C# Visual Studio，在用户单击按钮时绘制Lorenz混沌
所以去年我用C写了一个程序，用洛伦兹方程和龙格库塔方法来解决微分方程，演示了混沌 我最近决定，我想重新审视这一点，并制作一个能够绘制粒子轨迹的程序。我成功地实现了这一点，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，以及其他参数（在我的例子中是a、b和r）。目前，程序运行后，我会立即绘制轨迹，但我想推迟，直到用户在一些文本框中输入参数，然后按下按钮。为此，我认为应该创建一个新类并将当前代码放入其中，然后在main.cs文件中的btn1_Click方法下调用它。然而，我在这方面遇到了相当大的麻烦，主要是不知道如何去做。在我迄今为止最好的尝试中，我遇到了一个与“createGraphics（）”相关的行相关的错误，即类文件中没有对它的定义。我在类顶部的using部分中有与主文件中相同的引用，在主文件中它工作得很好 此外，如果有人能给我任何关于我的代码的反馈（如任何不好的做法或我过度复杂的地方）或任何改进建议，我将不胜感激，如果您需要我提供更多信息来帮助，我将尽我所能回答C# Visual Studio，在用户单击按钮时绘制Lorenz混沌,c#,graphic,C#,Graphic,所以去年我用C写了一个程序，用洛伦兹方程和龙格库塔方法来解决微分方程，演示了混沌 我最近决定，我想重新审视这一点，并制作一个能够绘制粒子轨迹的程序。我成功地实现了这一点，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，以及其他参数（在我的例子中是a、b和r）。目前，程序运行后，我会立即绘制轨迹，但我想推迟，直到用户在一些文本框中输入参数，然后按下按钮。为此，我认为应该创建一个新类并将当前代码放入其中，然后在main.cs文件中的btn1_Click方法下调用它。然而，我在这方面遇到了相
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);
}
}
}
}
使用系统；
使用System.Collections.Generic；
使用系统组件模型；
使用系统数据；
使用系统图；
使用System.Linq；
使用系统文本；
使用System.Threading.Tasks；
使用System.Windows.Forms；
洛伦兹混沌
{
公共部分类Form1:Form
{
公共表格1（）
{
初始化组件（）；
}
私有void Form1_Paint（对象发送器、PaintEventArgs e）
{
双a=10，b=（8/3），r=28；//洛伦兹模型的标准值
/*m定义for循环的迭代次数，因此绘制的线数
保持m与dt（时间间隔）成反比是个好主意。较小的dt将
平均较小的线，因此更平滑的总体图纸m=50000和dt=0.0005是一个良好的起点
这很好地说明了混乱*/
双m=500000，dt=0.00005；
//龙格库塔法的演化值
//第一个粒子的值
双y11、y12、y13；
双y21、y22、y23；
双y31、y32、y33；
双y41、y42、y43；
双y51、y52、y53；
绘制1粒子轨迹的双席、易、XF、YF、/坐标
双精度f10，f11，f12，f13；//要计算的函数值，
double f20，f21，f22，f23；//对于fxy（x>1），这些是不同条件下的中间fn计算
双f30，f31，f32，f33；//伦加库塔中的次数
//第二个粒子的值
双z11、z12、z13；
双z21，z22，z23；
双z31，z32，z33；
双z41，z42，z43；
双z51、z52、z53；
双ai，双bi，双af，双bf；//绘制粒子2轨迹的坐标（名称不正确…）
双g10，g11，g12，g13；//相当于粒子2的f值
g20、g21、g22、g23双倍增长；
双g30、g31、g32、g33；
//其他所需数量
int i；//对于循环迭代整数
int k1=20；//制作图形填充表单的比例因子
int k2=9；
int y0=450；//表格上图形中心的偏移值
int x0=550；
int start=10；//计算的起始位置
double diff=0.01；//两个粒子之间的初始位移
//粒子的起始位置
y11=开始；//粒子1
y12=启动；
y13=启动；
z11=start+diff；//粒子2
z12=启动+差异；
z13=启动+差异；
//t=0时粒子的初始坐标
席＝（Y11）*K1+X0；
yi=（y12）*k2+y0；
ai=（z11）*k1+x0；
bi=（z12）*k2+y0；
对于（i=1；i将Form1\u Paint
的代码放在一个单独的方法中，例如DrawLorenzChaos（Graphics Graphics Sobj，double a，double b，double r）
。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，只需删除以下两行：
System.Drawing.Graphics graphicsObj;
graphicsObj = this.CreateGraphics();
编辑：您可以从一开始就尝试这段代码，然后逐步改进，这就是我的做法（我会添加更好的同步，但基本上就是这样）。为了尝试这段代码，您需要一个按钮和一个大小为（10001000）的图片盒。请注意，我稍微更改了开始位置
基本上，这里有一个单独的线程在位图上绘制Lorenz混沌。该位图在UI线程中的PictureBox上绘制，在一个单独的线程中绘制每一行之后。您可以使用互斥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); });
}
}
公共部分类表单1:表单
{
位图偏移CRBUFF；
互斥mut；
int指数=0；
公共表格1（）
{
初始化组件（）；
offScrBuff=新位图（10001000）；
mut=新的互斥体（）；
pictureBox1.Paint+=新的PaintEventHandler（pictureBox1\u Paint）；
button1.Click+=newsystem.EventHandler（this.button1\u Click）；
}
void pictureBox1_Paint（对象发送器，PaintEventArgs e）
{
mut.WaitOne（）；
e、 Graphics.DrawImage（offScrBuff，0,0）；
mut.ReleaseMutex（）；
}
无效拉深（双a，双b，双r）
{
//双a=10，b=（8.0/3.0），r=28；//洛伦兹模型的标准值
/*m定义for循环的迭代次数，因此绘制的线数
把我留在家里是个好主意