Visual Studio，在用戶點擊按鈕時繪製Lorenz混沌

Question

所以去年我寫了一個C程序，用於演示使用Lorenz方程和Runge Kutta方法求解微分方程的混沌。

我最近決定，我想重新考慮這個，並製作出能夠繪製出粒子軌跡的程序。我得到這個成功的工作，但現在想擴大這個，使用戶可以輸入參數，如粒子的起始位置，和其他參數（在我的情況下，a，b和r）。目前我的程序運行的時候軌跡就被繪製出來了，但是我想延遲這個軌跡直到用戶輸入他們的參數到一些文本框然後按下一個按鈕。要做到這一點，我想我應該創建一個新的類，並將我的當前代碼放到那裏，然後在btn1_Click方法下的主.cs文件中調用它。不過，我在這方面遇到了相當大的麻煩，主要還是不知道如何去做。在我迄今爲止的最佳嘗試中，我對包含「createGraphics（）」的一行有錯誤，即在類文件中沒有定義它。我在頂部使用部分的頂部具有所有相同的引用，就像它在主要文件中工作正常的那樣。

此外，如果任何人都可以給我任何有關我的代碼（即任何不良行爲或我過於複雜的事情的地方）或任何建議，使其更好，我會非常感激，如果你需要任何更多我的幫助信息，然後我會盡我所能來回答！

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

把你的Form1_Paint的代碼在一個單獨的方法，例如DrawLorenzChaos(Graphics graphicsObj , double a, double b, double r)。當您在表單中設置參數時，只需將一些bool值設置爲true即可。檢查代碼

private void Form1_Paint(object sender, PaintEventArgs e) 
{ 

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

此外，在DrawLorenzChaos方法只是刪除這兩行：

System.Drawing.Graphics graphicsObj; 

graphicsObj = this.CreateGraphics(); 

編輯：你可以試試這個代碼只是開始，你可以慢慢改進它，這是我該怎麼做（我會添加更好的同步，但基本上就是這樣）。爲了嘗試代碼，您將需要一個按鈕和一個大小爲（1000,1000）的PictureBox。請注意，我改變了一點起始位置。

基本上這裏是一個單獨的線程在位圖上繪製洛倫茲混沌。該位圖繪製在每個線條繪製在單獨的線程後在UI線程中的PictureBox。你有Mutex控制訪問位圖。

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); }); 
    } 
}