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graphics3d - How to avoid the wiggly text on Ticks and Labels when rotating 3D objects


Motivation



I'm trying to do a nice animation of the rotation of a ParametricPlot3D . My problem is that the Ticks numbers and AxesLabel text wiggle with an undesirable noisy component as the ViewPoint changes.


Rotating ParametricPlot3D


Questions


How can I figure out why it wiggles?


How do I avoid it?


I'm guessing that there is some "round up to nice values" going on somewhere, but the output of TracePrint its not too revealing to me.


Code


examplePlot = ParametricPlot3D[
  Evaluate@Table[
    {

     k
     , s
     , Sin[k s] + k s/50
     }
    , {k, 7}
    ]
  , {s, 0, 4 Pi}
  , PlotRange -> {{-2, 4 Pi}, {0, 4 Pi}, {-2, 4}}
  , BoxRatios -> {1, 3, 1}
  , PlotStyle -> Array[Hue, 7, {0, 0.75}]

  , PlotPoints -> 150
  , MaxRecursion -> 5
  , BaseStyle -> {FontSize -> 14, FontFamily -> "Helvetica", 
    FontTracking -> "Plain", TextJustification -> 0, 
    PrivateFontOptions -> {"OperatorSubstitution" -> False}}
  , ImageSize -> {700, 300}
  , ViewAngle -> 0.19
  , Ticks -> {Range[7], Automatic, Automatic}
  ]


animExample = Table[
   Show[
    examplePlot
    , ViewPoint -> {3, 0.4 + 0.5 Sin[j], 0.5 + 0.2 Cos[j]}
    , RotationAction -> "Clip"
    , ViewVertical -> {0, 0, 1}
    , ViewAngle -> 0.22
    , AxesEdge -> {{1, -1}, Automatic, {1, -1}}
    , AxesLabel -> {"Axis 1", "Axis 2", "Axis 3"}
    ]

   , {j, 0, 2 π, π/25}];

Export["animExample.GIF", animExample, "DisplayDurations" -> 0.15, 
 "AnimationRepetitions" -> Infinity]

Answer



Not a complete answer, but I think this can get you close to the solution.


If you use images instead of text, there's less (or even no) jumping around. I only worked on the ticks.


To have the ticks numbers rasterized, I made a variation of this, but there's probably a simpler way (I didn't try to put your ticks specification, but it should be easy).


Then, I played with the sizes and resolutions, and my end result still needs a lot of tuning: line thickness / darkness are a little lost in rasterings and resizings, numbers are flickering (but I do believe that they are not jumping; you tell me...)


enter image description here



I hope this helps as a start:


tickF[div1_, div2_: - 1] := (If[div2 == -1, 
    Thread[{#, #, {.02, 0}}, List, 2] &@FindDivisions[{#1, #2}, div1],
     Join @@ 
     MapAt[Join @@ # &, {Function[{p}, {p, 
            Magnify[Rasterize[p, RasterSize -> 150], 3], {.02, 
             0}}] /@ #[[1]], 
         Thread[{#, "", {.01, 0}}, List, 2] & /@ #[[2]]} &@
       FindDivisions[{#1, #2}, {div1, div2}], {2}]]) &



examplePlot[j_] := 
 ParametricPlot3D[
  Evaluate@Table[{k, s, Sin[k s] + k s/50}, {k, 7}], {s, 0, 4 Pi}, 
  PlotRange -> {{-2, 4 Pi}, {0, 4 Pi}, {-2, 4}}, 
  BoxRatios -> {1, 3, 1}, PlotStyle -> Array[Hue, 7, {0, 0.75}], 
  PlotPoints -> 150, MaxRecursion -> 5, 
  BaseStyle -> {FontSize -> 14, FontFamily -> "Helvetica", 
    FontTracking -> "Plain",
    TextJustification -> 0, 

    PrivateFontOptions -> {"OperatorSubstitution" -> False}}, 
  ImageSize -> {3*700, 3*300},
  Ticks -> 
   Evaluate@({(t1 = {##}; tickF[8, 5][##]) &, (t2 = {##}; 
        tickF[8, 5][##]) &, (t3 = {##}; N /@ tickF[8, 5][##]) &}),
  ViewPoint -> {3, 0.4 + 0.5 Sin[j], 0.5 + 0.2 Cos[j]},
  RotationAction -> "Clip",
  ViewVertical -> {0, 0, 1},
  ViewAngle -> 0.22,
  AxesEdge -> {{1, -1}, Automatic, {1, -1}},

  AxesLabel -> {"Axis 1", "Axis 2", "Axis 3"}];

animExample = 
 Table[ImageResize[Rasterize[examplePlot[j], "Image"], 700], {j, 0, 2 \[Pi], \[Pi]/25}];

EDIT


Still based on rasterization, but better looking:


enter image description here


tickF[div1_, 
  div2_: - 1] := (If[div2 == -1, 

    Thread[{#, #, {.02, 0}}, List, 2] &@FindDivisions[{#1, #2}, div1],
     Join @@ 
     MapAt[Join @@ # &, {Function[{p}, {p, p, {.02, 0}}] /@ #[[1]], 
         Thread[{#, "", {.01, 0}}, List, 2] & /@ #[[2]]} &@
       FindDivisions[{#1, #2}, {div1, div2}], {2}]]) &

examplePlot[j_, factor_] := 
 ImageResize[
  Rasterize[
   ParametricPlot3D[

    Evaluate@Table[{k, s, Sin[k s] + k s/50}, {k, 7}], {s, 0, 4 Pi}, 
    PlotRange -> {{-2, 4 Pi}, {0, 4 Pi}, {-2, 4}}, 
    BoxRatios -> {1, 3, 1}, 
    PlotStyle -> Array[{Hue[#], Thickness[0.006]} &, 7, {0, 0.75}], 
    PlotPoints -> 150, MaxRecursion -> 5, 
    BaseStyle -> {FontSize -> factor*14, FontFamily -> "Helvetica", 
      FontTracking -> "Plain",
      TextJustification -> 0, 
      PrivateFontOptions -> {"OperatorSubstitution" -> False}}, 
    ImageSize -> {factor*700, factor*300},

    ViewPoint -> {3, 0.4 + 0.5 Sin[j], 0.5 + 0.2 Cos[j]},
    RotationAction -> "Clip",
    ViewVertical -> {0, 0, 1},
    ViewAngle -> 0.22,
    AxesEdge -> {{1, -1}, Automatic, {1, -1}},
    AxesLabel -> {"Axis 1", "Axis 2", "Axis 3"},
    Ticks -> 
     Evaluate@({(t1 = {##}; tickF[8, 5][##]) &, (t2 = {##}; 
          tickF[8, 5][##]) &, (t3 = {##}; N /@ tickF[8, 5][##]) &}),
    BoxStyle -> Directive[Thickness[0.003]]

    ], "Image", RasterSize -> 4000], 700, Resampling -> "Linear"]


animExample6 = Table[examplePlot[j, 6], {j, 0, 2 \[Pi], \[Pi]/25}];
Export["animExample.GIF", animExample6, 
 "DisplayDurations" -> 0.15, "AnimationRepetitions" -> Infinity]

(not sure if factor is doing that much... but at least it is better looking, simpler and faster)


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