// ketlb
use("KetCindyPlugin");
Dircdy=loaddirectory;
setdirectory(plugindirectory);
import("ketcindy.ini");

X.x=pi;
pC=[-1,0];
pO=[0,0];
Lastx=0;
ptL=[[0,0],[pi,0]];
kcL=[];
ctrall=12;
drwsin=0;
Opt=["dr,2","Color=red","Msg=n"];
Findpointongraph(x,tt):=(
  regional(xmx,//tt,
     t2,flg,posx,tmp,tmp1,pP,pQ,
    op,eps);
  eps=5*10^(-2);
  flg=0;
  xmx=3.5;
  tt=2*seconds();
  posx=0;
  if(posx>x-eps,
    stopanimation();
    flg=1;
  );
  if((flg==0)&(tt<=pi/2),
    Listplot("t",[[0,0],x*[cos(tt),sin(tt)]],Opt);
    flg=1;
  );
  if((flg==0)&(tt-pi/2<x+eps),
    t2=min([tt-pi/2,x]);
    Listplot("y",[[0,0],x*[0,1]],Opt);
    Expr([0,x],"e","x");
    tmp=Assign("Rng=[0,t]",["t",t2]);
    Circledata("t1",[pC,pO],append(Opt,tmp));
    pP=pC+[cos(t2),sin(t2)];
    pQ=pP+(x-t2)*[-sin(t2),cos(t2)];
    Listplot("t",[pP,pQ],Opt);
    flg=1;
  );
  if((flg==0)&(tt-pi/2<x+xmx),
    t2=tt-pi/2-x;
    Listplot("y",[[0,0],x*[0,1]],Opt);
    Expr([0,x],"e","x");
    tmp=Assign("Rng=[0,t]",["t",x]);
    Circledata("t1",[pC,pO],append(Opt,tmp));
    pP=pC+[cos(x),sin(x)];
    op=["Color=blue","Msg=n"];
    Listplot("tc",[pC,pP],op);
    Anglemark("1",[pO,pC,pP],append(op,"E=x"));
    op=concat(op,["do","size->2"]);
    t2=min([t2,2]);
    posx=pP_1+t2/2*(X.x-pP_1);
    pQ=[posx,pP_2];
    Listplot("h",[pP,pQ],op);
    if(abs(posx-X.x)<eps,
      tmp=[X.x,pP_2];
      Listplot("v",[tmp,X],op);
      if(length(ptL)==0,
        ptL=append(ptL,tmp);
      ,
        tmp1=apply(ptL,|#-tmp|);
        if(min(tmp1)>eps,
          Lastx=tmp_1;
          ptL=append(ptL,tmp);
          ptL=sort(ptL,[#_1]);
        );
      );
    );
    flg=1;
  );
);

Initbezier(ptL):=(
  regional(kL,cL,pt1,pt2,tmp,tmp1);
  kL=ptL;
  if(!contains(ptL,[0,0]),
    kL=prepend([0,0],kL);
  );
  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);
    Ptpos(tmp+"1",(2*pt1+pt2)/3);
    tmp1=tmp+"2.xy="+Textformat((pt1+2*pt2)/3,3)+";";
    parse(tmp1);
    Ptpos(tmp+"2",(pt1+2*pt2)/3);
    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=[7,YMAX-#/4];
    tmp2=[7.5,YMAX-#/4];
    Putpoint(tmp+"1",tmp1):Putpoint(tmp+"2",tmp2):
    inspect(parse(tmp+"1"),"ptsize",2);
    inspect(parse(tmp+"2"),"ptsize",2);
    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([7,YMAX-#/4],5);
    tmp2=Textformat([7.5,YMAX-#/4],5);
    parse(tmp+"1.xy="+tmp1+";");
    Ptpos(tmp+"1",[7,YMAX-#/4]);
    parse(tmp+"2.xy="+tmp2+";");
    Ptpos(tmp+"2",[7.5,YMAX-#/4]);
  );
  homectr=true;
);

stopanimation();

Resetctrpt(ctrall);

///////////////////////////////////////////////
//figure
///////////////////////////////////////////////
Ketinit();
Setparent(Cdyname()+"fig");
Setketcindyjs(["Scale=1.2","Nolabel=all","Grid=[0,0,0,0.2]"]);
Setwindow([-2.5,6.5],[-1.5,pi]);
Slider("X",[0,0],[2*pi,0]);
//parse("Xl.xy=[0,0];");
//parse("Xr.xy=[2*pi,0];");
//Addax(0);

Setax([7,"se"]);
Circledata("0",[pC,pO],["dr,1.5","Msg=n"]);
Bowdata("0",[pC,pO],[1.4,0.3,"E=1","do,1,1.2","Msg=n"]);
Letter([[2,YMAX],"s1","Graph of $y=\sin x$"],["size->30"]);
Listplot("0",[pO,[x,0]],Opt);
x=X.x;
x=round(x*100)/100;
Expr([x,-0.05],"s1","x",[]);
Expr([x,0.1],"n1",text(x),[]);
Htickmark([1,"1",2,"2",3,"3",4,"4",5,"5",6,"6"]);
Vtickmark([-1,"-1",1,"1",2,"2",3,"3"]);
op=["Msg=n","do,0.8"];
forall(1..6,
  Listplot("v"+text(#),[[#,-1],[#,3]],op);
);
forall(remove((-1)..3,[0]),
  Listplot("h"+text(#+2),[[0,#],[6,#]],op);
);

if(length(ptL)>0,
  Pointdata("0",ptL,["Size=3","Color=green","Msg=n"]);
);

//if(abs(Lastx-x)>0.09,
 Findpointongraph(x,2*seconds());
//);

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-sin(#_1)));
  mean=sum(tmp)/length(bz1);
  tmp="Diff : "+Sprintf(mean*1000,2)+" ($\times 10^{-3}$)";
  Letter(A,"e",tmp,["size->24"]);
);

if(drwsin,
  Plotdata("sin","sin(x)","x=[0,XMAX]",["Color=blue"]);
);

Figpdf();
Windispg();