//
//  diffeq.java
//  diffeq
//
//  Created by me on Sun Apr 13 2003.
//  Copyright (c) 2003 __MyCompanyName__. All rights reserved.
//  A simple Java applet
//

import java.awt.*;
import java.applet.*;
import java.awt.event.*;

public class diffeq extends Applet {
    double delta_t=0.001;  // delta t
    double delta_xy=1.0E-10; // regard the point is fixed if move is less than delta_xy 
    long count;
	long maxCount=10000; //Stop plot after 10,000 th iterations
	
    double x0=-10.0, y0=-10.0, x1=10.0, y1=10.0; //coord of left-top and right-bottom points
//	double a=3.0, b=1.0, m=0.5, c=4.0, d=1.0, n=1.0;  //coefficients of diff. eq.
	double a1=-1.0, h1=-0.5, b1=0.0, p1=3.0, q1=0.0, r1=0.0;  //coefficients of diff. eq.
	double a2=0.0,  h2=-1.0, b2=-1.0, p2=0.0, q2=4.0, r2=0.0;  //coefficients of diff. eq.
	
	double xpressed, ypressed, xreleased, yreleased;
	boolean dragging=false;

	Label label1_1, label1_2;
	Label label2_1, label2_2;
	Label label31, label32;
	Label label41, label42;
	Label label51, label52;
	Label label61, label62;
	Label label71, label72;
	Label label81, label82;
	Label label7;
	Label label8;
	Label label9;
	Label label10;
	Label label11;
	Label label12;
	Label label13;
	Label label14;
    
	TextField a1Text, a2Text;
	TextField h1Text, h2Text;
	TextField b1Text, b2Text;
	TextField p1Text, p2Text;
	TextField q1Text, q2Text;
	TextField r1Text, r2Text;
	
    TextField x0Text;
    TextField y0Text;
    TextField x1Text;
    TextField y1Text;
    TextField xText;
    TextField yText;

	Button set_a_B;
    Button set_x_B;
    Button zoom_B;
    // Button show_fp_B;
    
	nCanvas plane;

	
	class vec{
		public double x;
		public double y;
		
		vec(double xval, double yval){
			x=xval; y=yval;
		}
	}


	public void paint(Graphics gtmp){
		int red_xPoints[]={135,135,145};
		int red_yPoints[]={67,73,70};
		int blue_xPoints[]={175,175,185};
		int blue_yPoints[]={67,73,70};
		
		gtmp.setColor(Color.red);
		gtmp.drawLine(120,70,160,70);
		gtmp.fillPolygon(red_xPoints,red_yPoints,3);
		gtmp.setColor(Color.blue);
		gtmp.drawLine(160,70,200,70);
		gtmp.fillPolygon(blue_xPoints,blue_yPoints,3);
		}
		
	public void init() {
		setLayout(null);
		resize(640,440);
		setBackground(Color.lightGray);

        label1_1 = new Label("x' = a1 x^2 + h1 xy + b1 y^2");
		label1_2 = new Label("+ p1 x + q1 y + r1");
		label1_1.reshape(5,2,200,15);
		label1_2.reshape(30,18,200,15);
		add(label1_1);
		add(label1_2);

		label2_1 = new Label("y' = a2 x^2 + h2 xy + b2 y^2");
		label2_2 = new Label("+ p2 x + q2 y + r2");
		label2_1.reshape( 5, 34,200,15);
		label2_2.reshape(30,50,200,15);
		add(label2_1);
		add(label2_2);
		
		// a1
        label31 = new Label("a1");
		label31.reshape(20,80,25,15);
		add(label31);

		a1Text = new TextField();
		a1Text.setText(String.valueOf(a1));
		a1Text.reshape(50,80,55,15);
		a1Text.setBackground(Color.white);
		add(a1Text);
		
		// h1
        label41 = new Label("h1");
		label41.reshape(20,100,25,15);
		add(label41);

		h1Text = new TextField();
		h1Text.setText(String.valueOf(h1));
		h1Text.reshape(50,100,55,15);
		h1Text.setBackground(Color.white);
		add(h1Text);
		
		// b1
        label51 = new Label("b1");
		label51.reshape(20,120,25,15);
		add(label51);

		b1Text = new TextField();
		b1Text.setText(String.valueOf(b1));
		b1Text.reshape(50,120,55,15);
		b1Text.setBackground(Color.white);
		add(b1Text);
		
		// p1
        label61 = new Label("p1");
		label61.reshape(20,140,25,15);
		add(label61);

		p1Text = new TextField();
		p1Text.setText(String.valueOf(p1));
		p1Text.reshape(50,140,55,15);
		p1Text.setBackground(Color.white);
		add(p1Text);
		
		// q1
        label71 = new Label("q1");
		label71.reshape(20,160,25,15);
		add(label71);

		q1Text = new TextField();
		q1Text.setText(String.valueOf(q1));
		q1Text.reshape(50,160,55,15);
		q1Text.setBackground(Color.white);
		add(q1Text);
		
		// r1
        label81 = new Label("r1");
		label81.reshape(20,180,25,15);
		add(label81);

		r1Text = new TextField();
		r1Text.setText(String.valueOf(r1));
		r1Text.reshape(50,180,55,15);
		r1Text.setBackground(Color.white);
		add(r1Text);
		
		// a2
        label32 = new Label("a2");
		label32.reshape(115,80,25,15);
		add(label32);

		a2Text = new TextField();
		a2Text.setText(String.valueOf(a2));
		a2Text.reshape(145,80,55,15);
		a2Text.setBackground(Color.white);
		add(a2Text);
		
		// h2
        label42 = new Label("h2");
		label42.reshape(115,100,25,15);
		add(label42);

		h2Text = new TextField();
		h2Text.setText(String.valueOf(h2));
		h2Text.reshape(145,100,55,15);
		h2Text.setBackground(Color.white);
		add(h2Text);

		// b2
        label52 = new Label("b2");
		label52.reshape(115,120,25,15);
		add(label52);

		b2Text = new TextField();
		b2Text.setText(String.valueOf(b2));
		b2Text.reshape(145,120,55,15);
		b2Text.setBackground(Color.white);
		add(b2Text);

		// p2
        label62 = new Label("p2");
		label62.reshape(115,140,25,15);
		add(label62);

		p2Text = new TextField();
		p2Text.setText(String.valueOf(p2));
		p2Text.reshape(145,140,55,15);
		p2Text.setBackground(Color.white);
		add(p2Text);

		// q2
        label72 = new Label("q2");
		label72.reshape(115,160,25,15);
		add(label72);

		q2Text = new TextField();
		q2Text.setText(String.valueOf(q2));
		q2Text.reshape(145,160,55,15);
		q2Text.setBackground(Color.white);
		add(q2Text);

		// r2
        label82 = new Label("r2");
		label82.reshape(115,180,25,15);
		add(label82);

		r2Text = new TextField();
		r2Text.setText(String.valueOf(r2));
		r2Text.reshape(145,180,55,15);
		r2Text.setBackground(Color.white);
		add(r2Text);


        //set_a_B
		set_a_B = new Button("set a,h,c,..");
		set_a_B.reshape(100,205,100,20);
        set_a_B.addMouseListener(new set_a_ma());
		add(set_a_B);


        label7 = new Label("x0");
        label7.reshape(20,240,30,15);
        add(label7);
        
		x0Text = new TextField();
		x0Text.setText(String.valueOf(x0));
		x0Text.reshape(50,240,150,15);
		x0Text.setBackground(Color.white);
		add(x0Text);

        label8 = new Label("y0");
        label8.reshape(20,260,30,15);
        add(label8);
        
		y0Text = new TextField();
		y0Text.setText(String.valueOf(y0));
		y0Text.reshape(50,260,150,15);
		y0Text.setBackground(Color.white);
		add(y0Text);

        label9 = new Label("x1");
        label9.reshape(20,280,30,15);
        add(label9);
        
		x1Text = new TextField();
		x1Text.setText(String.valueOf(x1));
		x1Text.reshape(50,280,150,15);
		x1Text.setBackground(Color.white);
		add(x1Text);

        label10 = new Label("y1");
        label10.reshape(20,300,30,15);
        add(label10);
        
		y1Text = new TextField();
		y1Text.setText(String.valueOf(y1));
		y1Text.reshape(50,300,150,15);
		y1Text.setBackground(Color.white);
		add(y1Text);

        //set_x_B
		set_x_B = new Button("set x's & y's");
		set_x_B.reshape(100,325,100,20);
        set_x_B.addMouseListener(new set_x_ma());
		add(set_x_B);

        //zoom_B
		zoom_B = new Button("zoom out");
		zoom_B.reshape(100,350,100,20);
        zoom_B.addMouseListener(new zoom_ma());
		add(zoom_B);

        /*
		//show_fp_B
		show_fp_B = new Button("show fixed pt");
		show_fp_B.reshape(100,345,100,20);
        //set_a_B.addMouseListener(new clear_ma());
		add(show_fp_B);
		*/

        // x, y
        label11 = new Label("x");
        label11.reshape(20,380,30,15);
        add(label11);
        
		xText = new TextField();
		xText.setText("");
		xText.reshape(50,380,150,15);
		xText.setBackground(Color.white);
		add(xText);

        label12 = new Label("y");
        label12.reshape(20,400,30,15);
        add(label12);
        
		yText = new TextField();
		yText.setText("");
		yText.reshape(50,400,150,15);
		yText.setBackground(Color.white);
		add(yText);


        //canvas
		plane = new nCanvas();
		plane.reshape(220,20,400,400);
		plane.setBackground(Color.white);
        plane.addMouseMotionListener(new plane_mma());
        plane.addMouseListener(new plane_ma());
		add(plane);

        plane.makeBuffer();

		plane.screen(x0,y0,x1,y1);
        plane.eraseBuff();
		
        //draw axis
        drawAxis();
        
	}
    

    /////////// EVENT HANDLERS
    
    // MouseAdapter for set_a button
    class set_a_ma extends MouseAdapter{
        public void mouseClicked(MouseEvent e){
            set_a_B_Clicked();
        }
    }
    
    void set_a_B_Clicked() {
        get_a();
		plane.eraseBuff();
		
		drawAxis();
	}

    // MouseAdapter for set_x button
    class set_x_ma extends MouseAdapter{
        public void mouseClicked(MouseEvent e){
            set_x_B_Clicked();
        }
    }
    
    void set_x_B_Clicked() {
        get_x();
		plane.screen(x0,y0,x1,y1);
		plane.eraseBuff();
		
		drawAxis();
	}

    // MouseAdapter for zoom button
    class zoom_ma extends MouseAdapter{
        public void mouseClicked(MouseEvent e){
            zoom_B_Clicked();
        }
    }
    
    void zoom_B_Clicked() {
        double xc,yc,wx,wy;
		
		xc=(x0+x1)/2; yc=(y0+y1)/2;
		wx=x1-x0; wy=y1-y0;
		
		x0=xc-wx; x1=xc+wx;
		y0=yc-wy; y1=yc+wy;
		
		x0Text.setText(String.valueOf(x0));
		x1Text.setText(String.valueOf(x1));
		y0Text.setText(String.valueOf(y0));
		y1Text.setText(String.valueOf(y1));
		
		plane.screen(x0,y0,x1,y1);
		plane.eraseBuff();
		
		drawAxis();
	}
    
    // MouseAdapter for plane
    class plane_ma extends MouseAdapter{
        public void mousePressed(MouseEvent e){
            plane_MousePressed(e);
        }
        
        public void mouseReleased(MouseEvent e){
            plane_MouseReleased(e);
        }
    }

    void plane_MousePressed(MouseEvent event) {
		xpressed=plane.eventRX(event);
		ypressed=plane.eventRY(event);
    }

    void plane_MouseReleased(MouseEvent event) {
		plane.update(plane.getGraphics());
		xreleased=plane.eventRX(event);
		yreleased=plane.eventRY(event);
		if(dragging){ // zoom in
			double xmin, ymin, xmax, ymax;
			
			xmin=Math.min(xpressed, xreleased);
			ymin=Math.min(ypressed, yreleased);
			xmax=Math.max(xpressed, xreleased);
			ymax=Math.max(ypressed, yreleased);
			
			set_x(xmin, ymin, xmax, ymax);
			dragging=false;
			
		} else {  // draw orbit
			drawOrbit(xreleased, yreleased);
		}
    }

    
    //MouseMotionAdapter for plane
    class plane_mma extends MouseMotionAdapter{
        public void mouseMoved(MouseEvent e){
            plane_MouseMoved(e);
        }

        public void mouseDragged(MouseEvent e){
            plane_MouseDragged(e);
        }

    }
    
    void plane_MouseMoved(MouseEvent event){  // show small green disk and write the coord of pointer
		double xtmp,ytmp;
		
        plane.update(plane.getGraphics());
        xtmp=plane.eventRX(event);
        ytmp=plane.eventRY(event);
        plane.setForeground(Color.green);
        plane.drawMarkTemp(xtmp,ytmp);
		
		xText.setText(String.valueOf(xtmp));
		yText.setText(String.valueOf(ytmp));
    }

    void plane_MouseDragged(MouseEvent event) {
		double xtmp,ytmp;
		int xi0,yi0,xi1,yi1;
		int xd,yd;
		Graphics gtmp=plane.getGraphics();


		dragging=true;
		
		plane_MouseMoved(event);  // write the coord of pointer
		
		xtmp=plane.eventRX(event);
		ytmp=plane.eventRY(event);
		
		xi0=plane.xInt(xpressed); xi1=plane.xInt(xtmp);
		yi0=plane.yInt(ypressed); yi1=plane.yInt(ytmp);
		
		xd=Math.abs(xi1-xi0); yd=Math.abs(yi1-yi0);
		xi0=Math.min(xi0,xi1); yi0=Math.min(yi0,yi1);
		
		plane.repaint();
		gtmp.setColor(Color.green);
		gtmp.drawRect(xi0,yi0,xd,yd);
    }

    
    // draw axis
	public void drawAxis(){
		plane.setForeground(Color.green);
        plane.drawLine(x0, 0.0 , x1 ,0.0);
		plane.drawLine(0.0, y0 , 0.0 , y1);
	}
	
    
	void getNumbers(){ // get a,... and x0,...
        get_a();
        get_x();
    }
    
    void get_a(){ //get a,b,c,d
		try{
			a1=Double.valueOf(a1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			a1Text.setText(String.valueOf(a1));
		};
		try{
			a2=Double.valueOf(a2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			a2Text.setText(String.valueOf(a2));
		};
		
		try{
			h1=Double.valueOf(h1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			h1Text.setText(String.valueOf(h1));
		};
		try{
			h2=Double.valueOf(h2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			h2Text.setText(String.valueOf(h2));
		};
		
		try{
			b1=Double.valueOf(b1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			b1Text.setText(String.valueOf(b1));
		};
		try{
			b2=Double.valueOf(b2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			b2Text.setText(String.valueOf(b2));
		};
		
		try{
			p1=Double.valueOf(p1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			p1Text.setText(String.valueOf(p1));
		};
		try{
			p2=Double.valueOf(p2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			p2Text.setText(String.valueOf(p2));
		};
		
		try{
			q1=Double.valueOf(q1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			q1Text.setText(String.valueOf(q1));
		};
		try{
			q2=Double.valueOf(q2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			q2Text.setText(String.valueOf(q2));
		};
		
		try{
			r1=Double.valueOf(r1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			r1Text.setText(String.valueOf(r1));
		};
		try{
			r2=Double.valueOf(r2Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			r2Text.setText(String.valueOf(r2));
		};


	}
    
    void get_x(){ //get x0,y0,x1,y1
		try{
			x0=Double.valueOf(x0Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			x0Text.setText(String.valueOf(x0));
		};
		try{
			y0=Double.valueOf(y0Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			y0Text.setText(String.valueOf(y0));
		};
		try{
			x1=Double.valueOf(x1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			x1Text.setText(String.valueOf(x1));
		};
		try{
			y1=Double.valueOf(y1Text.getText()).doubleValue();
        }catch(NumberFormatException e){
			y1Text.setText(String.valueOf(y1));
		};
	}
    
    void set_x(double xmin, double ymin, double xmax, double ymax){ //set text field
		x0Text.setText(String.valueOf(xmin));
		y0Text.setText(String.valueOf(ymin));
		x1Text.setText(String.valueOf(xmax));
		y1Text.setText(String.valueOf(ymax));
	}


    //Draw orbit through (xgiven,ygiven)
    void drawOrbit(double xgiven, double ygiven){
        double x,y, xnew,ynew;
		vec v = new vec(0.0,0.0);

        // draw FORWARD orbit in BLUE
        x=xgiven; y=ygiven;
        plane.setForeground(Color.blue);
		count=0;
		while(true){
            plane.drawPoint(x,y);

            //xnew=next_x(x,y,delta_t);
            //ynew=next_y(x,y,delta_t);
            v=next_xy(x,y,delta_t);
			xnew=v.x; ynew=v.y;
			
            if(x<=x0 || x>=x1 || y<=y0 || y>=y1) break;
            if(Math.abs(xnew-x)<delta_xy && Math.abs(ynew-y)<delta_xy) break;
			count++; if(count>maxCount) break;
            x=xnew; y=ynew;
        }
		
        // draw BACKWORD orbit in RED
        x=xgiven; y=ygiven;
        plane.setForeground(Color.red);
		count=0;
        while(true){
            plane.drawPoint(x,y);

            //xnew=next_x(x,y,-delta_t);
            //ynew=next_y(x,y,-delta_t);
            v=next_xy(x,y,-delta_t);
			xnew=v.x; ynew=v.y;
			
            if(x<=x0 || x>=x1 || y<=y0 || y>=y1) break;
            if(Math.abs(xnew-x)<delta_xy && Math.abs(ynew-y)<delta_xy) break;
			count++; if(count>maxCount) break;
            x=xnew; y=ynew;
        }
    }
        
	// get next x and y by EULER METHOD
	public double next_x(double x, double y, double dt){
		double xnew;
		
		xnew=x+f(x,y)*dt;
		return(xnew);
	}
	
	public double next_y(double x, double y, double dt){
		double ynew;
		
		ynew=y+g(x,y)*dt;
		return(ynew);
	}

	// get next x and y as a vector by RUNGE-KUTTA METHOD
	public vec next_xy(double x, double y, double dt){
		double xnew, ynew;
		double kx1, kx2, kx3, kx4, ky1, ky2, ky3, ky4;
		
		kx1=dt*f(x,y);
		ky1=dt*g(x,y);
		
		kx2=dt*f(x+kx1/2,y+ky1/2);
		ky2=dt*g(x+kx1/2,y+ky1/2);
		
		kx3=dt*f(x+kx2/2,y+ky2/2);
		ky3=dt*g(x+kx2/2,y+ky2/2);
		
		kx4=dt*f(x+kx3,y+ky3);
		ky4=dt*g(x+kx3,y+ky3);
		
		xnew=x+(kx1+2*kx2+2*kx3+kx4)/6;
		ynew=y+(ky1+2*ky2+2*ky3+ky4)/6;
		
		return(new vec(xnew, ynew));
	}
	
	
	
    // dx/dt = f(x,y)
    public double f(double x, double y){
        return(a1*x*x + h1*x*y + b1*y*y + p1*x + q1*y + r1);
    }
    // dy/dt = g(x,y)
    public double g(double x, double y){
        return(a2*x*x + h2*x*y + b2*y*y + p2*x + q2*y + r2);
    }
}