// Interactive 2D B-spline, Evgeny Demidov  5 August 2001
  import java.awt.*;
  import java.awt.event.*;
  import java.util.StringTokenizer;
  
  public class applet-math-bspline extends java.applet.Applet
    implements MouseMotionListener{
  Image buffImage;          Graphics buffGraphics;
  int n=1, k=2, n1, nt, Tmin,Tmax, w,h,h1,w2;
  double[] Px,Py, ti;
  double N[][];
  Color col[];
  
  public void drawFun(){
    double step = (ti[nt-1]-ti[0])/(w2-.9), t = ti[0];
    Color[] iColor = {Color.red, new Color(0f,.7f,0f), Color.blue, Color.magenta,
     new Color(0f,.8f,.8f), new Color(.9f,.9f,0f), Color.gray };
    buffGraphics.clearRect(0,0, w, h);
    Tmin = (int)((ti[k-1]-ti[0])/step) + 1;
    Tmax = (int)((ti[n1]-ti[0])/step);
    int i1 = 0;
    for (int l = 0; l < w2; l++){
     while (t >= ti[i1] ) i1++;
     int i = i1-1;
     col[l] = iColor[(i+8-k) % 7];
     for (int j = 0; j < nt; j++) N[j][l] = 0;
     N[i][l] = 1;
  
     for (int m = 2; m <= k; m++){        //  basis functions calculation
      int jb = i-m+1;  if (jb < 0) jb = 0;
      for (int j = jb; j <= i; j++){
       N[j][l] = N[j][l]*(t - ti[j])/(ti[j+m-1] - ti[j]) +
        N[j+1][l]*(ti[j+m] - t)/(ti[j+m] - ti[j+1]);}}
  
     t += step;}
    for (int j = 0; j < n1; j++){
     buffGraphics.setColor(iColor[j % 7]);
     t = ti[0];
     int to = (int)t;
     for (int l = 1; l < w2; l++){
      t += step;
      int t1 = (int)t;
      buffGraphics.drawLine(to, h1-(int)(h1*N[j][l-1]),
       t1, h1-(int)(h1*N[j][l]) );
      to = t1;}}
    for (int l = k; l <= n1; l++){
     buffGraphics.setColor(iColor[(l-k) % 7]);
     buffGraphics.drawLine((int)ti[l-1], 1, (int)ti[l], 1);}
    buffGraphics.setColor(Color.black);
    for (int l = 0; l < nt; l++)
     buffGraphics.drawRect((int)ti[l]-1, 0, 3,3);
  }
  
  public void drawSpline(){
    int X,Y;
    buffGraphics.clearRect(0,0, w2, h);
    buffGraphics.setColor(Color.blue);
    for (int i = 0; i < n1; i++){
     X = (int)Px[i];  Y = h1-(int)Py[i];
     buffGraphics.drawRect(X-1,Y-1, 3,3);}
    if ( k > 2 ){
     int Xo = (int)Px[0], Yo = h1-(int)Py[0];
     for (int i = 1; i < n1; i++){
      X = (int)Px[i];  Y = h1-(int)Py[i];
      buffGraphics.drawLine(Xo,Yo, X,Y);
      Xo = X;  Yo = Y;}
    }
    double sX = 0, sY = 0;
    for (int j = 0; j < n1; j++){
     sX += Px[j]*N[j][Tmin];  sY += Py[j]*N[j][Tmin];}
    int Xold = (int)sX, Yold = h1-(int)sY;
    for (int k = Tmin+1; k <= Tmax; k++){
     sX = 0;  sY = 0;
     for (int j = 0; j < n1; j++){
       sX += Px[j]*N[j][k];  sY += Py[j]*N[j][k];}
     X = (int)sX;  Y = h1-(int)sY;
     buffGraphics.setColor(col[k]);
     if ( (X < w2) && (Xold < w2) ) buffGraphics.drawLine(Xold,Yold, X,Y );
     Xold = X; Yold = Y;
    }
  }
  
  public void init() {
    w = Integer.parseInt(getParameter("width"));
    h = Integer.parseInt(getParameter("height"));  h1 = h-1; w2 = w/2;
    String s = getParameter("N");
    if (s != null){
     StringTokenizer st = new StringTokenizer(s);
     n = Integer.parseInt(st.nextToken());
     k = Integer.parseInt(st.nextToken());}
    n1 = n+1;
    nt = n+k+1;
    Px = new double[n1];  Py = new double[n1];  ti = new double[nt+k];
    col = new Color[w2];
    N = new double[nt+1][w2];
    s=getParameter("pts");
    if (s != null){
     StringTokenizer st = new StringTokenizer(s);
     for (int i = 0; i < n1; i++){
      Px[i] = w2*Double.valueOf(st.nextToken()).doubleValue();
      Py[i] = h1*Double.valueOf(st.nextToken()).doubleValue();}}
    else{ Px[0] = .2*w2; Px[1] = .8*w2;  Py[0] = .8*h1; Py[1] = .2*h1;}
    s=getParameter("knots");
    if (s != null){
     StringTokenizer st = new StringTokenizer(s);
     for (int i = 0; i < nt; i++)
      ti[i] = Double.valueOf(st.nextToken()).doubleValue();}
    else{ ti[0] = 0; ti[1] = 1; ti[2] = 2; ti[3] = 3; }
    double to = ti[0], dt = ti[nt-1]-to;
    for (int i = 0; i < nt; i++) ti[i] = w2 + w2*(ti[i]-to)/dt;
    buffImage = createImage(w, h);
    buffGraphics = buffImage.getGraphics();
    setBackground(Color.white);
    buffGraphics.clearRect(0,0, w, h);
    addMouseMotionListener(this);
    drawFun();
    drawSpline();
  }
  
  public void destroy(){ removeMouseMotionListener(this); }
  public void mouseMoved(MouseEvent e){}  //1.1 event handling
  
  public void mouseDragged(MouseEvent e) {
    int y = h1 - e.getY();  if (y < 0) y = 0;  if (y > h1) y = h1;
    int x = e.getX();
     int iMin = 0;
     double Rmin = 1e10, r2,xi,yi;
    if ( x < w2){
     if (x > w2-10) return;
     if (x < 0) x = 0;
     for (int i = 0; i < n1; i++){
      xi = (x - Px[i]); yi = (y - Py[i]);
      r2 = xi*xi + yi*yi;
      if ( r2 < Rmin ){ iMin = i; Rmin = r2;}}
     Px[iMin] = x; Py[iMin] = y;}
    else{
     if ( x > w ) x = w;
     for (int i = 0; i < nt; i++)
      if ( (r2 = Math.abs(ti[i]-x) ) < Rmin ){ iMin = i; Rmin = r2;}
     ti[iMin] = x;
     drawFun();}
    drawSpline();
    repaint();
  }
  
  public void paint(Graphics g) {
    g.drawImage(buffImage, 0, 0, this);
  //  showStatus( " " + x +"  " + y);
  }
  
  public void update(Graphics g){ paint(g); }
  
  }