//ketlib

ptL=apply((-3)..3,[#,#^2]);
kcL=[];
ctrall=12;
drwgraph=false;
Opt=["dr,2","Color=red","Msg=n"];
homectr=true;

Plotptongraph(x):=(
  regional(y);
  y=x^2;
  ptL=append(ptL,[x,y]);
  ptL=sort(ptL,[#.x]);
);

Initbezier(ptL):=(
  regional(kL,cL,pt1,pt2,tmp,tmp1);
  kL=ptL;
  cL="";
  forall(2..(length(kL)),
    pt1=kL_(#-1);
    pt2=kL_#;
    tmp=unicode(text(64+#-1),base->10);
    tmp1=tmp+"1.xy="+Textformat((2*pt1+pt2)/3,3)+";";
    parse(tmp1);
    tmp1=tmp+"2.xy="+Textformat((pt1+2*pt2)/3,3)+";";
    parse(tmp1);
    cL=cL+","+tmp+"1,"+tmp+"2";
  );
  cL="["+substring(cL,1,length(cL))+"];";
  cL=parse(cL);
  homectr=false;
  [kL,cL];
);

Preparectrpt(nn):=( //no ketjs on
  regional(tmp,tmp1,tmp2,out);
  out=[];
  forall(1..nn,
    tmp=unicode(text(64+#),base->10);
    tmp1=[4.5,YMAX-#/4];
    tmp2=[5,YMAX-#/4];
    Putpoint(tmp+"1",tmp1):Putpoint(tmp+"2",tmp2):
    inspect(parse(tmp+"1"),"ptsize",3);
    inspect(parse(tmp+"2"),"ptsize",3);
    inspect(parse(tmp+"1"),"labeled",false);
    inspect(parse(tmp+"2"),"labeled",false);
    out=concat(out,[parse(tmp+"1"),parse(tmp+"2")]);
  );
  out;
); //no ketjs off

Resetctrpt(nn):=(
  regional(tmp,tmp1,tmp2);
  forall(1..nn,
    tmp=unicode(text(64+#),base->10);
    tmp1=Textformat([4.5,YMAX-#/4],5);
    tmp2=Textformat([5,YMAX-#/4],5);
    parse(tmp+"1.xy="+tmp1+";");
    parse(tmp+"2.xy="+tmp2+";");
  );
  homectr=true;
);

//figure
Ketinit();
Setparent(Cdyname()+"fig");

Setwindow([-4,4],[-0.5,10]);
Setketcindyjs(["Grid=0.2","Nolabel=all","Color=lightgray"]);

//Preparectrpt(12); //only once
Slider("S",[-3.5,-1],[3.5,-1]);

ctr=11;
forall(1..10,
  Listplot(text(ctr),[[-3,#],[3,#]],["dr,0.5","Msg=n"]);
//  Expr([[0,#],"w",text(#)]);
  Vtickmark([#,text(#)]);
  ctr=ctr+1;
);

forall(remove((-3)..3,[0]),
  Listplot(text(ctr),[[#,0],[#,10]],["dr,0.5","Msg=n"]);
//  Expr([[#,0],"s",text(#)]);
  Htickmark([#,text(#)]);
  ctr=ctr+1;
);

Expr([1,YMAX],"ne","y=x^2",["size->20"]);


if(length(ptL)>0,
  Pointdata("0",ptL,["Size=3","Color=blue","Msg=n"]);
);
if(length(kcL)==0, //no ketjs on
  tmp=Preparectrpt(ctrall);
); //no ketjs off
if(!homectr,
  Bezier("1",kcL_1,kcL_2,["Num=20"]);
  tmp=apply(bz1,abs(#_2-(#_1)^2));
  mean=sum(tmp)/length(bz1);
  tmp="D="+Sprintf(mean*1000,2);//+"($\times 10^{-3}$)";
   Expr(A,"e",tmp,["notex","size->24"]);
);

if(drwgraph,
  Plotdata("qg","x^2","x",["Color=blue"]);
);


Figpdf();
Windispg();