Ketinit();
Setparent(Cdyname()+"fig");
Setketcindyjs(["Size=1","No=all","Col=[0,0,0,0.2]"]);

Addax(0);

div=50;
A.xy=2*[0,2];
B.xy=2*[-sqrt(3),-1];
C.xy=2*[sqrt(3),-1];

a=|C-B|; b=|A-C|; c=|B-A|;
len=a+b+c;
Delta=(len/2)/div;

Slider("S",[-len/4,YMIN-0.5],[len/4,YMIN-0.5]);

Listplot("P",[A,B,C,A],["dr,2"]);
Shade(["sgP"],["Color=greenyellow"]);

Triangle(s):=(
  regional(t,p1,p2,p3);
  if(s<c,
    t=s/c; p1=(1-t)*A+t*B;
    ,
    if(s<c+a,
      t=(s-c)/a; p1=(1-t)*B+t*C;
    ,
      t=(s-c-a)/b; p1=(1-t)*C+t*A;
    );
  );
  if(s<a,
    t=s/a; p2=(1-t)*B+t*C;
    ,
    if(s<a+b,
      t=(s-a)/b; p2=(1-t)*C+t*A;
    ,
      t=(s-a-b)/c; p2=(1-t)*A+t*B;
    );
  );
  if(s<c,
    t=s/c; p3=(1-t)*C+t*A;
    ,
    if(s<b+c,
      t=(s-c)/b; p3=(1-t)*A+t*B;
    ,
      t=(s-b-c)/a; p3=(1-t)*B+t*C;
    );
  );
  [round(s/Delta),p1,p2,p3];
);

Ch=[1];
if(contains(Ch,1),
 n2=floor(2*(S.x+len/4)/Delta);
 tL=select(tL,#_1<n2);
 if(length(tL)==0,
   n1=0;
 ,
   n1=max(apply(tL,#_1));
 );
 ctr=1;
 forall(tL,
   p1=#_2; p2=#_3; p3=#_4;
   Listplot(text(ctr),[p1,p2,p3,p1],["Color=blueviolet"]);
   ctr=ctr+1;
 );
 forall(n1..n2,
   s=#*Delta;
   dt=Triangle(s);
   p1=dt_2; p2=dt_3; p3=dt_4;
   if(#==n2,
     Pointdata(text(ctr),[p1,p2,p3],["Size=3","Color=blue"]);
   );
   Listplot(text(ctr),[p1,p2,p3,p1],["Color=blueviolet"]);
   tL=append(tL,dt);
   ctr=ctr+1;
 );
);

if(contains(Ch,2),
 mf(n):=(
  regional(dt,p1,p2,p3);
  forall(0..n,
    dt=Triangle(#*Delta);
    p1=dt_2; p2=dt_3; p3=dt_4;
    if(#==n,
      Pointdata(text(#),[p1,p2,p3],["Size=3","Color=blue"]);
    );
    Listplot(text(#),[p1,p2,p3,p1],["Color=blueviolet"]);
  );
 );
 rng=Assign("n=[0,div]",["div",div]);
 Setpara("trianglerotate","mf(n)",rng,["Div="+div]);
);//1

Figpdf();
Windispg();