Rotate 3D plot into animation

Question

I know this is not the first question on creating an animation of a 3D plot, but I found no answer to the following question: How can I create an animated rotating plot with axes labels that are readable? What I currently have doesn't look good. The axes colors are weird and irregular, the cube rotates not around its center and the axes labels jump around to different axes.

My code currently is adapted from this answer

anim = Table[
     RegionPlot3D[
      0 <= x <= y <= z <= 1, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, 
      PlotRange -> {{0, 1.2}, {0, 1.2}, {0, 1.2}}, 
      PlotStyle -> Opacity[0.7], Boxed -> False, 
      ViewCenter -> {0.5, 0.5, 0.5}, 
      ViewVector -> {5 Sin[t], 5 Cos[t], 0} ], {t, 0, 2*Pi, 
      Pi/30}]; Export["animated.gif", anim]

I want it to look similar to the following. Also the plot should rotate exactly once around its axis so that the loop of the gif isn't noticeable. Great would be if there was one variable which allows to quickly change the speed of the rotation without breaking that it rotates exactly once.

Answer 1

It all comes down to first inspect if the frames you create are of good quality. I would in this step create an image from your plot because then you directly see what will be encoded in the gif.

I adjusted three things

1. Opacity and mesh-lines look somehow not really nice together on my machine. Your example is different. The meshed surface is fully opaque and only the non-meshed sides have transparency.
2. You definitely need to adjust PlotPoints and MaxRecursion. Your region is highly affected by the way RegionPlot3D samples the domain.
3. I'm using SphericalRegion because it removes the "jumping around" in the animation.

The code needs some time because of the higher quality, so get a tea during the creation of all frames

makePlot[t_?NumericQ] := 
 Rasterize[
  RegionPlot3D[0 <= x <= y <= z <= 1, {x, 0, 1}, {y, 0, 1}, {z, 0, 1},
    PlotRange -> {{0, 1.2}, {0, 1.2}, {0, 1.2}},
   ViewCenter -> {0.5, 0.5, 0.5}, 
   ViewVector -> {5 Sin[t], 5 Cos[t], 2 Sin[t] + 1/2},
   SphericalRegion -> True,
   MaxRecursion -> 5, PlotPoints -> 150
   ]]

anim = ParallelTable[makePlot[t], {t, 0, 2*Pi, Pi/30}];
Export["~/tmp/animated.gif", anim, "AnimationRepetitions" -> Infinity]

On OS X

With a Mac there seems to be some trial and error involved. It turns out that you have to adjust the MeshStyle make it look OK. The value of the thickness depends on the image size you are creating:

makePlot[t_?NumericQ] := 
 Rasterize[
  RegionPlot3D[0 <= x <= y <= z <= 1, {x, 0, 1}, {y, 0, 1}, {z, 0, 1},
    PlotRange -> {{0, 1.2}, {0, 1.2}, {0, 1.2}}, 
   ViewCenter -> {0.5, 0.5, 0.5}, 
   ViewVector -> {5 Sin[t], 5 Cos[t], 2 Sin[t] + 1/2}, 
   SphericalRegion -> True, MaxRecursion -> 5, PlotPoints -> 150,
   MeshStyle -> AbsoluteThickness[1]],
  ImageResolution -> 150
  ]