/* Java Applet "Thin" computes the solution to the
   thin obstacle problem for the Dirichlet integral, for
   variable obstacle height and boundary values. This program is released
   under the GNU GPL; copyright is retained by
   the author, Danny Calegari. See http://www.gnu.org 

   For information about the thin obstacle problem, see
   the following paper:

   J. Nitsche, "Variational problems with inequalities as boundary
   conditions; or How to Fashion a Cheap Hat for Giacometti's Brother"
   Arch. Rational Mech. Anal. (35) pp. 83-112

   For applications of the thin obstacle problem to shrinkwrapping
   and a proof of the tameness conjecture, see:

   D. Calegari and D. Gabai, "Shrinkwrapping and the taming of
   hyperbolic 3-manifolds", eprint math.GT/0407151
*/

import java.applet.Applet;
import java.awt.*;
import java.awt.geom.*;
import java.awt.event.*;
import java.lang.Math;

public class thin2 extends Applet 
    implements MouseListener, MouseMotionListener, ActionListener {
    int i,j,k,l;
    int a,b,c,d,e;
    int x,y;
    int dragwhichx,dragwhichy;
    int dragwherex,dragwherey;
    int guessX,guessY;
    double r,s;
    double m,n;
    double height[][];
    double hit[][];
    int reflect;
    int polyx[],polyy[];
    int besterror,errorterm;
    int currentX, currentY;
    Polygon poly;
    int maxheight;
    Scrollbar mh = new Scrollbar(Scrollbar.HORIZONTAL,20,10,120,260);
    boolean adjuststate;
    boolean dragging;
    boolean gridon;
    Button adjustbutton, solvebutton, raisebutton, lowerbutton, gridbutton;

    
    public void init() {
	setLayout( new FlowLayout(10));
	addMouseListener(this);
	addMouseMotionListener(this);
	adjustbutton = new Button("Adjust boundary values");
	add(adjustbutton);
	adjustbutton.addActionListener(this);
	solvebutton = new Button("Solve thin obstacle problem");
	add(solvebutton);
	solvebutton.addActionListener(this);
	raisebutton = new Button("Raise obstacle");
	add(raisebutton);
	raisebutton.addActionListener(this);
	lowerbutton = new Button("Lower obstacle");
	add(lowerbutton);
	lowerbutton.addActionListener(this);
	gridbutton = new Button("Grid on/off");
	add(gridbutton);
	gridbutton.addActionListener(this);
	height = new double[40][40];
	hit = new double[40][40];
	poly = new Polygon();
	polyx = new int[4];
	polyy = new int[4];
      	maxheight=170;
	m=0.0;
	for(i=0;i<40;i++){
	    n=0.0;
	    for(j=0;j<40;j++){
	       	height[i][j]=100+70*(Math.sin(m/5.0))+100*(Math.cos(n/6.0));
		if(j==i){
		    if (height[i][j]<maxheight){
			height[i][j]=maxheight;
		    }
		}
		hit[i][j]=height[i][j];
		n=n+1.0;
	    }
	    m=m+1.0;
	}
	shrink();
	adjuststate=true;
	dragging=false;
	gridon=false;
    }
    
    public void paint( Graphics graphics ) {
	if(adjuststate==false){
	    graphics.setColor( Color.gray );
	    for(i=0;i<39;i++){
		for(j=0;j<39;j++){
		    a=100+(i*6)+(j*6);
		    x=(2*j)-(3*i);
		    b=(int) (450-x-height[i][j]);
		    c=(int) (448-x-height[i][j+1]);
		    d=(int) (451-x-height[i+1][j+1]);
		    e=(int) (453-x-height[i+1][j]);
		    polyx[0]=a;
		    polyx[1]=a+6;
		    polyx[2]=a+12;
		    polyx[3]=a+6;
		    polyy[0]=b;
		    polyy[1]=c;
		    polyy[2]=d;
		    polyy[3]=e;

		    poly=new Polygon(polyx, polyy, 3);
		    reflect=(int) (256.0*200.0/((height[i][j]-height[i][j+1])*(height[i][j]-height[i][j+1])+
			   (height[i][j+1]-height[i+1][j+1])*(height[i][j+1]-height[i+1][j+1])+200.0));
		    
		    graphics.setColor( new Color(reflect,reflect,reflect));
		    graphics.fillPolygon(poly);

		    polyy[1]=e;
		    poly=new Polygon(polyx, polyy, 3);
		    reflect=(int) (256.0*200.0/((height[i][j]-height[i+1][j])*(height[i][j]-height[i+1][j])+
			   (height[i+1][j]-height[i+1][j+1])*(height[i+1][j]-height[i+1][j+1])+200.0));
		    graphics.setColor( new Color(reflect,reflect,reflect));
		    graphics.fillPolygon(poly);

		    if(gridon==true){
			polyy[1]=c;
			poly=new Polygon(polyx, polyy, 4);
			graphics.setColor( Color.black );
			graphics.drawPolygon(poly);
		    };

		    if((i==j) && (height[i][j]==maxheight) && (height[i+1][j+1]==maxheight)){
			graphics.setColor( Color.red );
			graphics.drawLine( 100+(i*6)+(j*6),450-(2*j)+(3*i)-(int) (maxheight),
					   112+(i*6)+(j*6),450-(2*j)+(3*i)-(int) (maxheight));
		    };
		}
	    }
	} else {
	    graphics.setColor( Color.black );
	    for(i=0;i<39;i++){
		for(j=0;j<40;j=j+39){
		    a=100+(i*6)+(j*6);
		    x=(2*j)-(3*i);
		    b=(int) (450-x-height[i][j]);
		    c=(int) (453-x-height[i+1][j]);
		    graphics.drawLine(a,b,a+6,c);
		    graphics.drawRect(a-1,b-1,2,2);
		}
	    }
	    for(j=0;j<39;j++){
		for(i=0;i<40;i=i+39){
		    a=100+(i*6)+(j*6);
		    x=(2*j)-(3*i);
		    b=(int) (450-x-height[i][j]);
		    c=(int) (448-x-height[i][j+1]);
		    graphics.drawLine(a,b,a+6,c);
		    graphics.drawRect(a-1,b-1,2,2);
		}
	    }
	    graphics.setColor( Color.blue );
	    graphics.drawLine(100,450-(int) (maxheight),100+(39*6)+(39*6),
			      450-(2*39)+(3*39)-(int) (maxheight));
	    if(dragging==true){
		a=100+(dragwhichx*6)+(dragwhichy*6);
		x=(dragwhichy*2)-(3*dragwhichx);
		b=(int) (450-x-height[dragwhichx][dragwhichy]);
		graphics.setColor( Color.red );
		graphics.drawRect(a-2,b-2,4,4);
	    }
	}
    }
    
    public void shrink() {
	for(k=1;k<400;k++){
	    for(i=1;i<39;i++){
		for(j=1;j<39;j++){
		    hit[i][j]=(height[i-1][j]+height[i+1][j]+
			       height[i][j-1]+height[i][j+1])/4.0;
		    if(j==i){
			if(hit[i][j]<maxheight){
			    hit[i][j]=maxheight;
			}
		    }
		}
	    }
	    for(i=1;i<39;i++){
		for(j=1;j<39;j++){
		    height[i][j]=hit[i][j];
		}
	    }
	}
    }
    
    public void mouseClicked( MouseEvent e) { }
    public void mouseEntered( MouseEvent e) { }
    public void mouseExited( MouseEvent e) { }
    public void mousePressed( MouseEvent e) { }
    public void mouseMoved( MouseEvent e) { }
    public void mouseDragged( MouseEvent e) { 
	if (adjuststate==true) {
	    if (dragging==false) {
		dragging=true;
		besterror=20000;
		currentX = e.getX();
		currentY = e.getY();
		for(i=0;i<40;i++){
		    for(j=0;j<40;j=j+39){
			guessX=100+(i*6)+(j*6);
			guessY=(int) (450-(j*2)+(i*3)-height[i][j]);
			errorterm=((guessX-currentX)*(guessX-currentX))+
			    ((guessY-currentY)*(guessY-currentY));
			if(errorterm < besterror){
			    besterror=errorterm;
			    dragwhichx=i;
			    dragwhichy=j;
			}
		    }
		}
		for(j=0;j<40;j++){
		    for(i=0;i<40;i=i+39){
			guessX=100+(i*6)+(j*6);
			guessY=(int) (450-(j*2)+(i*3)-height[i][j]);
			errorterm=((guessX-currentX)*(guessX-currentX))+
			    ((guessY-currentY)*(guessY-currentY));
			if(errorterm < besterror){
			    besterror=errorterm;
			    dragwhichx=i;
			    dragwhichy=j;
			}
		    }
		}
	    } else {
		dragwherey=e.getY();
		height[dragwhichx][dragwhichy]=(450-(dragwhichy*2)+(dragwhichx*3))-dragwherey;
	    }
	    repaint();
	}
    }
    public void mouseReleased( MouseEvent e) {
	if(dragging==true){
	    dragging=false;
	    dragwherey=e.getY();
	    height[dragwhichx][dragwhichy]=(450-(dragwhichy*2)+(dragwhichx*3))-dragwherey;
	}
	repaint();
    }

    public void actionPerformed( ActionEvent e ) {
	if( e.getSource() == adjustbutton ) {
	    adjuststate=true;
	    repaint();
	};
	if( e.getSource() == solvebutton ) {
	    adjuststate=false;
	    shrink();
	    repaint();
	};
	if( e.getSource() == raisebutton ) {
	    maxheight=maxheight+10;
	    shrink();
	    repaint();
	};
	if( e.getSource() == lowerbutton ) {
	    maxheight=maxheight-10;
	    shrink();
	    repaint();
	};
	if( e.getSource() == gridbutton ) {
	    gridon=!gridon;
	    repaint();
	};
    }
}