8
$\begingroup$

I would like to learn how to code within Mathematica the following picture:

enter image description here

I tried using

planarShadow[x_, direction_, normal_, darkShadow_: True] := 
 Module[{d, n}, d = Normalize[direction];
  n = Normalize[normal];
  x /. Graphics3D[gr_, opts___] :> 
    Graphics3D[{If[darkShadow, Black], 
      GeometricTransformation[
       If[darkShadow, 
        gr /. {Glow[_] -> Glow[], 
          r_?(MemberQ[{RGBColor, Hue, CMYKColor, GrayLevel}, 
               Head[#]] &) -> Black}, gr], 
       Composition[TranslationTransform[direction], 
        Quiet[RotationTransform[{d, n}], {RotationMatrix::degen, 
          RotationTransform::spln}], ScalingTransform[10^-3, d], 
        Quiet@Check[ScalingTransform[1./(n.d), n - (n.d) d], 
          Identity]]]}, opts]]

With[{cp3d = 
   ParametricPlot3D[{{u - 2, u^2, u^3}, {-u + 1, (1/2) u - 4, 
       u^2}, {Sin[u - 0.5], 2 u - 2, (1/10) u^3}, {u - 5, u, u}, {-u, 
       u + 2.5, -u}}, {u, -4, 4}, 
     PlotStyle -> {Orange, Green, Yellow, Blue, Purple}, 
     PlotRange -> {-4, 4}] /. 
    Line[pts_, rest___] :> Tube[pts, 0.4, rest]},
 Show[cp3d, planarShadow[cp3d, {0, 0, -4.97}, {0, 0, -1}, True], 
  PlotRange -> {-5, 5}]]

and got a fairly inadequate comparison.

enter image description here

Any help would be appreciated.

$\endgroup$
  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory Tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$ – bbgodfrey Aug 28 '15 at 1:23
  • $\begingroup$ For the right half with the 3D curves with white outlines, see my answer here. $\endgroup$ – Rahul Aug 28 '15 at 2:57
5
$\begingroup$

Let us draw some random smooth curves:

pts = 4;
curves = 3;
SeedRandom[9];
f = Table[
   Interpolation[Table[{t, RandomReal[1, {3}]}, {t, 0, 1, 1/pts}], 
    Method -> "Spline"], {curves}];
plot = ParametricPlot3D[
  Evaluate@Table[f[[i]][t], {i, curves}], {t, 0, 1}, 
  PlotPoints -> 300, MaxRecursion -> 0, PlotRange -> All, 
  PlotRangePadding -> 0.05]

enter image description here

After post-processing:

r = 0.020;
r2 = 1.3 r;
range = {{x1, x2}, {y1, y2}, {z1, z2}} = Charting`get3DPlotRange@plot;
shadows = Show[plot /. Line[pts_] :> {Black, Opacity[0.1], Tube[pts, r]}, 
  Lighting -> {{"Ambient", White}}, ViewPoint -> {0, 0, ∞}, 
  Boxed -> False, Axes -> False, PlotRange -> range];
img = ImageResize[Colorize[Rasterize[shadows, ImageSize -> 900], 
    ColorFunction -> (Hue[-# - 1/3, 1 - #^2] &)], Scaled[1/3]];
res = Show[Graphics3D[{EdgeForm[], Opacity[0.75], Texture[img], 
     Polygon[{{x1, y1, z2}, {x1, y2, z2}, {x2, y2, z2}, {x2, y1, z2}},
       VertexTextureCoordinates -> {{0, 0}, {0, 1}, {1, 1}, {1, 0}}]}], plot /. 
    Line[pts_] :> {Tube[pts, r], FaceForm[Opacity[0], Glow[White]], 
      Tube[pts, r2]}, Lighting -> {{"Ambient", White}}, PlotRange -> range];
Style[Row@{img, res}, ImageSizeMultipliers -> {1, 1}]

enter image description here

Post-processing consists of two separate parts:

2D shadows

The main idea is to render gray curves with opacity and colorize the result with appropriate color function. For better quality I generate a big raster and scale it down to increase antialisaing. The shadow looks strange near sharp turns, but it is not possible to avoid this if you highlight self-intersections.

3D curves

White outlines is a thicker copy of curves, which is transparent outside and white inside (see Rahul's answer here or my answer here). Curves are flattened with Lighting -> {{"Ambient", White}}. I also use Charting`get3DPlotRange to automatically obtain plot range (see here). You can put some fixed values there.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.