#plane3.maple
#
P:=ParameterizePlane(l3, p3, u, -v):
clll:=traceHyperboloid(l1,l2,l4, Eqs[3]):
cllk:=traceHyperboloid(l1,l2,k4, Eqs[3]):
clkl:=traceHyperboloid(l1,k2,l4, Eqs[3]):
clkk:=traceHyperboloid(l1,k2,k4, Eqs[3]):
ckll:=traceHyperboloid(k1,l2,l4, Eqs[3]):
cklk:=traceHyperboloid(k1,l2,k4, Eqs[3]):
ckkl:=traceHyperboloid(k1,k2,l4, Eqs[3]):
ckkk:=traceHyperboloid(k1,k2,k4, Eqs[3]):

cllm:=traceHyperboloid(l1,l2,m4, Eqs[3]):

K:=ParameterizeLine(LineInPlane(P,k3),t):
L:=ParameterizeLine(LineInPlane(P,l3),t):
M:=ParameterizeLine(LineInPlane(P,m3),t):

Clll:=CurveInPlane(P,clll):
Cllk:=CurveInPlane(P,cllk):
Clkl:=CurveInPlane(P,clkl):
Clkk:=CurveInPlane(P,clkk):
Ckll:=CurveInPlane(P,ckll):
Cklk:=CurveInPlane(P,cklk):
Ckkl:=CurveInPlane(P,ckkl):
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=-0.5..0.3],color=magenta,thickness=2,numpoints=2):

lll:=plot([Clll[],t=-0.1...1.1],color=blue,thickness=2,numpoints=100):
llk:=plot([Cllk[],t=-1.22..1.2],color=brown,thickness=2,numpoints=100):
llm:=plot([Cllm[],t=-4..0.8],color=cyan,thickness=2,numpoints=200):

Cplot:=[lll,llk,llm]:

#display([Cplot[],k,l,m],view=[-0.6..1.6,-0.15..0.5],title="Plane 3",axes=BOXED);
###############################################################################

l:=plot([L[],t=-5..15],color=red,thickness=2,numpoints=2):
k:=plot([K[],t=-5..15],color=brown,thickness=2,numpoints=2):
m:=plot([M[],t=-0.002..0.002],color=magenta,thickness=2,numpoints=2):
#display([k,l,m],title="Triangle in Plane 3",axes=BOXED);

###############################################################################
Clll:=shear(M,Clll):
Cllk:=shear(M,Cllk):
Clkl:=shear(M,Clkl):
Clkk:=shear(M,Clkk):
Ckll:=shear(M,Ckll):
Cklk:=shear(M,Cklk):
Ckkl:=shear(M,Ckkl):
Ckkk:=shear(M,Ckkk):
K:=shear(M,K):
L:=shear(M,L):
M:=shear(M,M):

lkk:=plot([Clkk[],t=1.054..1.064],color=black,thickness=2,numpoints=100):
llk:=plot([Cllk[],t=1.054..1.064],color=brown,thickness=2,numpoints=100):

kkk:=plot([Ckkk[],t=1.054..1.064],color=blue,thickness=2,numpoints=100):
klk:=plot([Cklk[],t=1.054..1.064],color=cyan,thickness=2,numpoints=100):

#lkl:=plot([Clkl[],t=0.9..1.1],color=green,thickness=2,numpoints=100):
#lll:=plot([Clll[],t=0.9..1.1],color=yellow,thickness=2,numpoints=100):

#kkl:=plot([Ckkl[],t=0.9..1.1],color=red,thickness=2,numpoints=100):
#kll:=plot([Ckll[],t=0.9..1.1],color=magenta,thickness=2,numpoints=100):

k:=plot([K[],t=-0.3..-0.1],color=brown,thickness=2,numpoints=2):
l:=plot([L[],t=-0.3..-0.1],color=red,thickness=2,numpoints=2):
m:=plot([M[],t=-0.005..0.02],color=magenta,thickness=2,numpoints=2):

Cplot:=[klk,kkk,lkk,llk]:#lkl,kll,kkl,,lll
display([Cplot[],k,l,m],view=[-0.18584..-0.1858,-0.008..0.001],title="Plane 3 up close",axes=BOXED);