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Text in front of objects in Graphics3D

In Graphics3D, Text objects are rendered in front of other objects. Does anyone have a workaround for turning off that feature? I need to render several hundred spheres, each with a bit of Text floating on top, and I would like to allow spheres in front to obscure those in back, including the text. I could render the spheres with ParamtricPlot3D, and use Texture to add a label to each. I'm hoping there's a simpler way.
POSTED BY: Bruce Torrence
7 Replies
Here's the code. The cover image used m=20, and the final ImageSize was set to 5200 (the highest value I could get without risking a crash). I exported the image as a PNG, and used Photoshop's shift-tilt filter to introduce the blurred edges. I could have done that in mma, of course, but it's hard to argue with the simplicity of the photoshop filter. If you run this with something small, like m=4, you can easily grab and rotate the resulting image to see the pyramid structure.

 Clear[s, e, n, w, dir, tab, m, \[Delta], positions, allPrimes,
   twinPrimes, sph, ulam];
 m = 4; (* m is the no. of spiral "laps", so (2m)^2 numbers will be \
 displayed *)
 \[Delta] = .1; (* \[Delta] = vertical depth added to \
 pyramid for each number *)
 dir = {s, e, n,
   w}; (* directions: south, east, north, west *)
 tab = {};
Do[dir = RotateLeft[dir]; AppendTo[tab, Table[First[dir], {k}]];
  dir = RotateLeft[dir];
  AppendTo[tab, Table[First[dir], {k}]], {k, 1, 2 m}];
positions =
  FoldList[Plus, {0, 0, 0},
   Take[Flatten[tab], 4 m^2 - 1] /. {e -> {\[Delta], -1, 0},
     n -> {\[Delta], 0, 1}, w -> {\[Delta], 1, 0},
     s -> {\[Delta], 0, -1}}];
allPrimes = PrimeQ[Range[4 m^2]];
twinPrimes =
  MapThread[
   Or, {MapThread[
     And, {allPrimes, Join[{False, False}, Drop[allPrimes, -2]]}],
    MapThread[
     And, {allPrimes, Join[Drop[allPrimes, 2], {False, False}]}]}];
sph[k_, pos_, highlight_] :=
  Translate[
   SphericalPlot3D[.3, {\[Theta], 0, Pi}, {\[Phi], 0, 2 Pi},
     Mesh -> None,
     PlotStyle ->
      Texture[Graphics[
        Style[Text[k, {0, 0}, {0, 0}, {0, 1}], 128,
         FontFamily -> "Optima"], AspectRatio -> 2,
        Background ->
         If[highlight, RGBColor[1.`, 1.`, 0.`], RGBColor[.5`, .5`, .5`]],
        ImageSize -> 400]],
     TextureCoordinateFunction -> ({#4, #5} &)][[1]], pos];
ulam = Graphics3D[{
   {Gray, Tube[positions, .05]},
   MapThread[sph, {Range[4 m^2], positions, twinPrimes}]
   }, ViewPoint -> {-1.8, 0, 0}, PlotRangePadding -> None,
  Boxed -> False, Lighting -> "Neutral", ImageSize -> 600,
  Background -> Black]
POSTED BY: Bruce Torrence
This is great, Bruce! Congratulations on the beautiful cover and, I am totally with Dan here, - yes, please share the code ;)
POSTED BY: Vitaliy Kaurov
Please do share the code you used! We'd love to see it.
POSTED BY: Dan Newman
The Sept. 2013 issue of Math Horizons just went to press this afternoon. Here's the cover -- it relates to a story by Jordan Ellenberg on Tom Zhang's bounded-gap theorem from last spring. The image is an Ulam spiral showing the first few twin primes. It was made with Mathematica using spheres & tubes, and texture wrapping each sphere with a wrapper showing its number. The spiral is really a pyramid viewed from above, which allows more numbers to be crammed in around the edges. I'm happy to share the code if anyone is interested.

POSTED BY: Bruce Torrence
That's what I did. Much slower, but it works like a charm. Look for the result on the cover of the Sept. 2013 issue of Math Horizons!
POSTED BY: Bruce Torrence
Bruce, We are glad it worked out for you. If there is any chance of posting cover image or at least linking to it after it comes out - please do! We will very much enjoy having it here and looking at your paper.
POSTED BY: Moderation Team
Text expressions don't really seem to inhabit the same space as graphics 3d expressions. See this example from the documentation:
Graphics3D[{Text[4 Pi r^2, {0, .5, .5}], Sphere[]}, Axes -> True]
The best way to get the text to actually be part of the 3D graphics is to make the text a texture on top of some sort of 3D graphic element. I don't know of any examples of this off the the top of my head, but basically, you want to Rasterize the text and use it as  Texture expression on a polygon or on the surface of your Sphere. This often requires some nontrivial tweaking to get something that you would want to present.
POSTED BY: Sean Clarke
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