3
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I am trying to adapt the solution here, which places text in 3D on the xy plane, so that the text can be placed in any orientation. So, I wrapped it in three Rotate statements, first by tilt around the x axis, then by elevation around the y-axis, then by longitude around the z-axis. However, this rotation happens after the text has been placed, away from the center of the axes. Trying to put the Rotation statements inside the meat of the function runs into the problem that I cannot tell from where the x and y coefficients are deriving so as to manipulate them using Rotate. Anyway, the original is

xyText[str_, scaling_: 1, location_: {0, 0, 0}] := 
 Module[{mesh = 
    DiscretizeGraphics[Text[Style[str, FontFamily -> "Times"]], _Text,
      MaxCellMeasure -> 0.2]}, 
  Join[{EdgeForm[]}, 
   MeshPrimitives[mesh, 
     2] /. {x_?NumberQ, 
      y_?NumberQ} :> (scaling {x, y, 0} + location), {Black}, 
   MeshPrimitives[BoundaryMesh[mesh], 
     1] /. {x_?NumberQ, 
      y_?NumberQ} :> (scaling {x, y, 0} + location)]]

and my inadequate adaptation is

ClearAll[xyText]
xyText[str_, scaling_: 1, location_: {0, 0, 0}, longitude_, 
  elevation_, tilt_] := 
 Module[{mesh = 
    DiscretizeGraphics[Text[Style[str, FontFamily -> "Times"]], _Text,
      MaxCellMeasure -> 0.2]}, Rotate[
   Rotate[
    Rotate[
     Join[{EdgeForm[]}, 
      MeshPrimitives[mesh, 
        2] /. {x_?NumberQ, 
         y_?NumberQ} :> (scaling {x, y, 0} + location)
      , {Black}, 
      MeshPrimitives[BoundaryMesh[mesh], 
        1] /. {x_?NumberQ, 
         y_?NumberQ} :> (scaling {x, y, 0} + location)], 
     tilt, {1, 0, 0}], elevation, {0, 1, 0}], longitude, {0, 0, 1}]]

The objective is for the yellow and the red "Dodecahedron" texts to intersect each other in this:

meshedSol = 
 Graphics3D[{Antialiasing -> True, Yellow, Opacity[.8], 
   PolyhedronData["Dodecahedron", "Faces"], 
   xyText["Dodecahedron", 0.2, {1, 1, 1}, 0, 0, 0],
   Red, xyText["Dodecahedron", 0.2, {1, 1, .9}, 0, 0, \[Pi]/2]}, 
  ViewPoint -> {-2, -2, 2}]

But instead, the red one is rotated after having been placed.

Update:

I gathered that x and y come from MeshPrimitives, so I made that 3D and wove in rotation matrices. Till we get a more elegant answer, I moved the result to be an answer.

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4
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I wove rotation matrices in the code and increased the resolution and it works, and now with Chip Hurst's improvement not so slow at all. Maybe it will get to be more elegant yet:

text3D[str_, location_: {0, 0, 0}, 
  scaling : {_?NumericQ, _?NumericQ} : { 1, 1}, 
  longitude : _?NumericQ : 0, 
  elevation : _?NumericQ : 0, 
  tilt : _?NumericQ : 0, 
  opt : OptionsPattern[]]:=Module[{
mesh=DiscretizeGraphics[
   Text[Style[str, opt, FontFamily -> "Times", 
   FontSize -> 12]], _Text, 
   MaxCellMeasure -> 0.04],
rotmatrx=RotationMatrix[longitude, {0, 0, 1}].
   RotationMatrix[-elevation, {0, 1, 0}].RotationMatrix[tilt, {1, 0, 0}]}, 
Join[{EdgeForm[]}, 
  MeshPrimitives[mesh,2] /. {x_?NumberQ, y_?NumberQ} :> (
      rotmatrx.(scaling~Join~{1} {x, y, 0}) + location)
(*
   ,{Black},
   MeshPrimitives[BoundaryMesh[mesh],1]/.{x_?NumberQ,y_?NumberQ}\[RuleDelayed]
   (rotmatrx.(scaling~Join~{1} {x,y,0})+location)
REMOVE REM IF NEEDING OUTLINES*)
]]

Then:

offset = 12; scale = {.5, .5};
Graphics3D[{
  Yellow,
  text3D["width\[LongRightArrow]", {offset, 0, 0}, scale, 
    FontSlant -> Italic],
  Blue,
  text3D["depth\[LongRightArrow]", {0, offset, 0}, scale, \[Pi]/2, 
    FontWeight -> Bold],
  Black,
  text3D["height\[LongRightArrow]", {0, 0, offset}, {.5, .8}, 
    0, \[Pi]/2, \[Pi]/2, FontFamily -> "Brush Script Std"],
  Red,
  Sphere[{offset, offset, offset/4}, 3]
}, Boxed -> False]

produces:

enter image description here

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  • 2
    $\begingroup$ I get about a 10 times speed up by precomputing M = scaling*RotationMatrix[longitude,{0,0,1}].RotationMatrix[-elevation,{0,1,0}].RotationMatrix[tilt,{1,0,0}] as a Module variable, i.e. this quantity only needs to be computed once. As you have it, it's being computed for every triangle created. $\endgroup$ – Chip Hurst Nov 23 '16 at 2:05
  • $\begingroup$ What a huge difference! Thanks. Adding it. $\endgroup$ – Nicholas G Nov 23 '16 at 2:12
  • 1
    $\begingroup$ Just a stylistic suggestion. In your projected text, you could use \[Rule] or \[LongRightArrow] instead of ->. $\endgroup$ – Chip Hurst Nov 23 '16 at 3:51
  • $\begingroup$ The italic Roman turns out not to have \[Rule], LOL, but it does have \[LongRightArrow]. $\endgroup$ – Nicholas G Nov 23 '16 at 10:14
  • $\begingroup$ What remains is for someone to enable left- and right-alignment of the text. As it is, the coordinates for its placement are at the center of the text. $\endgroup$ – Nicholas G Nov 23 '16 at 12:14

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