Figures that illustrate two rectangular factorizations of a bivector in R3.

<<peeters`

(*relative to ~/physicsplay*)
peeters`setGitDir[ "../project/figures/GAelectrodynamics" ]

ClearAll[a,b,c,d,ab,cd,o]

a = {1,1,-2};
b = {-1,1,0}/2;
ab = Cross[a,b]// Normalize
c = {0,-1,1}/2;
d = {2,-1,-1};
cd = Cross[c,d]//Normalize
o = {0,0,0};

(*check*)
(*a.b
a.ab
b.ab

c.d
c.cd
d.cd*)

Graphics3D[{
Parallelepiped[o,{a,b,ab/50}],
Parallelepiped[o,{c,d,cd/50}],
Red//Darker,
Arrowheads[0.05],
Arrow[Tube[{o,a},0.03]],
Arrow[Tube[{a, a + b},0.03]],
Blue//Darker,
Arrow[Tube[{o,c},0.03]],
Arrow[Tube[{c, c + d},0.03]]
}
]

p1=;

p2 = ;

peeters`exportForLatex["bivectorFactorizationFig1", p1]
peeters`exportForLatex["bivectorFactorizationFig2", p2]