#plane1.maple
#
P:=ParameterizePlane(l1, p1, u, -v):

clll:=traceHyperboloid(l3,l4,l2, Eqs[1]):
cllk:=traceHyperboloid(l3,k4,l2, Eqs[1]):

cklk:=traceHyperboloid(l3,k4,k2, Eqs[1]):
clkk:=traceHyperboloid(k3,k4,l2, Eqs[1]):
ckkk:=traceHyperboloid(k3,k4,k2, Eqs[1]):

cllm:=traceHyperboloid(l3,m4,l2, Eqs[1]):
#fsolve(denom(clkk[1])=0,t);
#fsolve(denom(cklk[1])=0,t);
#fsolve(denom(ckkl[1])=0,t);
#fsolve(denom(ckkk[1])=0,t);

K:=ParameterizeLine(LineInPlane(P,k1),t):
L:=ParameterizeLine(LineInPlane(P,l1),t):
M:=ParameterizeLine(LineInPlane(P,m1),t):

Clll:=CurveInPlane(P,clll):
Cllk:=CurveInPlane(P,cllk):

Clkk:=CurveInPlane(P,clkk):
Cklk:=CurveInPlane(P,cklk):
Ckkk:=CurveInPlane(P,ckkk):

Cllm:=CurveInPlane(P,cllm):

l:=plot([L[],t=-1.5..2.],color=red,thickness=2,numpoints=2):
k:=plot([K[],t=-1.5..2.],color=brown,thickness=2,numpoints=2):
m:=plot([M[],t=-0.1..0.3],color=magenta,thickness=2,numpoints=2):

lll:=plot([Clll[],t=-0.03..1.01],color=blue,thickness=2,numpoints=100):
llk:=plot([Cllk[],t=-0.2..1.217],color=brown,thickness=2,numpoints=100):
llm:=plot([Cllm[],t=0.93..1.22],color=cyan,thickness=2,numpoints=200):

Cplot:=[lll,llk,llm]:

#display([Cplot[],k,l,m],view=[-1.5..1.5,-0.05..0.32],title="Plane 1",axes=BOXED);
###############################################################################

l:=plot([L[],t=-15..5],color=red,thickness=2,numpoints=2):
k:=plot([K[],t=-15..5],color=brown,thickness=2,numpoints=2):
m:=plot([M[],t=-0.0000000000004..0.0000000000001],color=magenta,thickness=2,numpoints=2):
#display([k,l,m],title="Triangle in Plane 1",axes=BOXED);
###############################################################################

Clkk:=shear(M,Clkk):
Cklk:=shear(M,Cklk):
Cllk:=shear(M,Cllk):
Ckkk:=shear(M,Ckkk):

K:=shear(M,K):
L:=shear(M,L):
M:=shear(M,M):

e:=10000000000000000:
f:=10000000:
g:=8000000:
Tt:=-1881570808298/10000000000000:

Clkk:=EXpand(Clkk,[M[1],0],Tt,e,f,g):
K:=EXpand(K,[M[1],0],XX,e,f,g):
L:=EXpand(L,[M[1],0],XX,e,f,g):
M:=EXpand(M,[M[1],0],XX,e,f,g):

lkk:=plot([Clkk[],t=-0.18816..-0.18815],color=black,thickness=2,numpoints=100):

k:=plot([K[],t=1.0628568342..1.0628568348],color=brown,thickness=2,numpoints=2):
l:=plot([L[],t=1.0628568342..1.0628568348],color=red,thickness=2,numpoints=2):
m:=plot([M[],t=-0.0000001..0.0000001],color=magenta,thickness=2,numpoints=2):

Cplot:=[lkk]:
display([Cplot[],k,l,m],view=[1.0628568342..1.0628568348,-0.000002..0.000005],title="Plane 1 up close",axes=BOXED);