#plane2.maple
#
P:=ParameterizePlane(l2, p2, u, v):

clll:=simplify(subs(t=t/(2*t-1), traceHyperboloid(l1,l3,l4, Eqs[2]))):
cllk:=simplify(subs(t=1/t, traceHyperboloid(l1,l3,k4, Eqs[2]))):

clkk:=simplify(subs(t=1/t, traceHyperboloid(l1,k3,k4, Eqs[2]))):
ckkk:=simplify(subs(t=1/t, traceHyperboloid(k1,k3,k4, Eqs[2]))):

cllm:=traceHyperboloid(l1,l3,m4, Eqs[2]):
#fsolve(denom(clll[1])=0,t);
#fsolve(denom(cllk[1])=0,t);
#fsolve(denom(cllm[1])=0,t);

K:=ParameterizeLine(LineInPlane(P,k2),t):
L:=ParameterizeLine(LineInPlane(P,l2),t):
M:=ParameterizeLine(LineInPlane(P,m2),t):

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

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

Cllm:=CurveInPlane(P,cllm):

l:=plot([L[],t=-0.9..2.5],color=red,thickness=2,numpoints=2):
k:=plot([K[],t=-0.9..2.5],color=brown,thickness=2,numpoints=2):
m:=plot([M[],t=-0.1..0.1],color=magenta,thickness=2,numpoints=2):

lll:=plot([Clll[],t=-0.08..1.025],color=blue,thickness=2,numpoints=100):
llk:=plot([Cllk[],t=-1.1..0.96],color=brown,thickness=2,numpoints=100):
llm:=plot([Cllm[],t=-1.5..0.1],color=cyan,thickness=2,numpoints=200):

Cplot:=[lll,llk,llm]:

#display([Cplot[],k,l,m],view=[-0.5..2.2,-0.15..0.7],title="Plane 2",axes=BOXED);
###############################################################################

l:=plot([L[],t=-60..10],color=red,thickness=2,numpoints=2):
k:=plot([K[],t=-60..10],color=brown,thickness=2,numpoints=2):
m:=plot([M[],t=-0.00002..0.00001],color=magenta,thickness=2,numpoints=2):
#display([k,l,m],title="Triangle in Plane 2",axes=BOXED);

###############################################################################
Clkk:=shear(M,Clkk):
Ckkk:=shear(M,Ckkk):

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


e:=100000:
f:=200:
g:=230:
Tt:=940861/1000000:

Clkk:=EXpand(Clkk,[M[1],0],Tt,e,f,g):
Ckkk:=EXpand(Ckkk,[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=0.9406..0.941],color=black,thickness=2,numpoints=100):
kkk:=plot([Ckkk[],t=0.9407..0.941],color=blue,thickness=2,numpoints=100):

k:=plot([K[],t=1.87..1.92],color=brown,thickness=2,numpoints=2):
l:=plot([L[],t=1.87..1.92],color=red,thickness=2,numpoints=2):
m:=plot([M[],t=-0.00004..0.0001],color=magenta,thickness=2,numpoints=2):

Cplot:=[kkk,lkk]:
display([Cplot[],k,l,m],view=[1.894217..1.894220,-0.003..0.001],title="Plane 2 up close",axes=BOXED);