Facing text in 3D graphics with full options
Mathematica Asked on July 27, 2021
I’m seeking a refinement/extension of the excellent and very valuable solution appearing here.
That solution indeed allows you to place text anywhere in a 3D graphics and then rotate it (by Euler angles) so it faces any direction you like.
However… it has two important limitations for my application:
- For some reason it does not handle subscripts and superscripts: they are lost and not rendered
- The solution does not allow a background color, such as
Background -> White. (I need this when I’m placing a label atop a black line and want to hide a short section of the line.)
In sum: I’m hoping to get a version of text3D that could work with Style, of the form:
text3D[Style[Subscript[x, o], Italic, 24, Background->Yellow],
{x-position, y-position, z-position},
EulerAngle1, EulerAngle2, EulerAngle3]
Minor point: I think the Euler angles should be grouped into a List… but again, minor suggestion:
text3D[Style[Subscript[x, o], Italic, 24, Background->Yellow],
{x-position, y-position, z-position},
{EulerAngle1, EulerAngle2, EulerAngle3}]
Here’s an example of what I’m seeking, where I used text3D:
My original file is .eps (and .pdf) [I had to convert it to .png to upload to this site.] The labels on the artwork and mirror were created using text3D and have that wonderful orientation, as desired. However, the labels along the bottom do NOT have that orientation. I added them as standard Text in order to get the subscripts and Background -> White to cover the lines.
THAT is the problem I’d like to fix.
One Answer
Perhaps you could use an adapted version of the billboard3D function that I adapted from a previous answer here How to write graffiti, i.e., text on a polygon surface in Graphics3D? that I ultimately adapted from a Wolfram-U video presentation
Advanced 3D Graphics in the Wolfram Language. It uses normals rather than Euler angles, but it should be straightforward to convert to the flavor of Euler angles you desire. Here is an example:
Clear[billboard3D];
billboard3D[s_,
width_, {x_, y_, z_}, {nx_, ny_, nz_}, {hx_, hy_, hz_},
bkgrd_ : None, raster_ : 1000] :=
Module[{img =
Rasterize[s, "Image", Background -> bkgrd, RasterSize -> raster],
height},
height = width ImageAspectRatio[img];
{
FaceForm[White], EdgeForm[],
Texture[ImageData[img]],
GeometricTransformation[
Polygon[{{-.5 width, .5 height, 0}, {.5 width, .5 height,
0}, {.5 width, -.5 height, 0}, {-.5 width, -.5 height, 0}},
VertexTextureCoordinates -> {{0, 1}, {1, 1}, {1, 0}, {0, 0}}],
Quiet@
Composition[TranslationTransform[{x, y, z}],
RotationTransform[{{0, 1, 0}, {hx, hy, hz}}],
RotationTransform[{{0, 0, 1}, {nx, ny, nz}}]]]
}
];
Framed[
Graphics3D[{
(* Add a Plot3D Object *)
Plot3D[
0.9 Exp[-9 ((x - 1/2)^2 + (y - 1/2)^2)], {x, 0, 1}, {y, 0, 1},
PlotRange -> {0, 2}, ColorFunction -> "TemperatureMap",
PlotStyle -> Directive[Opacity[0.5], Red]][[1]],
(* View frustum *)
FaceForm[], EdgeForm[GrayLevel[.25]], Cuboid[],
(* Camera *)
FaceForm[GrayLevel[.25]], EdgeForm[], Specularity[White, 30],
Cuboid[{.45, -1, .4}, {.55, -1.3, .6}],
Cylinder[{{.475, -1.1, .65}, {.525, -1.1, .65}}, .05],
Cylinder[{{.475, -1.2, .65}, {.525, -1.2, .65}}, .05],
Cylinder[{{.5, -1, .5}, {.5, -.9, .5}}, .05],
Cylinder[{{.5, -1.15, .5}, {.5, -.9, 0}}, .01],
Cylinder[{{.5, -1.15, .5}, {.35, -1.3, 0}}, .01],
Cylinder[{{.5, -1.15, .5}, {.65, -1.3, 0}}, .01],
billboard3D[
Style["ViewPoint", 24, Bold,
FontFamily -> "Courier"], .4, {.5, -1.15, .8}, {1, 0, 0}, {0, 0,
1}],
(* View span *)
GrayLevel[.25],
With[{p = {.5, -.9, .5}},
Line[{{p, {0, 0, 0}}, {p, {1, 0, 0}}, {p, {0, 0, 1}}, {p, {1, 0,
1}}}]],
(* View angle *)
Gray, Dashed,
With[{p = {.5, -.9, .5}}, Line[{{p, {.5, 0, 1}, {.5, 0, 0}, p}}]],
Arrowheads[{-.015, .015}],
Arrow[BezierCurve[{{.5, -.5,
0.28}, {.5, -.4, .5}, {.5, -.5, .72}}]],
billboard3D[
Style["ViewAngle", 24, Bold,
FontFamily -> "Courier"], .3, {.5, -.4, .45}, {1, 0, 0}, {0, 0,
1}],
(* View vertical *)
billboard3D[
Style["ViewVertical", 24, Bold,
FontFamily -> "Courier"], .35, {.5, -.05, .75}, {1, 0,
0}, {0, -1, 0}],
(* View center *)
PointSize[Large], Point[{{.5, .5, .5}, {.5, 0, .5}}],
Arrowheads[.015], Arrow[{{.5, .5, .5}, {.5, 0, .5}}],
billboard3D[
Style["ViewCenter", 24, Bold,
FontFamily -> "Courier"], .25, {.5, .25, .55}, {1, 0, 0}, {0, 0,
1}],
(* View range *)
Gray,
Line[{{{1, 0, 0}, {1, 0, -.1}}, {{1, 1, 0}, {1, 1, -.1}}}],
Arrowheads[{-.02, .02}], Arrow[{{1, 0, -0.05}, {1, 1, -.05}}],
billboard3D[
Style["ViewRange", 24, Bold,
FontFamily -> "Courier"], .4, {1.075, .5, -.1}, {1, 0, 0}, {0, 0,
1}],
(* View left wall *)
billboard3D[
Style["!(*SubscriptBox[(Left), (Wall)])", 24, Bold,
FontFamily -> "Courier"], .35, {0, 0.5, .5}, {1, 0, 0}, {0, 0,
1}, Yellow],
(* View right wall *)
billboard3D[
Style["!(*SubscriptBox[(Right), (Wall)])", 24, Bold,
FontFamily -> "Courier"], .35, {1, 0.5, .5}, {1, 0, 0}, {0, 0,
1}, Green],
(* View top wall *)
billboard3D[
Style["Top Wall", 24, Bold, FontFamily -> "Courier"], .35, {0.5,
0.5, 1}, {0, 0, 1}, {0, 1, 0}],
(* View bottom wall *)
billboard3D[
Style["Bottom Wall", 24, Bold,
FontFamily -> "Courier"], .35, {0.5, 0.5, 0}, {0, 0, 1}, {0, 1,
0}],
(* View front wall *)
billboard3D[
Style["Front Wall", 24, Bold, FontFamily -> "Courier"], .35, {0.5,
0, 0.5}, {0, 0, 1}, {0, 0, 1}],
(* View back wall *)
billboard3D[
Style["!(*SuperscriptBox[(Back), (Wall)])", 24, Bold,
FontFamily -> "Courier"], .35, {0.5, 1, 0.5}, {0, 0, 1}, {0, 0,
1}, Orange]
},
Boxed -> False, ImageSize -> 750, Lighting -> "Neutral",
ViewPoint -> {5, -2, 1.5}
],
FrameMargins -> 20, FrameStyle -> GrayLevel[.75]]
Update
I modified the billboard3D function to pass in an Euler angles and a translation list. In the process of testing the function, I noticed that it was difficult to match a white background, as shown below:
I could circumvent the issue by supplying a White Glow directive to Graphics3D as shown in the following workflow:
Clear[transformFn]
transformFn[angles_List, translation_List] := Module[{m},
(* Set up Transform Function*)
m = IdentityMatrix[4];
(* Rotation Part *)
m[[1 ;; 3, 1 ;; 3]] = EulerMatrix[angles];
(* Translation Part *)
m[[1 ;; 3, -1]] = translation;
TransformationFunction[m]
]
Clear[billboard3DEuler];
billboard3DEuler[s_, width_, angles_List, translation_List,
bkgrd_ : None, raster_ : 1000] :=
Module[{img =
Rasterize[s, "Image", Background -> bkgrd, RasterSize -> raster],
height}, height = width ImageAspectRatio[img];
{FaceForm[White], EdgeForm[], Texture[ImageData[img]],
GeometricTransformation[
Polygon[{{-.5 width, .5 height, 0}, {.5 width, .5 height,
0}, {.5 width, -.5 height, 0}, {-.5 width, -.5 height, 0}},
VertexTextureCoordinates -> {{0, 1}, {1, 1}, {1, 0}, {0, 0}}],
Quiet@transformFn[angles, translation]]}];
(*Set up unit vectors*)
null = {0, 0, 0};
(* Unit Vectors *)
{ex, ey, ez} = UnitVector[3, #] & /@ {1, 2, 3};
(*Create reference axes*)
axesfn = {Red, Arrow[Tube[{null, #1 ex}, #2]], Green,
Arrow[Tube[{{null, #1 ey}}, #2]], Blue,
Arrow[Tube[{{null, #1 ez}}, #2]]} &;
axes = Graphics3D@axesfn[4, 0.04];
(*Manipulate rotation and translation*)
Manipulate[Show[{axes, Graphics3D[{
(* View left wall *)
Glow[White],
billboard3DEuler[
Style["!(*SubscriptBox[(x), (o)])", 24,(*Bold,*)
FontFamily -> "Lucida Calligraphy"],
1.5, {Dynamic@α, Dynamic@β,
Dynamic@γ}, {Dynamic@x, Dynamic@y, Dynamic@z}, White,
500]
}]}, Boxed -> False, ViewPoint -> {Infinity, Infinity, Infinity},
PlotRange -> 4 {{-1, 1}, {-1, 1}, {-0.5, 1}},
ImageSize -> Large], {{α, 0}, 0, 2 Pi, Pi/2}, {{β, 0},
0, 2 Pi, Pi/2}, {{γ, 0}, 0, 2 Pi, Pi/2}, {{x, 0}, -2,
2}, {{y, 0}, -2, 2}, {{z, 0}, -2, 2}, ControlPlacement -> Left]
Correct answer by Tim Laska on July 27, 2021
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