// 3D Gauss mountains,  Evgeny Demidov  10 Oct 2001
  import java.awt.*;
  import java.awt.event.*;
  import java.util.StringTokenizer;
  public class applet-math-3d-lorenze extends java.applet.Applet
      implements MouseListener, MouseMotionListener {
    int n = 2, n1,  h,w,h2,w2, mx0,my0,  xPol[],yPol[];
    double fiX = .2, fiY = .3, dfi = .01, scale = 1, m20,m21,m22;
    double vert[][][], vert1[][][], Norm[][][][], Norm1z[][][];
    Image buffImage;     Graphics buffGraphics;
    Color[] col;
    boolean painted;
  
  public void init(){
    w = getSize().width;  h = getSize().height;   w2 = w/2;  h2 = h/2;
    String s=getParameter("N");  if (s != null) n = Integer.parseInt(s);
    xPol = new int[3];  yPol = new int[3];
    buffImage = createImage(w, h);   buffGraphics = buffImage.getGraphics();
    col = new Color[256];
    for (int i = 0; i < 256; i++) col[i] = new Color(i, i, i);
    s = getParameter("bgColor"); if (s != null){
    StringTokenizer st = new StringTokenizer(s);
     int red = Integer.parseInt(st.nextToken());
     int green = Integer.parseInt(st.nextToken());
     int blue = Integer.parseInt(st.nextToken());
     setBackground( new Color(red, green, blue));}
    else setBackground(new Color(255,255,255));
    addMouseListener(this);
    addMouseMotionListener(this);
    setup();
  }
  
  public void setup(){
    n1 = n-1;
    vert = new double[n][n][3];  vert1 = new double[n][n][2];
    double n2 = n/2., dx = w2/n2;
    for (int i = 0; i < n; i++) 
     for (int j = 0; j < n; j++){
      double x = dx*i - w2,  z = dx*j - w2;
      vert[i][j][0] = x;  vert[i][j][1] = Fun(x,z);  vert[i][j][2] = z;}
    Norm = new double[n][n][2][3];  Norm1z = new double[n][n][2];
    for (int i = 0; i < n1; i++)
     for (int j = 0; j < n1; j++){
      Norm[i][j][0][0] = vert[i][j][1] - vert[i+1][j][1];
      Norm[i][j][0][1] = dx;
      Norm[i][j][0][2] = vert[i+1][j][1] - vert[i+1][j+1][1];
      double mod = Math.sqrt(Norm[i][j][0][0]*Norm[i][j][0][0] + Norm[i][j][0][1]*
       Norm[i][j][0][1] + Norm[i][j][0][2]*Norm[i][j][0][2]) / 255.5;
      Norm[i][j][0][0] /= mod; Norm[i][j][0][1] /= mod; Norm[i][j][0][2] /= mod;
      Norm[i][j][1][0] = vert[i][j+1][1] - vert[i+1][j+1][1];
      Norm[i][j][1][1] = dx;
      Norm[i][j][1][2] = vert[i][j][1] - vert[i][j+1][1];
      mod = Math.sqrt(Norm[i][j][1][0]*Norm[i][j][1][0] + Norm[i][j][1][1]*
       Norm[i][j][1][1] + Norm[i][j][1][2]*Norm[i][j][1][2]) / 255.5;
      Norm[i][j][1][0] /= mod; Norm[i][j][1][1] /= mod; Norm[i][j][1][2] /= mod;}
    rotate();
  }
  
  public double Fun(double x, double z){
    return 2000000./(x*x + z*z + 10000.) - 100.;
  }
  
  public void destroy() {
    removeMouseListener(this);
    removeMouseMotionListener(this);
  }
  public void mouseClicked(MouseEvent e){}       // event handling
  public void mousePressed(MouseEvent e) {
    mx0 = e.getX();  my0 = e.getY();
    if ( e.isControlDown() ) {
      n /= 2;  if (n < 4) n = 4;
      setup();
      repaint();}
    if ( e.isAltDown() ){
      n *= 2;
      setup();
      repaint();}
    e.consume();
  }
  public void mouseReleased(MouseEvent e){}
  public void mouseEntered(MouseEvent e) {}
  public void mouseExited(MouseEvent e)  {}
  public void mouseDragged(MouseEvent e) {
    int x1 = e.getX();  int y1 = e.getY();
    if ( e.isShiftDown() )  scale *= Math.exp(-(y1 - my0)/(double)w);
    else   fiX += dfi*(y1 - my0);
    fiY += dfi*(x1 - mx0);   mx0 = x1;  my0 = y1;
    rotate();
    repaint();
    e.consume();
  }
  
  public void rotate(){
    double ct = Math.cos(fiX), cf = Math.cos(fiY),
           st = Math.sin(fiX), sf = Math.sin(fiY),
           m00 =  scale*cf,    m02 =  scale*sf,
           m10 = scale*st*sf, m11 =  scale*ct, m12 = -scale*st*cf;
           m20 = -ct*sf; m21 = st; m22 = ct*cf;
    for (int i = 0; i < n; i++)
     for (int j = 0; j < n; j++){
      vert1[i][j][0] = m00*vert[i][j][0] + m02*vert[i][j][2];
      vert1[i][j][1] = m10*vert[i][j][0] + m11*vert[i][j][1] + m12*vert[i][j][2];}
    for (int i = 0; i < n1; i++)
     for (int j = 0; j < n1; j++)
      for (int k = 0; k < 2; k++)
       Norm1z[i][j][k] = m20*Norm[i][j][k][0] + m21*Norm[i][j][k][1] +
        m22*Norm[i][j][k][2];
    painted = false;
  }
  
  public void mouseMoved(MouseEvent e) {}
  
  public void paint(Graphics g) {
   if ( !painted ){
    buffGraphics.clearRect(0, 0, w, h);
    int ib=0, ie=n1, sti=1,  jb=0, je=n1, stj=1;
    if (m20 < 0){ ib = n1; ie = -1; sti = -1;}
    if (m22 < 0){ jb = n1; je = -1; stj = -1;}
    for (int i = ib; i != ie; i += sti)
     for (int j = jb; j != je; j += stj){
      if (Norm1z[i][j][0] > 0){
       xPol[0] = w2 + (int)vert1[i][j][0];
       xPol[1] = w2 + (int)vert1[i+1][j][0];
       xPol[2] = w2 + (int)vert1[i+1][j+1][0];
       yPol[0] = h2 - (int)vert1[i][j][1];
       yPol[1] = h2 - (int)vert1[i+1][j][1];
       yPol[2] = h2 - (int)vert1[i+1][j+1][1];
       buffGraphics.setColor(col[(int)(Norm1z[i][j][0])]);
       buffGraphics.fillPolygon(xPol,yPol, 3);}
      if (Norm1z[i][j][1] > 0){
       xPol[0] = w2 + (int)vert1[i][j][0];
       xPol[1] = w2 + (int)vert1[i][j+1][0];
       xPol[2] = w2 + (int)vert1[i+1][j+1][0];
       yPol[0] = h2 - (int)vert1[i][j][1];
       yPol[1] = h2 - (int)vert1[i][j+1][1];
       yPol[2] = h2 - (int)vert1[i+1][j+1][1];
       buffGraphics.setColor(col[(int)(Norm1z[i][j][1])]);
       buffGraphics.fillPolygon(xPol,yPol, 3);} }
    painted = true;}
   g.drawImage(buffImage, 0, 0, this);
   showStatus( "n=" + n);
  }
  public void update(Graphics g){ paint(g); }
  
  }