How to label Graphics3D objects?

Question

Suppose I have Graphics3D objects like Arrows that I'd like to label, such as

ClearAll[o, e1, e2, e3]

o = {0, 0, 0};
{e1, e2, e3} = IdentityMatrix[3];

justgrid[f1_, f2_, f3_, c1_, c2_, c3_, s1_, s2_, s3_] := Module[{ts},
  
  ts = 0.02;
  Graphics3D[{
    
    AspectRatio -> 1
    , Black
    , PointSize[0.015]
    , Table[
     Point[i f1 + j f2 + k f3], {i, 0, s1 + 1}, {j, 0, s2 + 1}, {k, 0,
       s3 + 1}]
    , Opacity[0.05]
    , Table[
     Parallelepiped[i f1 + j f2 + k f3, {f1, f2, f3}], {i, 0, s1}, {j,
       0, s2}, {k, 0, s3}]
    
    , Arrowheads[0.05]
    , Opacity[1]
    , Red // Darker // Darker
    , Arrow[Tube[{o, f1}, ts]]
    , Black
    , Text[c1, f1/2]
    
    , Green // Darker // Darker
    , Arrow[Tube[{o, f2}, ts]]
    , Black
    , Text[c2, f2/2]
    
    , Blue // Darker // Darker
    , Arrow[Tube[{o, f3}, ts]]
    , Black
    , Text[c3, f3/2]
    
    , Opacity[0.05]
    , Pink // Lighter 
    , Parallelepiped[o, {(s1 + 1) f1, (s2 + 1) f2, 0.01 f3}]
    , Parallelepiped[o, {(s2 + 1) f2, (s3 + 1) f3, 0.01 f1}]
    
    }]
  ]

justgrid[e1, e2, e3,
  "\!\(\*SubscriptBox[\(e\), \(1\)]\)", "\!\(\*SubscriptBox[\(e\), \
\(2\)]\)", "\!\(\*SubscriptBox[\(e\), \(3\)]\)", 1, 1, 1]

Observe that my labels are obscured by the objects, but it is not easily obvious what directions to offset them to make them show up better:

Is it possible to use the Plot3D Callout[] mechanism within Graphics3D to automatically position the labels in a non-obscured fashion?

If not, is there a way to create a background behind the label (relative to the viewpoint), so that the label shows up more clearly?

Answer 1

Maybe you can show up the labels more clearly including a labeled in the Text objects as follows:

Text[Labeled[c1, "", Background -> White], f1/2]

Applying this to the three Text gives the output (with FontSize->14)

Even you can add a Framed as follows:

Text[Labeled[Framed@c1, "", Background -> White], f1/2]

to get