source: git/Singular/LIB/surf.lib @ 05d2e8

///////////////////////////////////////////////////////////////////////////////
version="$Id: surf.lib,v 1.16 2001-01-10 15:40:19 Singular Exp $";
category="Visualization";
info="
LIBRARY: surf.lib    Procedures for Graphics with Surf
AUTHOR: Hans Schoenemann, 
        the program surf is written by Stefan Endrass

NOTE:
 @texinfo
 To use this library requires the program @code{surf} to be installed.
 @code{surf} is only available for Linux PCs and Sun workstations.
 You can download @code{surf} either from
  @uref{http://sourceforge.net/projects/surf}
  or from @uref{ftp://www.mathematik.uni-kl.de/pub/Math/Singular/utils/}.
 @end texinfo

PROCEDURES:
 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,list #)
"USAGE:   plot(I);  I ideal
RETURN: nothing
NOTE: requires the external program 'surf' to be installed
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)
  {
    ERROR("Cannot plot equations with", n, "variables");
  }
  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=1.5;");
    if (size(#)>0) 
    {
      write(l,#[1]);
    }
    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;");
     if (size(#)>0) 
       {   
         write(l,#[1]);
       }
      write(l,"surface=",I[1],";");
      write(l,"draw_surface;");
    }
    else
    {
      ERROR("cannot plot"+string(ncols(I))+"equations in"
             +string(n)+"variables");
    }
  }
  string surf_call = "surf ";
  if (defined(extra_surf_opts))
  {
    surf_call = surf_call + extra_surf_opts + " ";
  }
//  "calling surf (by Stephan Endrass) for drawing";
  i=system("sh",surf_call + l +" >/dev/null 2>&1");
  if (i!=0)
  {
    ERROR("calling `surf` failed. (the shell return the error code"
          +string(i)+")."+newline+
    "probably the executable `surf` is not found.");
  }
  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);


}
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