# Tag Info

78

TL;DR: A package (Mathematica v10) can be found at the very bottom of this post. UPDATES 6: Tiny update: Import can now use the ".bvh" extension to determine the import type. The code that does this is ugly, but I don't see any other way at the moment. out = Import["C:\\Female1_C03_Run.bvh"] 5: Added error checking and registered the package as an ...

53

Edit: Added the reversal and some refinements ω = 1; posP[t_, φ_] := Sin[ω t + φ] {Cos[φ], Sin[φ]} posL[φ_] := {-#, #} &@{Cos[φ], Sin[φ]} Animate[ Graphics[{PointSize[0.02], Table[{Black, Line[posL[π i]], Hue[i], Point[posP[t, π i]]}, {i, 0, 1, 1/(3π-Abs[9.43-t])}] }, PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}} ], {t, 0, 6π, 0.2} ]

49

The idea behind this solution is to construct a superposition of Gaussian surfaces whose amplitude decay in time, and use DensityPlot to plot the trail: trail[fun_, {t_, tmin_, tmax_, dt_}, k_, lam_][xxx_, yyy_] := Module[{trange, xrange, yrange, twindow, trailf, sel, decayf}, decayf[x0_, y0_, t0_] := Exp[-k t0 - lam^2 (x0^2 + y0^2)]; twindow = 6/k; ...

48

Let me join. logo = Cases[ p7 /. triangulate /. moretriangles /. shrink /. shrink /. shrink /. colour3[] /. colour4["SunsetColors", 1, 28/34] , {c__, Polygon[pts__]}, \[Infinity]]; logo = SortBy[logo, First]; p = Evaluate[InterpolatingPolynomial[{ {0, {0, 0, 0, 0}}, {Pi, {Pi, 0, 0, 0, 0}}, {2 Pi, {2 Pi, 0, 0, 0}}},#]] &; pp[a_] := If[Abs[a - ...

48

I'd like to expand on Quantum_Oli's answer to give an intuitive explanation for what's happening, because there's a neat geometric interpretation. At one point in the animation it looks like there is a circle of colored dots moving about the center, this is a special case of so called hypocycloids known as Cardano circles. A hypocyloid is a curve generated ...

46

Breathing with occluded borders, per Toad's request: Run the following command to get the Mathematica code NotebookPut@ImportString[Uncompress@FromCharacterCode@Flatten@ImageData[ Import@ "http://i.stack.imgur.com/VqjJ9.png","Byte"],"NB"]

43

Here is a simple approach to create a ghost trail: obj[{xfunc_, yfunc_}, rad_, lag_, npts_][x_] := MapThread[ {Opacity[#1, ColorData["SunsetColors", #1]], Disk[{xfunc@#2, yfunc@#2}, rad Exp[#1 - 1]]} &, Through[{Rescale, Identity}[Range[x - lag, x, lag/npts]]]] frames = Most@Table[Graphics[obj[{Sin[2 #] &, Sin[3 #] &}, 0.1, 1, 500][u], ...

40

After correcting the syntax errors in the original code, the actual question can be addressed: How to display the four variables x1[t]...y2[t] as an animation in a way that conveys their meaning? The basic idea is to use ListAnimate on a list of frames that I define below: Clear[phi1, phi2, t]; sol = First[ NDSolve[{2*phi1''[t] + phi2''[t]*Cos[phi1[t] - ...

38

My simple version using Image: size = 300; r = ListConvolve[DiskMatrix[#], RandomInteger[BernoulliDistribution[0.001], {5 size, size}], {1, 1}] & /@ {1.5, 2, 3}; Dynamic[Image[(r[[#]] = RotateRight[r[[#]], #]) & /@ {1, 2, 3}; Total[r[[All, ;; size]]]]] Update A slightly prettier version, same basic idea but now with flakes. flake := Module[...

37

As per the blog: Export["breathing.gif", Table[Graphics[ p7 /. triangulate /. moretriangles /. shrink /. shrink /. shrink /. colour3[] /. colour4["SunsetColors", 1, 28/34] /. curve /. bolicsn[(1 - Cos[2 \[Pi] t])/2], ImageSize -> 150], {t, 0, 1, 0.05}]]; Some good old fashioned colour cycling: Clear[f]; f[c_] /; c > 2 := c - 2; f[c_] /;...

37

Who wanted the automagic? :) mmastar[as_, nn_: 1] := Graphics[ Scale[#, 1/max@#, {0, 0}] &[ Polygon[pt /@ as] /. triangulate /. moretriangles /. shrink /. shrink /. shrink /. colour3[] /. colour4[] /. curve /. bolicsn[nn]], AspectRatio -> Automatic, PlotRange -> 0.025]; da = 0.0001; max[zu_] := Cases[zu, {_?NumericQ, _?...

36

The first step is to rasterize the points, so let's just start there as an example: n = 512; g = Image[Map[Boole[# > 0.001] &, RandomReal[{0, 1}, {n, n}], {2}]] The trick is to exploit the distance image. Almost all the work is done here (and it's fast): i = DistanceTransform[g] // ImageAdjust // ImageData; We need a little more precomputation ...

36

A textbook-like animation turns = 10; aa = Table[Framed@ Show[ParametricPlot3D[ Piecewise[{{{1, x, 0}, x <= 0}, {{Cos[2 Pi turns x/r], x, Sin[2 Pi turns x/r]}, 0 < x <= r}, {{1, x, 0}, x > r}}], {x, -.5, r + .5}, PlotStyle -> {Gray, Specularity[Gray, 10]}, Lighting -&...

34

Note that ViewPoint is given in specially scaled coordinates which depend on amongst things the size of the bounding box. To get better control over the positioning of the camera you could use ViewVector instead, which is given in terms of the coordinates of the plot. You could for example do something like this: rotateMeHarder1[g_, vertical_, viewpoint0_, ...

33

Here is an example of how to create an animation from DensitPlot results. I have chosen a simple Gaussian function to plot, but its center depends on a parameter t. Now I create a table of plots for many different values of t, and then I take several different steps to create various kinds of movies from it. The parameter t and its step size is going to be ...

33

My approach. The main distinguishing feature being the ridiculously clumsy and inefficient way of calculating the faces... v = Tuples[{-1, 1}, 4]; e = Select[Subsets[Range[Length[v]], {2}], Count[Subtract @@ v[[#]], 0] == 3 &]; f = Select[Union[Flatten[#]] & /@ Subsets[e, {4}], Length@# == 4 &]; f = f /. {a_, b_, c_, d_} :> {b, a, c, d}; rotv[...

33

Usage Just use this function with any polyhedron in in form: GraphicsComplex[pts_, Polygon[vertices_, ___]]. When I find time and motivation maybe I will add more DownValues so it can be more general. At the moment you can play with solids given by PolyhedronData[... "Faces"]: polyhedronRandomWalk[ PolyhedronData["DuerersSolid", "Faces"] ] It ...

32

Load some images: size = {200, 200}; foot = ImageResize[Import[ "http://upload.wikimedia.org/wikipedia/commons/a/ab/Monty_python_foot.png" ], size]; spikey = ImageResize[Import[ "http://upload.wikimedia.org/wikipedia/en/b/bf/MathematicaSpikeyVersion8.png" ], size]; mse = ImageResize[Import[ "http://i.stack.imgur.com/yjrEY.png" ], size]; ...

30

Here you have a toy to start playing with: Edit preventing the animation running at different speeds in different machines by using Clock[] and DynamicWrapper[] (due credit to @jVincent) n = 500; (*number of managed particles*) x[i_][t_] := (vx0[i] (t - delay[i])) UnitStep[t - delay[i]]; y[i_][t_] := Module[{k}, If[(k = (-#^2 + vy0@i #) UnitStep@#) < ...

29

Edit I had some time so I've added full surface torus. Old code in edit history. DynamicModule[{x = 2., l = 100., x2 = 2., l2 = 100., grid, fast, slow}, Grid[{{ Graphics3D[{ Dynamic[Map[{Blue, Polygon[#[[{1, 2, 4, 3}]]]} &, Join @@@ (Join @@ Partition[#, {2, 2}, 1]) ]&[ ...

28

Since you want the animation to have explanatory content, I thought it might be best to incorporate the explanatory 2D diagram into the 3D scene. So I imagine the 2D plot as a "sticker" that can be put onto the cylinder, like a label on a bottle. That way, you can see the explanatory diagram itself wrap around the cylinder and become identical to the ...

27

Here's a spinning "3D version" of the logo Using the code from meta/blog to create the logo (assigned to the variable logo), continue with the following steps: side[o_] := Block[{z, pts = Partition[ Table[N[{Cos[t], Sin[t], z}], {t, Pi/14, 2 Pi, 2 Pi/7}], 2, 1, 1]}, Composition[Polygon, Flatten[#, 1] &] /@ Thread[{pts /. z -> o/2, Reverse /...

27

Read comments to your post - many good links there. Additionally, are a few thoughts on the topic. 1) Avoid PPT, - use built-in Mathematica slideshow templates, they were recently updated and are beautiful. Advantage is - you preserve computations and native graphics (like rotations in 3D, etc.). You can read more in this post: Best way to give ...

27

Edit V10! This is simple example what we can now do in real time! R = RegionUnion @@ Table[Disk[{Cos[i], Sin[i]}, .4], {i, 0, 2 Pi, Pi/6.}]; R2 = RegionBoundary@DiscretizeRegion@R; go[] := (While[r > .105, x += v; r = RegionDistance[R2, x]; Pause[.01]]; bounce[];) bounce[] := With[{normal = Normalize[x - RegionNearest[R2, x]]}, If[break, Abort[]]; ...

27

I think you might be better off creating Graphics directly instead of using the StreamPlot style options. In this example I use StreamPlot just once and extract the coordinates of the arrows, which I use to create Line objects with VertexColors. The animation is made by cycling the vertex colors. plot = StreamPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y,...

26

n = 100; (*number of points*) s = RandomSample@Range@n; (*the initial set*) (*some aux functions*) head[{x_, xs___}] := Select[{xs}, # <= x &]; tail[{x_, xs___}] := Select[{xs}, # > x &]; (*qsort function modified for sowing the information needed*) qsort[{}] = {}; qsort[l : {x_, ___}] := Module[{lh, lt}, (Sow@{l, lh = head@l, x, lt = tail@l}; ...

26

Generally always check Demonstrations site for good code. I cannot not mention an excellent "classic" of planar three body problem by Stephen Wolfram and Michael Trott. Code is short and I verified it runs in the latest M10.1. I slightly changed variable labels so code parses better here, removed MaxRecursion -> ControlActive[3, 9] from plot option and ...

25

The following is a little involved, but it calculates the "minimum displacement" evolution by choosing the least total displacement alternatives from the permutations generated by the "AutomorphismGroup" of the graph: {n, edges, coords1, perms} = GraphData["PappusGraph", {"VertexCount", "EdgeList", "...

24

Try a simple way. Typical key frame animation is done by nothing more than n-degree interpolation (and n is usually 1), and they look quite reasonable. Here is how I would tackle (it is generic version, so individual points have its own colors). Define "start" and "final" positions: startPos = RandomReal[{-2, 2}, {4000, 2}]; normalRDN[μ_, σ_, No_] := ...

24

Here's my contribution. I know you asked for hints only, but I couldn't resist text = Style["This is some text on a Möbius strip", FontFamily -> "Helvetica", FontSize -> 35]; img = ImageData@Image[Rasterize[text, Background -> None, ImageSize -> 1000]]; Manipulate[ ParametricPlot3D[{4 Cos[a] + r Cos[a] Cos[a/2], 4 Sin[a] + r Sin[a] Cos[...

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