//
//  parabola.java
//  
//
//  Created by Chris Thiel on Tue September 20, 2004.
//  Copyright (c) 2004 Chris Thiel. 
//  Free for Educational Use (with permission). All rights reserved.
//  A simple Java applet (520 x 300) 
//  that uses three sliders to control the three coeefs of a quadratic function
//  Updated 26 Sep 2005 - fixed "typos"

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

public class parabola extends Applet implements MouseMotionListener  {

    static final String message = "Hello World!";
    static final int S3_LOCATION =508;
    static final int S2_LOCATION =450;
    static final int S1_LOCATION =398;
    static final int SLIDER_LENGTH = 200;
    static final int SLIDER_TOP=90;
    int SLIDER_BOTTOM=SLIDER_TOP+SLIDER_LENGTH;

    private Font font = new Font("sansserif", Font.ITALIC + Font.BOLD, 12);
    int ax, ay, bx, by, cx, cy,j;
    double a,b,c, sx, sy, fociX, fociY;
	double h,k,r1,r2; // parabola vars for vertex and roots
   
    
    public void init() {
        setLayout (null);
        this.setBackground(new Color(0xFFEEAA));
        addMouseMotionListener(this);
        a=1.0; b=4.0; c=-5.0;
        ax=S1_LOCATION;  
        ay=SLIDER_TOP+99;
        bx=S2_LOCATION; 
        by=SLIDER_TOP+99;
        cx=S3_LOCATION; 
        cy=SLIDER_TOP+99;
    }
    private double f(double x){
        return 1.0*a*x*x+b*x+c;
    }
    private int screenX (double x){
        return (int)(160+10*x+20); //converts -15<x<15 to screen coords
    }
    private int screenY (double y){
        return (int)(150-10*y+10); //converts -15<y<15 to screen coords
    }
    
    public void paint (Graphics g) {
        //Draw Grid
        g.setColor(new Color(0x108000));
        g.fillRect(10,10,340,280);
        g.setColor(new Color(0x08602F)); //lines
        for(int i = -16; i< 18; i++){
         g.drawLine( screenX(i),10,screenX(i) ,289); // verticals
        }
        for(int i = -13; i< 16; i++) {
         g.drawLine( 10, screenY(i), 350, screenY(i) ); //horizontals
        }
        g.setColor(Color.black); 
        g.drawLine( 10, screenY(0), 350, screenY(0) ); // x-axis
        g.drawLine( screenX(0),10,screenX(0) ,289);  // y=axis
        g.setFont (new Font("serif", 0, 9));

        for(int i = 2; i< 10; i+=2) g.drawString(i+" ", screenX(i)-1, screenY(0)+9); 
        for(int i = 10; i< 18; i+=2) g.drawString(i+" ", screenX(i)-4, screenY(0)+9);
	for(int i = -8; i< 0; i+=2) g.drawString(i+" ", screenX(i)-4, screenY(0)+9);  
	for(int i = -16; i< -9; i+=2) g.drawString(i+" ", screenX(i)-7, screenY(0)+9); 
	
	for(int i = 2; i< 16; i+=2) g.drawString(i+" ", screenX(0)+2, screenY(i)+4);
	for(int i = -12; i< 0; i+=2) g.drawString(i+" ", screenX(0)+2, screenY(i)+4);
       
        
         
        //Draw Curve
        // if a=0 it is a line y=-c/b
		if (a==0.0 && b!=0.0){
		g.setColor(Color.cyan);
		g.drawLine(10,screenY(-1.0*c/b),350 , screenY(-1.0*c/b));	
		}
		
		// if a!=0 then parabola
		// vertex at (h,k) where 
		// h=-1*b/(2*a) and k=f(h)=a*h*h+b*h+c=(4*a*c-b*b)/4*a
		// axis of symmetry is x=h
		// alternate equation is a(x-h)^2 + k
		if (a!=0.0){
		h=-1.0*b/(2.0*a);
		k=(4.0*a*c-b*b)/(4.0*a);
		double d2=b*b-4.0*a*c; // the discriminate
		g.setFont (new Font("serif", Font.ITALIC+Font.BOLD, 14));
		g.setColor(Color.orange);
		if(d2>=0){
			g.setColor(Color.orange);
			r1=(-1.0*b-Math.sqrt(d2))/(2.0*a);
			r2=(-1.0*b+Math.sqrt(d2))/(2.0*a);
			g.drawString("1st root: "+r1,30,275);
			g.drawString("2nd root: "+r2,25,290);
		}
		if (d2<0){
		   // g.setColor(new Color(0x3F1212));//dark brown
			g.setColor(Color.pink);
			r1=(-1.0*b)/(2.0*a);
			r2=Math.sqrt(-1.0*d2)/(2.0*a);
			g.drawString("Complex roots: ", 30,275);
			g.drawString(r1+" ± "+r2+" i",30,290);
		}
		g.setFont (new Font("sansserif", Font.ITALIC+Font.BOLD, 14));
		g.setColor(new Color(0x108000)); //dark green
		g.drawString("f(x)="+a+"(x-("+h+"))^2 + ("+k+")",360 ,45 );
		//
		//
		//Draw the axis of symmetry
		g.setColor(Color.orange);
		g.drawLine(screenX(h),0 , screenX(h), 300);
		
		//
		// Draw the parabola
		g.setColor(Color.cyan);
		for (double i=-17.0;i<18.0;i=i+.5){
			g.drawLine(screenX(i),screenY(f(i)),screenX(i+.5), screenY(f(i+.5)));
		}
		//
		// Draw vertex 
		g.setColor(Color.yellow);
		g.drawOval(screenX(h)-1,screenY(k)-1,2,2);
		}//end of paraboloa drawing
		
		
       
        
        // Draw Controls
        g.setColor(Color.red);
        g.fillOval(ax-5,ay-5,10,10);
        g.setColor(Color.blue);
        g.fillOval(bx-5,by-5,10,10);
        g.setColor(Color.magenta);
        g.fillOval(cx-5,cy-5,10,10);
        g.setColor(Color.black);
        
        g.setFont (new Font("serif", Font.ITALIC + Font.BOLD, 16));
		g.setColor(Color.black);
		g.drawString("f(x)=", 352, 28);
		if(a!=0)g.drawString("x", 415, 28);
        if (b!=0) g.drawString("x", 478, 28);
        g.setFont (new Font("serif", Font.BOLD, 12));
        if (a!=0)g.drawString("2", 422, 21);
        		
		// Draw the Equation in Standard form
        g.setFont (new Font("sansserif", Font.BOLD, 16));
        g.setColor(Color.red);
		if (a!=0) g.drawString(Math.abs(a)+"", 390, 28);
        g.setColor(Color.blue);
		if (b!=0) g.drawString(Math.abs(b)+"", 445, 28);
        g.setColor(Color.magenta);
		if (c!=0) g.drawString(Math.abs(c)+" ",500, 28);
		g.setColor(Color.black);
         g.setFont (new Font("serif", Font.BOLD, 20));
        if (a<0) {
			g.setColor(Color.red);
			g.drawString("-", 385, 28);
			g.setColor(Color.black);
			}
        if (b<0) g.drawString("-",430, 28);
        if (b>0) g.drawString("+", 430, 30);
		if (c<0) g.drawString("-",488, 28);
        if (c>0) g.drawString("+", 488, 30);

        g.setFont (new Font("serif", Font.ITALIC + Font.BOLD, 12));
        
        g.drawString("a = "+a,S1_LOCATION-15, SLIDER_TOP-12);
        g.drawString("b = "+b,S2_LOCATION-15, SLIDER_TOP-12);
        g.drawString("c = "+c,S3_LOCATION-15, SLIDER_TOP-12);
        g.drawLine(S1_LOCATION,SLIDER_TOP,S1_LOCATION,SLIDER_BOTTOM);
        g.drawLine(S2_LOCATION,SLIDER_TOP,S2_LOCATION,SLIDER_BOTTOM);
        g.drawLine(S3_LOCATION,SLIDER_TOP,S3_LOCATION,SLIDER_BOTTOM);
		for(int j=0;j<21;j=j+5){
		 g.drawLine(S1_LOCATION-6,SLIDER_TOP+j*SLIDER_LENGTH/20,S1_LOCATION+6,SLIDER_TOP+j*SLIDER_LENGTH/20);
		 g.drawLine(S2_LOCATION-6,SLIDER_TOP+j*SLIDER_LENGTH/20,S2_LOCATION+6,SLIDER_TOP+j*SLIDER_LENGTH/20);
		 g.drawLine(S3_LOCATION-6,SLIDER_TOP+j*SLIDER_LENGTH/20,S3_LOCATION+6,SLIDER_TOP+j*SLIDER_LENGTH/20);
		}
    }
    public void mouseMoved(MouseEvent e) {}
    public void mouseDragged(MouseEvent e) {
    int mx=e.getX();
    int my=e.getY();
    // check if inside red or blue dot
    // put in approporiate 
        //if (Math.abs(my-ry)<17 && Math.abs(mx-rx)<17){  
        if (my>SLIDER_TOP-17 && Math.abs(mx-S1_LOCATION)<17){        
		ax = S1_LOCATION;
                if (my>SLIDER_BOTTOM) my=SLIDER_BOTTOM;
                if (my<SLIDER_TOP) my=SLIDER_TOP;
                ay = my;
               	a=(190-ay)/10.0;	
        }
        if (my>=SLIDER_TOP-17 && Math.abs(mx-S2_LOCATION)<17){        
		bx = S2_LOCATION;
                if (my>SLIDER_BOTTOM) my=SLIDER_BOTTOM;
                if (my<SLIDER_TOP) my=SLIDER_TOP;
                by = my;
               	b=(190-by)/2.0;	
        }
        if (my>=SLIDER_TOP-17 && Math.abs(mx-S3_LOCATION)<17){        
		cx = S3_LOCATION;
                if (my>SLIDER_BOTTOM) my=SLIDER_BOTTOM;
                if (my<SLIDER_TOP) my=SLIDER_TOP;
                cy = my;
               	c=(190-cy)/2.0;	
        }
        repaint();

    }
}