Skip to main content

table - issue with Animate


I want to make a animation based on the dataset like


data = Flatten[Table[{x, y, x^2 - y^2}, {x, -3, 3}, {y, -3, 3}], 1];

I show this data using a ListPlot3D.


p2[θ_] := RotationTransform[θ, {0, 0, 1}]

When I use Table to generate the different images, it works fine.


test11 = Table[
  ListPlot3D[p2[a][data] /. {x_, y_, z_} -> {x, y, z*a}, Mesh -> 5, 

   MeshStyle -> White, Axes -> {False, False, True}, 
   PlotRange -> {{-4, 4}, {-4, 4}, {-10, 10}}], {a, -1, 1, 0.1}]

Export["anigraf2.GIF", test11, "DisplayDurations" -> 1]

When I use 'Animate' to create the same output, Mathematica stops responding en I have to restart the software.


Animate[ListPlot3D[p2[a][data] /. {x_, y_, z_} -> {x, y, z*a}, 
  Mesh -> 5, MeshStyle -> White, Axes -> False, 
  PlotRange -> {{-4, 4}, {-4, 4}, {-10, 10}}], {a, -1, 1, 0.1}, 
 AnimationDirection -> ForwardBackward, AnimationRunning -> True, 

 SaveDefinitions -> True]

Is there somebody who has suggestion for this issue?



Answer



For anything but the simplest of graphics objects, always avoid Animate and use ListAnimate instead.


The difference is that ListAnimate works on a pre-defined list of images to create an animation. All the rendering is done beforehand. With Animate, it attempts to do the rendering on the fly, when you are moving the slider.


So this will make the animation you are looking for,


data = Flatten[Table[{x, y, x^2 - y^2}, {x, -3, 3}, {y, -3, 3}], 1];
p2[θ_] := RotationTransform[θ, {0, 0, 1}];
imglist = Table[

   ListPlot3D[p2[a][data] /. {x_, y_, z_} -> {x, y, z*a}, Mesh -> 5, 
    MeshStyle -> White, Axes -> {False, False, True}, 
    PlotRange -> {{-4, 4}, {-4, 4}, {-10, 10}}]
   , {a, -1, 1, 0.1}];
ListAnimate[
 imglist,
 AnimationDirection -> ForwardBackward, AnimationRunning -> True, 
 SaveDefinitions -> True]

Another option is to use Manipulate instead of Animate. Manipulate will render the 3D graphics using fewer points when you are moving the slider, giving you the changes quickly when it can at the expense of quality, and then generating the higher quality images when the slider stops moving. (Correct me if I am wrong here) I do not think that Animate does this.



So this runs relatively quickly on my machine,


Manipulate[
 ListPlot3D[p2[a][data] /. {x_, y_, z_} -> {x, y, z*a}, Mesh -> 5, 
  MeshStyle -> White, Axes -> {False, False, True}, 
  PlotRange -> {{-4, 4}, {-4, 4}, {-10, 10}}]
 , {a, -1, 1, 0.05}]

enter image description here


Comments

Post a Comment

Popular posts from this blog

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

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

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more