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1; # Prevent Octave from thinking that this is a function
   # though one is defined here
   
  function w = f(x2,y2,z2,c,r,e) 
   x  = (x2-c(1))/r(1);
   y  = (y2-c(2))/r(2);
   z  = (z2-c(3))/r(3);

   xp = x+sin((z*0.5).^2).*z*0.2;
   yp = y+cos((z*0.5).^2).*z*0.2;
   yp2 =  -y+cos((z*0.5).^2).*z*0.2;
   zp = z;


   # function at origin must be <0, and >0 far enough away.  w=0 defines the surface
   w = (1.0)./(((((1/2)*z-0)).^4+(1.66*x).^2+(1*y).^2)+0.01);
   w = w + (1.0)./((((1/4)*zp).^2+(5*xp).^4+(3*(yp-1.2)).^4)+0.01);
   w = w + (1.0)./((((1/4)*zp).^2+(5*xp).^4+(3*(yp2-1.2)).^4)+0.01);
   w = w- 1.0;
   endfunction;