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

Ketinit();
Ketinit3d();

//figures
Start3d();

Ptseg3data();
Putaxes3d(4);
Xyzax3data("","x=[-3,3]","y=[-3,3]","z=[-3,3]");

// z=(x^2-y^2)/(x^2+y^2)

fd=[
  "p","x=U*cos(V)","y=U*sin(V)","z=cos(V)^2-sin(V)^2",
  "U=[0,2]","V=[0,2*pi]","e"
];

Deffun("cot(t)",["regional(y)","y=cos(t)/sin(t)","y"]);

Deffun("fx2(v)",["regional(x)",
"if(abs(sin(v))<1/sqrt(2),x=sign(cos(v)),x=sign(sin(v))*cot(v))",
"x"]); 
Deffun("fy2(v)",["regional(y)",
"if(abs(cos(v))<1/sqrt(2),y=sign(sin(v)),y=sign(cos(v))*tan(v))",
"y"]); 

fd2=[
  "z=(x^2-y^2)/(x^2+y^2)","x=U*fx2(V)","y=U*fy2(V)",
  "U=[0.5,3]","V=[0,2*pi]","ewns"];

Sf3data("1",fd);

Ch=[1];
if(contains(Ch,1),

// normal vector of Fd
Mkobjnrm("1",fd);
cmdL1=[
  "assume",["U>0"],
  "a:trigsimp",[nrm1],
  "a",[]
];
CalcbyM("norm1",cmdL1,[""]);

tmp1=indexof(norm1,"/");
tmp2=indexof(norm1,",");
den1=substring(norm1,tmp1,tmp2-1);
if(substring(den1,0,4)=="sqrt",
  tmp1=Parlevel(den1);
  tmp=select(tmp1,#_2==-1);
  if(length(tmp)==1 & tmp_1_1==length(den1),
    den1=substring(den1,tmp1_1_1,tmp_1_1-1);
  );
);
den1=Assign(den1,["cos(V)","C","sin(V)","S"]);
tmp=Assign(den1,["U",0]);
Mxfun("1","solve",[tmp,"C"]);
cmdL=[
  "assume",["U>0"],
  "a1:limit",[norm1,"V","0"],
  "a2:limit",[norm1,"V","%pi/2"],
  "a3:limit",[norm1,"V","3/2*%pi"],
  "a4:limit",[norm1,"V","%pi"],
  "a5:limit",[norm1,"V","2*%pi"],
  "a1::a2::a3::a4::a5",[]
];
CalcbyM("lim1",cmdL,[""]);
//println(lim1);

Deffun("norm1(U,V)",
 ["regional(Nv)",
 "if(abs(V*(V-pi/2)*(V-3/2*pi)*(V-pi)*(V-2*pi))<10^(-6),
  Nv=[0,0,1],Nv="+norm1+")",
 "Nv"]); 

// normal vector of Fd2
tmp="[x,y,(x^2-y^2)/(x^2+y^2)],x,y";
Mkobjnrm("2",tmp);
norm2=Assign(nrm2,["x","(U*fx2(V))","y","(U*fy2(V))"]);
Deffun("norm2(x,y)",
 ["regional(Nv)","Nv="+nrm2,"Nv"]);

Mkobjthickcmd("1",fd,"norm1(U,V)",[0.05,"+n+s-e-w+"]);
Mkobjthickcmd("2",fd2,"norm2(U*fx2(V),U*fy2(V))",
  [0.05,"+n+s-e-w+"]);
Mkobjcrvcmd("3","ax3d");
Mkobjsymbcmd("x",0.1,0,[0,1,0],[3.2,0,0]);
Mkobjsymbcmd("y",0.1,0,[1,0,0],[0,3.2,0]);
Mkobjsymbcmd("z",0.1,0,[1,1,0],[0,0,3.2]);
Setobj();

);

Windispg();