Pictoral addition of different size and shape bivectors.

<<peeters` ;
peeters`setGitDir[ "../project/figures/GAelectrodynamics" ]

ClearAll[e1,e2,e3, area, bold, b, arc, rarc, sz, esub]
{e1,e2,e3} = IdentityMatrix[3];

(*2D vector inputs*)
area[a_, b_] := Module[{aa,bb},
aa = {a,0} // Flatten;
bb = {b,0} // Flatten;
Cross[aa,bb]//Norm
];
bold := Style[#, Bold] &;


arc[or_, r_] := Arrow[Take[CirclePoints[or,{r,0}, 10],8]// BSplineCurve ]
rarc[or_, r_] := Arrow[Take[CirclePoints[or,{r,0}, 10],8]//Reverse// BSplineCurve ]
sz := Style[#, FontSize -> 14]&;
esub[i_] := Subscript["e" // bold , i];
b[v_, i_, j_, p_] := Text[Row[{v//sz, esub[i]//sz, esub[j]//sz}], p]
p = Module[{o, o1, o2, o0, o3, a1,b1, f1, f2, arcrad},
{f1, f2} = IdentityMatrix[2];
a1 = {1,1/2};
b1 = -{0.2, -2};
b1 = b1/area[a1,b1];
o = {-0,-1/2};
o1 = o - 0.5f2 ;
o2 = {5,0};
arcrad = 0.7/2/Sqrt[Pi];
o0 = {-2.5,0};
o3 = {8,-1};

Graphics[{ 
Arrowheads[0.02],
Blue//Lighter,
Rotate[Disk[o0,{1.5, 2/Pi}], 2Pi/3], (*1, ellipse: summand: +3 *)
Green// Lighter,
Parallelogram[o1, {2a1, b1}], (*2, parallelogram: summand: -2*)
Red//Lighter,
Disk[o2,Sqrt[5/Pi]], (*3, circle: summand: +5*)
Purple// Lighter,
Parallelogram[o3, {3f1, 2f2}],(*sum: rectangle: 6 *)
Black,
Thick,
Arrowheads[0.03],
arc[o0,2.5arcrad], (*blue ellipse*)
rarc[o1 + 2a1/2+ b1/2,1.5arcrad], (*green parallelogram*)
arc[o2,4arcrad],(* red circle*)
arc[o3+(3f1+2f2)/2,4arcrad], (*purple rectangle*)
Text["+"//sz, {-1,0}] ,
Text["+"//sz, {3,0}] ,
Text["="//sz, {7,0}] ,
b[+3, 1, 2, o0-2f2],
b[-2, 1, 2, o1-f2+f1],
b[+5, 1, 2, o2-2f2],
b[+6, 1, 2, o3-f2+1.5f1]
}]
]

peeters`exportForLatex["bivectorAdditionInPlaneFig1", p]