// July 2002, java applet by Oliver Knill  for the CCP project
// Vector Fields and Line Integrals  by Oliver Knill and Dale Winter
// Harvard University, Nov 15, 2002. See
// http://www.math.duke.edu/education/ccp/materials/mvcalc/vfield/index.html
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License of the Free Software Foundation for
// details.  Compile with 
// javac pencil.java vectorfield.java lineintegral.java

import java.lang.Math;
import java.awt.*;

class vectorfield {

private int cx1, cy1;             // previous plot point
private int cx2, cy2;             // next plot point
private int cx3, cy3;             // midpoint of last two points
private int cx1_old, cy1_old;     // previous plot point
private int cx2_old, cy2_old;     // previous plot point
private int grid1=10;             // number of grid points for vector field
private int grid=1000;            // number of grid points *100 for vector field
private int re,gr,bl;             // red, green, blue
private int re0,gr0,bl0;          // red, green, blue
private int i,j,k;                // indices
private double sum=0;             // line integral sum
private int x,y,x_old,y_old;      // pointer location 
private int left_border=80;       // left border for menu
private int xx[];                 // x-coordinates of traced curve
private int yy[];                 // y-coordinates of traced curve
private int length=1000;          // maximal number of points in curve
private int t=-1;                 // time, parameter to trace curve
private int dx=0,dy=0;            // distance of beginning and end point
private int tx=14, ty=70;         // place to put comments
private int n0,n0_old;            // sums to be written 

private boolean finished=false;   // curve closed
private boolean smoothed=false;   // curve smoothed

public void draw_text(Graphics g, int red, int green, int blue,
                         int center_x,int center_y,
                         int size,String text) {
  g.setColor(new Color(red,green,blue));
  Font f = new Font("Helvetica",Font.BOLD,size); g.setFont(f);
  g.drawString(text,center_x+10,center_y);
}

public vectorfield(int width,int height) {
  grid=100*grid1;
  xx=new int[length]; for (i=0; i<length; i++) { xx[i]=0; }
  yy=new int[length]; for (i=0; i<length; i++) { yy[i]=0; }
  finished=false;
  smoothed=false;
}

private int ff(int s, int xx, int yy, int field) {
  double xxx,yyy,rrr; 
  int res;
  xxx=1.0*xx/grid; yyy=1.0*yy/grid;
  rrr=Math.sqrt(xxx*xxx+yyy*yyy);  if (rrr==0) {rrr=1; }
  switch(field) {
    case 1:  res=(int) (s*xxx/rrr);   break; 
    case 2:  res=(int) (-s*yyy/rrr);  break; 
    case 3:  res=(int) (s*(xxx-yyy/rrr));  break; 
    case 4:  res=(int) (s*xxx/rrr);  break; 
    case 5:  res=(int) (s*xxx*yyy/(rrr*rrr));  break; 
    case 6:  res=(int) (s*xxx);  break; 
    case 7:  res=(int) (s*yyy);  break; 
    default: res=0; break;
  }
  return(res); 
}

private int gg(int s, int xx, int yy, int field) {
  double xxx,yyy,rrr; 
  int res;
  xxx=1.0*xx/grid; yyy=1.0*yy/grid;
  rrr=Math.sqrt(xxx*xxx+yyy*yyy); if (rrr==0) {rrr=1; }
  switch(field) {
    case 1:  res=(int) (s*yyy/rrr);  break; 
    case 2:  res=(int) (s*xxx/rrr);  break; 
    case 3:  res=(int) (s*(xxx+yyy/rrr));  break; 
    case 4:  res=(int) 0;  break; 
    case 5:  res=(int)  (s*(xxx*xxx/(rrr*rrr)-yyy*yyy/(rrr*rrr)));  break;
    case 6:  res=(int) (s*yyy); break; 
    case 7:  res=(int) (s*xxx); break; 
    default: res=0; break;
  }
  return(res); 
}

public void draw_vector(Graphics g, int x1, int y1, int x2, int y2) {
int d,e,r,a,b,u,v;
int len; 

d=x1-x2; e=y1-y2;                                 // (d,e) translated to zero
r  =(int) (Math.sqrt(d*d+e*e)); if (r==0) {r=1;}  // length
len=(int) (r/3); 
a=(int) (len*d/r);  b=(int) (len*e/r);            // unit vector 
u=(int) (-len*e/r); v=(int) (len*d/r);            // orthogonal unit vector 
g.drawLine(x1,y1,x2+a,y2+b); 
g.drawLine(x2,y2,x2+a-u,y2+b-v); 
g.drawLine(x2,y2,x2+a+u,y2+b+v); 
g.drawLine(x2+a-u,y2+b-v,x2+a+u,y2+b+v); 
}

public void draw_field(Graphics g,
                         int red, int green, int blue,
                         int center_x,int center_y,
                         int scale_x,int scale_y, int grid, 
                         int vector_length,int vectorfield) {
  g.setColor(new Color(red,green,blue));
  for (i=-grid1+1; i<grid1; i++) { for (j=-grid1+1; j<grid1; j++) {
      cx1=(int) (center_x+scale_x*i/grid1);
      cy1=(int) (center_y+scale_y*j/grid1); 
      cx2=(int) (cx1+ff(vector_length,100*i,100*j,vectorfield)); 
      cy2=(int) (cy1+gg(vector_length,100*i,100*j,vectorfield)); 
      draw_vector(g,cx1,cy1,cx2,cy2);
  } }
}

public void draw_single_vector(Graphics g,
                         int red, int green, int blue,
                         int center_x,int center_y,
                         int vector_length,int vectorfield) {
  cx1=center_x;
  cy1=center_y;
  cx2=(int) (cx1+2*ff(vector_length,(int) ((cx1-300)*grid/250),(int) ((cy1-250)*grid/250),vectorfield));
  cy2=(int) (cy1+2*gg(vector_length,(int) ((cx1-300)*grid/250),(int) ((cy1-250)*grid/250),vectorfield));
  g.setColor(new Color(0,0,0));
  if (cx1_old>left_border) { draw_vector(g,cx1_old,cy1_old,cx2_old,cy2_old); }
  g.setColor(new Color(red,green,blue));
  if (center_x>left_border) { draw_vector(g,cx1,cy1,cx2,cy2); }
  cx1_old=cx1; cy1_old=cy1; 
  cx2_old=cx2; cy2_old=cy2; 
}

public void put_single_vector(Graphics g,
                         int red, int green, int blue,
                         int center_x,int center_y,
                         int vector_length,int vectorfield) {
  cx1=center_x;
  cy1=center_y;
  cx2=(int) (cx1+2*ff(vector_length,(int) ((cx1-300)*grid/250),(int) ((cy1-250)*grid/250),vectorfield));
  cy2=(int) (cy1+2*gg(vector_length,(int) ((cx1-300)*grid/250),(int) ((cy1-250)*grid/250),vectorfield));
  g.setColor(new Color(red,green,blue));
  draw_vector(g,cx1,cy1,cx2,cy2); 
  cx1_old=cx1; cy1_old=cy1;
  cx2_old=cx2; cy2_old=cy2;
}



public void erase(Graphics g) {
int l;
   for (l=1; l<8; l++) { draw_field(g,0,0,0,300,250,250,250,10,15,l); }
}

public void menu(Graphics g,boolean over,int vectorfield) {
   re0=255; gr0=127; bl0=0; 
   if (over) { sum=0; re=255; gr=255; bl=0; } else { re=255; gr=200; bl=0; }
   write_sum(g,sum);
   
   g.setColor(new Color(125,0,125));               // menu field around result
   g.drawRect(0,0,50,75);

   g.setColor(new Color(125,50,0));                // menu field around vectorfields
   g.drawRect(0,left_border,50,400);

   g.setColor(new Color(255,200,0));
   draw_text(g,re0,gr0,bl0,0,100,12,"New"); 
   for (k=1; k<8; k++) { if (k !=vectorfield) { draw_text(g,re0,gr0,bl0,8,100+k*50,30,""+k); } }
   draw_text(g,re,gr,bl,8,100+vectorfield*50,30,""+vectorfield); 
}

public void read_pointer(int x, int y) { 
  this.x = x; this.y = y; 
}

public void erase_old_curve(Graphics g) {
  if (t>1) {
    g.setColor(new Color(0,0,0));           
    g.fillOval(xx[2]-3,yy[2]-3,6,6); 
    for (i=2; i<t; i++) { g.drawLine(xx[i],yy[i],xx[i+1],yy[i+1]); }
    g.drawLine(xx[2],yy[2],xx[t],yy[t]);
  }
  sum=0; write_sum(g,sum); 
}

private void draw_new_curve(Graphics g) {
  g.setColor(new Color(0,255,0));      
  if (t>1) {
    g.fillOval(xx[2]-3,yy[2]-3,6,6); 
    for (i=2; i<t; i++) { g.drawLine(xx[i],yy[i],xx[i+1],yy[i+1]); }
    if (finished) {g.drawLine(xx[2],yy[2],xx[t],yy[t]); }
  }
}

public void smooth_curve() {
int xx1[],yy1[]; 
xx1=new int[length]; yy1=new int[length];
for (i=0; i<length; i++) { xx1[i]=xx[i]; yy1[i]=yy[i]; }
  for (i=2; i<=t; i++) { 
    if (i==2)     { j=t;   } else {j=i-1;   } 
    if (i==t)     { k=2;   } else {k=i+1;   } 
    xx[i]=(int) ((xx1[j]+xx1[k])/2); 
    yy[i]=(int) ((yy1[j]+yy1[k])/2); 
  }
}

public void write_sum( Graphics g,double sum1 ) {
  Font f = new Font("Helvetica",Font.BOLD,12); g.setFont(f);
  n0=(int) (sum1/10);

  g.setColor(new Color(0,0,0));                   // erase old number
  g.drawString(""+n0_old,tx,ty);

  g.setColor(new Color(255,0,255));               // write integral int v ds 
  g.fillOval(            tx-9 ,ty-58,6,6); 
  g.setColor(new Color(0,0,0)); 
  g.fillOval(tx-7,ty-56,4,4); 
  g.setColor(new Color(255,0,255)); 
  g.drawString("|"      ,tx-10,ty-46); 
  g.drawString("| v ds=",tx-10,ty-40); 
  g.drawString("|"      ,tx-10,ty-43); 
  g.drawString("|"      ,tx-10,ty-33); 
  g.fillOval(            tx-13,ty-35,6,6); 
  g.setColor(new Color(0,0,0)); 
  g.fillOval(tx-13,ty-36,4,4); 

  g.setColor(new Color(255,0,255));              // write new number
  g.drawString(""+n0,tx,ty);
  n0_old=n0;                                     // store old value
}

public void line_integral(Graphics g,int c) {
sum=0; 
for (i=2; i<=t; i++) {
   if (i==2)     { j=t;   } else {j=i-1;   }
   cx1=(xx[i]-300)*grid/250; cy1=(yy[i]-250)*grid/250; 
   cx2=(xx[j]-300)*grid/250; cy2=(yy[j]-250)*grid/250; 
   cx3=(int) (cx1+cx2)/2; cy3=(int) (cy1+cy2)/2; 
   sum+=((cx1-cx2)*ff(10,cx3,cy3,c)+(cy1-cy2)*gg(10,cx3,cy3,c));
}
if (t>0) { write_sum(g,sum); }
}


public void trace_curve(Graphics g, int c) {
for (i=2; i<=t; i=i+5) {
  put_single_vector(g,255,255,0,xx[i],yy[i],20,c);
}
}

public void erase_trace_curve(Graphics g) {
for (i=2; i<=t; i=i+5) {
  for (j=1; j<8; j++) { put_single_vector(g,0,0,0,xx[i],yy[i],20,j); }
}
}

public void update(Graphics g,int c) {
  draw_field(g,255,127,0,300,250,250,250,10,15,c);
  if (!finished) { draw_single_vector(g,255,255,0,x,y,20,c); }
  else           { draw_single_vector(g,0,0,0,x,y,20,c);     }

  if (x>left_border)           {
     draw_new_curve(g);
  }
  if (finished && (!smoothed)) {
      erase_old_curve(g);
      draw_single_vector(g,0,0,0,x,y,20,c);
      smooth_curve(); smooth_curve();
      draw_new_curve(g);
      smoothed=true;
  }
  if (finished) { 
      trace_curve(g,c); 
      line_integral(g,c); 
  }
  if (x<=left_border)   {
      erase_old_curve(g);
      erase_trace_curve(g);
      t=-1;
      finished=false;
      smoothed=false;
  }
  x_old=x; y_old=y;
  if (!finished) {
    t++; while (t>length) {t=t-length; } 
    xx[t]=x_old; yy[t]=y_old;
    if (t<=2)  { i=2; j=2; sum=0;  } else {i=t; j=t-1;   }
    cx1=(xx[i]-300)*grid/250; cy1=(yy[i]-250)*grid/250;
    cx2=(xx[j]-300)*grid/250; cy2=(yy[j]-250)*grid/250;
    cx3=(int) (cx1+cx2)/2; cy3=(int) (cy1+cy2)/2; 
    sum+=((cx1-cx2)*ff(10,cx3,cy3,c)+(cy1-cy2)*gg(10,cx3,cy3,c));
    write_sum(g,sum);
    dx=xx[t]-xx[2]; dy=yy[t]-yy[2];
  }
  if (((dx*dx+dy*dy)<20) && (t>20)) { finished=true; }

}


}