            xf = (y51) * k1 + x0;
            yf = (y52) * k2 + y0;

            //second particle calculation
            g10 = a * (z12 - z11);
            g20 = r * z11 - z12 - z11 * z13;
            g30 = z11 * z12 - b * z13;

            z21 = z11 + g10 * dt / 2;               //finding y1 y2 y3 at the first
            z22 = z12 + g20 * dt / 2;               //fraction of dt
            z23 = z13 + g30 * dt / 2;

            g11 = a * (z22 - z21);
            g21 = r * z21 - z22 - z21 * z23;
            g31 = z21 * z22 - b * z23;

            z31 = z11 + g11 * dt / 2;               //finding y1 y2 y3 at the second
            z32 = z12 + g21 * dt / 2;               //fraction of dt
            z33 = z13 + g31 * dt / 2;

            g12 = a * (z32 - z31);
            g22 = r * z31 - z32 - z31 * z33;
            g32 = z31 * z32 - b * z33;

            z41 = z11 + g12 * dt;               //finding y1 y2 y3 at the third
            z42 = z12 + g22 * dt;               //fraction of dt
            z43 = z13 + g32 * dt;

            g13 = a * (z42 - z41);
            g23 = r * z41 - z42 - z41 * z43;
            g33 = z41 * z42 - b * z43;

            z51 = z11 + (g10 + 2 * g11 + 2 * g12 + g13) * dt / 6; //final y values at y(t+dt)
            z52 = z12 + (g20 + 2 * g21 + 2 * g22 + g23) * dt / 6; //then to be repesated in for loop for all steps
            z53 = z13 + (g30 + 2 * g31 + 2 * g32 + g33) * dt / 6;

            af = (z51) * k1 + x0;
            bf = (z52) * k2 + y0;


            //DRAWING LINE JUST CALCULATED
            System.Drawing.Graphics graphicsObj;

            graphicsObj = this.CreateGraphics();

            Pen myPen = new Pen(System.Drawing.Color.Red, 1);

            //myPen.DashStyle = System.Drawing.Drawing2D.DashStyle.DashDotDot;

            graphicsObj.DrawLine(myPen, (int)xi, (int)yi, (int)xf, (int)yf);

            myPen.Color = System.Drawing.Color.RoyalBlue;

            graphicsObj.DrawLine(myPen, (int)ai, (int)bi, (int)af, (int)bf);

            //REDEFINING COORDS AND VALUES FOR NEXT LOOP
            //first particle
            xi = (y51) * k1 + x0;
            yi = (y52) * k2 + y0;
            y11 = y51;
            y12 = y52;
            y13 = y53;

            //second particle
            ai = (z51) * k1 + x0;
            bi = (z52) * k2 + y0;
            z11 = z51;
            z12 = z52;
            z13 = z53;

            /*even at 1 the below makes the program far too slow, need an alternative
             intention was for it to allow user to see the particle trajectories better*/
            //System.Threading.Thread.Sleep(1);
        }

    }


}
}

Answer 1

将 Form1_Paint 的代码放在一个单独的方法中，例如 DrawLorenzChaos(Graphics graphicsObj , double a, double b, double r)。当您在表单中设置参数时，只需将一些 bool 值设置为 true。检查代码

private void Form1_Paint(object sender, PaintEventArgs e)
{  

     if(startDrawing)
           DrawLorenzChaos(e.Graphics, aVal, bVal, rVal);
}

此外，在 DrawLorenzChaos 方法中只需删除这两行:

System.Drawing.Graphics graphicsObj;

graphicsObj = this.CreateGraphics();

编辑: 您可以从一开始就尝试此代码，然后您可以逐渐改进它，这就是我的做法(我会添加更好的同步，但基本上就是这样)。为了尝试代码，您需要一个按钮和一个大小为 (1000,1000) 的 PictureBox。请注意，我稍微更改了起始位置。

基本上这里有一个单独的线程在位图上绘制洛伦兹混沌。在单独的线程中绘制每条线后，该位图在 UI 线程中的 PictureBox 上绘制。您有 Mutex 来控制对位图的访问。

public partial class Form1 : Form
{
    Bitmap offScrBuff;
    Mutex mut;
    int index = 0;
    public Form1()
    {
        InitializeComponent();
        offScrBuff = new Bitmap(1000, 1000);
        mut = new Mutex();
        pictureBox1.Paint += new PaintEventHandler(pictureBox1_Paint);
        button1.Click += new System.EventHandler(this.button1_Click);
    }

    void pictureBox1_Paint(object sender, PaintEventArgs e)
    {
        mut.WaitOne();
        e.Graphics.DrawImage(offScrBuff, 0, 0);
        mut.ReleaseMutex();
    }

    void DrawLorenzChaos(double a, double b, double r)
    {
        //double a = 10, b = (8.0 / 3.0), r = 28;     //standard values for lorenz model

        /*m defines the number of iterations of the for loop so the number of lines drawn
        good idea to keep m inversely proportional to dt (the time interval). A smaller dt will
        mean smaller lines so smoother overall drawing m=50000 and dt=0.0005 is a good starting point
        that demonstrates chaos well*/
        double m = 500000, dt = 0.00005;

        //EVOLUTION VALUE FOR RUNGE_KUTTA METHOD
        //values for first particle
        double y11, y12, y13;
        double y21, y22, y23;
        double y31, y32, y33;
        double y41, y42, y43;
        double y51, y52, y53;
        double xi, yi, xf, yf;           //coordinates for drawing particle 1 trajectory

        double f10, f11, f12, f13;      //function values to be calculated, 
        double f20, f21, f22, f23;      //for fxy (x>1) these are intermediate fn calculations at different
        double f30, f31, f32, f33;      //times in Runga Kutta

        //values for second particle
        double z11, z12, z13;
        double z21, z22, z23;
        double z31, z32, z33;
        double z41, z42, z43;
        double z51, z52, z53;
        double ai, bi, af, bf;          //coordinates for drawing particle 2 trajectory (these are badly named...)

        double g10, g11, g12, g13;      //equivalent of f values for particle 2 
        double g20, g21, g22, g23;
        double g30, g31, g32, g33;

        //OTHER NEEDED QUANTITIES
        int i;          //for loop iteration integer
        int k1 = 20;    //scaling factors to make drawing fill form
        int k2 = 9;
        int y0 = 280;   //offset values to centre drawing on form
        int x0 = 400;
        int start = 10;   //starting position for calculations
        double diff = 0.01;//initial displacement between two particles

        //starting positions for particles            
        y11 = start;//particle 1
        y12 = start;
        y13 = start;

        z11 = start + diff;//particle 2
        z12 = start + diff;
        z13 = start + diff;

        //initial coords for particles at t=0
        xi = (y11) * k1 + x0;
        yi = (y12) * k2 + y0;
        ai = (z11) * k1 + x0;
        bi = (z12) * k2 + y0;
        for (i = 1; i <= m; i++)
        {
            f10 = a * (y12 - y11);
            f20 = r * y11 - y12 - y11 * y13;
            f30 = y11 * y12 - b * y13;

            y21 = y11 + f10 * dt / 2;               //finding y1 y2 y3 at the first
            y22 = y12 + f20 * dt / 2;               //fraction of dt
            y23 = y13 + f30 * dt / 2;

            f11 = a * (y22 - y21);
            f21 = r * y21 - y22 - y21 * y23;
            f31 = y21 * y22 - b * y23;

            y31 = y11 + f11 * dt / 2;               //finding y1 y2 y3 at the second
            y32 = y12 + f21 * dt / 2;               //fraction of dt
            y33 = y13 + f31 * dt / 2;

            f12 = a * (y32 - y31);
            f22 = r * y31 - y32 - y31 * y33;
            f32 = y31 * y32 - b * y33;

            y41 = y11 + f12 * dt;               //finding y1 y2 y3 at the third
            y42 = y12 + f22 * dt;               //fraction of dt
            y43 = y13 + f32 * dt;

            f13 = a * (y42 - y41);
            f23 = r * y41 - y42 - y41 * y43;
            f33 = y41 * y42 - b * y43;

            y51 = y11 + (f10 + 2 * f11 + 2 * f12 + f13) * dt / 6; //final y values at y(t+dt)
            y52 = y12 + (f20 + 2 * f21 + 2 * f22 + f23) * dt / 6; //then to be repesated in for loop for all steps
            y53 = y13 + (f30 + 2 * f31 + 2 * f32 + f33) * dt / 6;

            xf = (y51) * k1 + x0;
            yf = (y52) * k2 + y0;

            //second particle calculation
            g10 = a * (z12 - z11);
            g20 = r * z11 - z12 - z11 * z13;
            g30 = z11 * z12 - b * z13;

            z21 = z11 + g10 * dt / 2;               //finding y1 y2 y3 at the first
            z22 = z12 + g20 * dt / 2;               //fraction of dt
            z23 = z13 + g30 * dt / 2;

            g11 = a * (z22 - z21);
            g21 = r * z21 - z22 - z21 * z23;
            g31 = z21 * z22 - b * z23;

            z31 = z11 + g11 * dt / 2;               //finding y1 y2 y3 at the second
            z32 = z12 + g21 * dt / 2;               //fraction of dt
            z33 = z13 + g31 * dt / 2;

            g12 = a * (z32 - z31);
            g22 = r * z31 - z32 - z31 * z33;
            g32 = z31 * z32 - b * z33;

            z41 = z11 + g12 * dt;               //finding y1 y2 y3 at the third
            z42 = z12 + g22 * dt;               //fraction of dt
            z43 = z13 + g32 * dt;

            g13 = a * (z42 - z41);
            g23 = r * z41 - z42 - z41 * z43;
            g33 = z41 * z42 - b * z43;

            z51 = z11 + (g10 + 2 * g11 + 2 * g12 + g13) * dt / 6; //final y values at y(t+dt)
            z52 = z12 + (g20 + 2 * g21 + 2 * g22 + g23) * dt / 6; //then to be repesated in for loop for all steps
            z53 = z13 + (g30 + 2 * g31 + 2 * g32 + g33) * dt / 6;

            af = (z51) * k1 + x0;
            bf = (z52) * k2 + y0;


            //DRAWING LINE JUST CALCULATED

            mut.WaitOne();
            System.Drawing.Graphics graphicsObj = Graphics.FromImage(offScrBuff);

            graphicsObj.DrawLine(Pens.Red, (int)xi, (int)yi, (int)xf, (int)yf);

            graphicsObj.DrawLine(Pens.RoyalBlue, (int)ai, (int)bi, (int)af, (int)bf);

            graphicsObj.Dispose();
            mut.ReleaseMutex();

            pictureBox1.Invalidate();


            //REDEFINING COORDS AND VALUES FOR NEXT LOOP
            //first particle
            xi = (y51) * k1 + x0;
            yi = (y52) * k2 + y0;
            y11 = y51;
            y12 = y52;
            y13 = y53;

            //second particle
            ai = (z51) * k1 + x0;
            bi = (z52) * k2 + y0;
            z11 = z51;
            z12 = z52;
            z13 = z53;
            /*even at 1 the below makes the program far too slow, need an alternative
             intention was for it to allow user to see the particle trajectories better*/
            //System.Threading.Thread.Sleep(1);
        }

    }

    private void button1_Click(object sender, EventArgs e)
    {
        Task.Factory.StartNew(() => { DrawLorenzChaos(10.0, 8.0 / 3.0, 28); });
    }
}