// $Id: surf.lib,v 1.3 1999-05-26 16:23:25 obachman Exp $
//
// author : Hans Schoenemann
//
///////////////////////////////////////////////////////////////////////////////
version="$Id: surf.lib,v 1.3 1999-05-26 16:23:25 obachman Exp $";
info="
LIBRARY: surf.lib    PROCEDURES FOR GRAPHICS WITH SURF (by Stephan Endrass)

 plot(I);  plots curves and surfaces
";

///////////////////////////////////////////////////////////////////////////////
static proc num_of_vars(ideal I)
{
  intvec v;
  int i;
  poly p;
  for(i=size(I);i>0;i--)
  {
    p=I[i];
    while(p!=0)
    {
      v=v+leadexp(p);
      p=p-lead(p);
    }
  }
  return(v);
}

proc  plot(ideal I)
"USAGE:   plot(I);  I ideal
RETURN:
NOTE: 
EXAMPLE: example plot; shows an example
"
{
  string l="/tmp/surf"+string(system("pid"));
  def base=basering;
  intvec v=num_of_vars(I);
  int i,j,n;
  for(i=size(v);i>0;i--)
  {
    if (v[i]!=0) { n++; }
  }
  if (n==0 or n>3)
  {
    "Cannot plot equations with", n, "variables";
    return();
  }
  ring r=0,(x,y,z),dp;
  short=0;
  map phi=base,0;
  j=1;
  for(i=1;i<=size(v);i++)
  {
    if (v[i]!=0)
    {
      phi[i]=var(j);
      j++;
      if(j==4) break;
    }
  }
  ideal I=simplify(phi(I),2);
  if (ncols(I)==1 and n<=2) // curve
  {
    write(":w "+l,"clip=none;");
      write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;");
    write(l,
    "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;");
    write(l, "curve_green=0; curve_blue=0; curve_width=4.5;");
    write(l,"curve=",I[1],";");
    write(l,"draw_curve;");
  }
  else
  {
    if (ncols(I)==1 and n==3) // surface
    {
      write(":w "+l,
      "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;");
     write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;");
      write(l,"rot_x=0.14; rot_y=-0.3;");
      write(l,"surface=",I[1],";");
      write(l,"draw_surface;");
    }
    else
    {
      "cannot plot",ncols(I),"equations in",n,"variables";
      return();
    }
  }
//  "calling surf (by Stephan Endrass) for drawing";
  i=system("sh","surf "+l+" >/dev/null 2>&1");
  i=system("sh","/bin/rm "+l);
}
example
{ "EXAMPLE:"; echo =2;
   // ---------  plane curves ------------
   ring rr0 = 0,(x1,x2),dp;

   ideal I = x1^3 - x2^2;
   plot(I);
   ideal J = x1^2-x1-x2^3;
   plot(J); 

   ring rr1 = 0,(x,y,z),dp;
   ideal I(1) = 2x2-1/2x3 +1-y+1;
   plot(I(1));
   ideal I(2) = x3-x-y; 
   plot(I(2));

  //  ---- Singular Logo --------------
  poly logo = ((x+3)^3 + 2*(x+3)^2 - y^2)*(x^3 - y^2)*((x-3)^3-2*(x-3)^2-y^2);
  plot(logo);

 
   // --------- implicit curves ------------
   // implicit curves
   ideal I(1) = y,-x2;
   plot(I(1));
   ideal I(2) = x2,-y2 +4;
   plot(I(2));

   //the lemniscate

   ideal I(3) = x4+2x2y2 + y4, x2-y2;
   plot(I(3));

   // a critical part
   // adjust the plotregion properly to get a good picture

   poly f = (x-y)*(x2+y);
   plot(f,1); 
   ideal J = jacob(f);
   J;
   plot(J);     // bad resolution

   // ----------- surfaces -------------------
   ideal J(1) = 3xy4 + 2xy2, x5y3 + x + y6,10x2;
   plot(J(1));

   // Steiner surface

   ideal J(2) = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z;
   plot(J(2));
  
  plot(x*(x2-y2)+z2);

  // E7
  plot(x^3-x*y^3+z^2);

  // Whitney umbrella
  plot(z^2-x^2*y);

  // A1
  plot(y2-xz);


}
///////////////////////////////////////////////////////////////////////////////