graphics3d - How to make this 3D animation

How to make an animation of following gif by using Mathematica?

Answer

You can use the new RandomPoint- function to sample points from a sphere and use the second argument of Text to position some text in 3D. Text will automatically make the string face towards the viewer/camera for you.

pts = RandomPoint[Sphere[{0, 0, 0}], 100];
Text["test", #] & /@ pts // Graphics3D[#, SphericalRegion -> True, Boxed -> False] &

Another approach is instead of rotating the entire graphic (as done above) to rotate the points themselves via RotationTransform. This enables the use of coordinate dependent color and size. An appropriate transformation could be

r[angle_?NumericQ, pivot : {_, _}] := RotationTransform[angle Degree, pivot];

and can be used as follows to archive something closer to what you are looking for with color and size scaling done in respect to the y-coordinate

Graphics3D[(Style[Text["test", #], FontSize -> 14 - 5*(#[[2]] + 1), 

FontColor -> Blend[{Black, White}, #[[2]]]] & /@ 
r[0, {{0, 0.2, 1}, {1, 0, 0}}] /@ pts), BoxRatios -> {1, 1, 1}, 
Boxed -> True, Axes-> True, AxesLabel -> {"x", "y", "z"}]

This can be animated for instance like this

Animate[Graphics3D[(Style[Text["test", #], 
FontSize -> 14 - 5*(#[[2]] + 1), 
FontColor -> Blend[{Black, White}, #[[2]]]] & /@ 
r[angle, {{0, 0, 1}, {0.2, -1, 0}}] /@ pts), 

BoxRatios -> {1, 1, 1}, SphericalRegion -> True, Boxed -> False, 
ViewPoint -> Front], {angle, 0, 360}]

To archive your desired look you might have to play around a bit with the color- and size scaling

Comments

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],

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