require "std";




c := widget Slider(0,2), init<-1;
a := widget Slider(0,2), init<-0.5;
b := widget Slider(0,2), init<-2;

d :=R: sqrt(b*b + c*c);
p := widget Slider(0,5), init<-2;

A:=[0,0,r1];
B:=[c,0,r2];
C:=[a,b,r3];

r1 := widget Slider(-1,2), init<-1.5;
r2 := widget Slider(-1,2), init<-0.4;
r3 := widget Slider(-1,2), init<-0.6;

f1 := R^2 -> R^3: [u,v] -> [r1*cos(u)*cos(v),r1*sin(u)*cos(v), r1* sin(v)];
f2 := R^2 -> R^3: [u,v] -> [r2*cos(u)*cos(v)+c,r2*sin(u)*cos(v), r2* sin(v)];
f3 := R^2 -> R^3: [u,v] -> [r3*cos(u)*cos(v)+a,r3*sin(u)*cos(v)+b, r3* sin(v)];

g1 := R -> R^3: u -> [r1*cos(u),r1*sin(u), 0];
g2 := R -> R^3: u -> [r2*cos(u)+c,r2*sin(u), 0];
g3 := R -> R^3: u -> [r3*cos(u)+a,r3*sin(u)+b, 0];

h1:= R -> R^3: t -> t[0,0,0] + (1-t)[c,0,0];
h2:= R -> R^3: t -> t[c,0,0] + (1-t)[a,b,0];
h3:= R -> R^3: t -> t[a,b,0] + (1-t)[0,0,0];


j1:= R^2  -> R^3: [t,u] -> t[0,0,r1*u] + (1-t)[c,0,r2*u];
j2:= R^2  -> R^3: [t,u] -> t[c,0,r2*u] + (1-t)[a,b,r3*u];
j3:= R^2  -> R^3: [t,u] -> t[a,b,r3*u] + (1-t)[0,0,r1*u];


k1:= R^2  -> R^3: [t,u] -> t*r2/(r2 -r1)*[0,0,r1*u] + (1-t*r2/(r2 -r1))*[c,0,r2*u];
k2:= R^2  -> R^3: [t,u] -> t*r3/(r3 -r2)*[c,0,r2*u] + (1-t*r3/(r3 -r2))*[a,b,r3*u];
k3:= R^2  -> R^3: [t,u] -> t*r1/(r1 -r3)*[a,b,r3*u] + (1-t*r1/(r1 -r3))*[0,0,r1*u];


m:= R^2 -> R^3:[t,u] -> [t,u,-0.01];
U:=Patch((0, 2*pi, 25),(-pi/2, pi/2, 13));
U1:=Patch((0,1,12),(0,1,12));
U2:=Patch((-p,p,2),(-p,p,2));
V:=interval(0, 2*pi,25);

W:=interval(0,1,2);

Triangle123:= R^?^3->{R^?}:[A,B,C]->triangle([A, B, C], 2);



/*Checkboxes for various options of turning things on or off*/
showspheres :=widget CheckBox, init <- True;
showcircles :=widget CheckBox, init <- False;

showsegments :=widget CheckBox, init <- False;
showboards :=widget CheckBox, init <- False;

showextensions :=widget CheckBox, init <- True;
showtriangle:=widget CheckBox, init <- False;
showplane:=widget CheckBox, init <- False;

myView := widget Show({});



widget  Color(f1(U) if showspheres else {}, "red"), parent<-`myView;
widget  Color(f2(U) if showspheres else {}, "yellow"), parent<-`myView;
widget  Color(f3(U) if showspheres else {}, "blue"), parent<-`myView;

widget  Color(g1(V) if showcircles else {}, "red"), parent<-`myView;
widget  Color(g2(V) if showcircles else {}, "yellow"), parent<-`myView;
widget  Color(g3(V) if showcircles else {}, "blue"), parent<-`myView;


widget  Color(h1(W) if showsegments  else {}, "orange"), parent<-`myView;
widget  Color(h2(W) if showsegments else {}, "green"), parent<-`myView;
widget  Color(h3(W) if showsegments  else {}, "purple"), parent<-`myView;

widget  Color(j1(U1) if showboards  else {}, "orange"), parent<-`myView;
widget  Color(j2(U1) if showboards else {}, "green"), parent<-`myView;
widget  Color(j3(U1) if showboards  else {}, "purple"), parent<-`myView;

widget  Color(k1(U1) if showextensions  else {}, "orange"), parent<-`myView;
widget  Color(k2(U1) if showextensions else {}, "green"), parent<-`myView;
widget  Color(k3(U1) if showextensions  else {}, "purple"), parent<-`myView;

widget  Color(m(U2) if showplane  else {}, "white"), parent<-`myView;


widget Color(Triangle123[A,B,C] if showtriangle else {}, "white"), parent <-`myView;