Skip to main content

graphics3d - How to make this 3D animation


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


enter image description here



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] &

gif



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"}]

picture2


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}]

final result


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


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

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}]
Post a Comment
Read more