#plotConics.maple
#
#  This plots the traces of the hyperboloid in each of the planes P_1---P_4.
#
###########################################################################################
interface(quiet=true):
read("procedures"):
Digits:=10:
with(plots):
with(plottools):
plotsetup(x11,plotoptions=`width=6in,height=6in`):
###########################################################################################
PConic:=proc(a,b,c,d)
 local A,v:
 global s,t,u:
 A:=ParameterizeLine(MakeRegulus(b, c, d, s),v):
 return(subs(op(solve({A[1]=a[1],A[2]=a[2],A[3]=a[3]},{t,u,v})),[t,u]))
end proc:
###########################################################################################
PL:=proc(a,b)
 local A:
 global s,t,u:
 A:=ParameterizeLine(b,s):
 return(subs(op(solve({A[1]=a[1],A[2]=a[2],A[3]=a[3]})),[t,u]))
end proc:
###########################################################################################
#
H := (t, a) ->  [t, a, t*a]:
l1:=[H(-1/2,1),  H(1/2,1)]:
l2:=[H(-1/2,-1), H(1/2,-1)]:
l3:=[[1/2,1/2,1/4], [-1/2,-1/2,1/4]]:
l4:=[H(-1/2,0),  H(1/2,0)]:
############################################################################
P1:=[t,1+u,t]:     # x-z=0   # l1 : (t,1,t)
P2:=[t,u-1,-t]:    # x+z=0   # l2 : (t,-1,-t)
P3:=[t,t,1/4+u]:   # x-y=0   # l3 : (t,t,1/4)
P4:=[t,0,u]:       # y=0     # l4 : (t,0,0)
###########################################################################################
macro(db=COLOR(RGB, 0,0,.8)):
macro(dr=COLOR(RGB, .8,0,0)):
macro(dg=COLOR(RGB, 0,.8,0)):
macro(dm=COLOR(RGB, .8, 0, .8)):
#
l1plot:=plot([t,0,t=-0.75..0.75],color=db,thickness=2,numpoints=2):
l2plot:=plot([t,0,t=-0.75..0.75],color=dr,thickness=2,numpoints=2):
l3plot:=plot([t,0,t=-0.75..0.75],color=dg,thickness=2,numpoints=2):
l4plot:=plot([t,0,t=-0.75..0.75],color=dm,thickness=2,numpoints=2):
###########################################################################################

#
C1:=simplify(subs(s=(s+1)/(2*s),PConic(P1,l2,l3,l4))):
#fsolve(denom(C1[1])=0):
C1plot:=plot([C1[],s=-1.03..1.1],color=brown):
#plotsetup(gif,plotoutput="P1.gif",plotoptions=`height=200,width=200`):
display(C1plot,l1plot,axes=boxed);

C2:=simplify(subs(s=(s+1)/(2*s),PConic(P2,l1,l3,l4))):
#fsolve(denom(C2[1])=0);
C2plot:=plot([C2[],s=-1.1..1.03],color=brown):
#plotsetup(gif,plotoutput="P2.gif",plotoptions=`height=200,width=200`):
display(C2plot,l2plot,axes=boxed);

C3:=simplify(subs(s=s,PConic(P3,l1,l2,l4))):
#fsolve(denom(C3[1])=0);
C3plot:=plot([C3[],s=-0.25...1.25],color=brown):
#plotsetup(gif,plotoutput="P3.gif",plotoptions=`height=200,width=200`):
display(C3plot,l3plot,axes=boxed);

C4:=simplify(subs(s=s,PConic(P4,l1,l2,l3))):
#fsolve(denom(C4[1])=0);
C4plot:=plot([C4[],s=-0.25...1.025],color=brown):
#plotsetup(gif,plotoutput="P4.gif",plotoptions=`height=200,width=200`):
display(C4plot,l4plot,axes=boxed);

T:=[line([9.5, 0.],[-.511, 0.],color=dm,thickness=2,numpoints=2),
    line([9.5, 0.],[-1.087391273, -.5164581109],color=dm,thickness=2,numpoints=2),
    line([-1.087391273, -.5164581109],[-.511, 0.],color=dm,thickness=2,numpoints=2)]:
#display(C4plot,T,axes=boxed);