Skip to main content

plotting - Animation: presenting events that persist in time



I have a list of events that occurred on specific moments in time. In the example below, the three events occurred at 23:09, 23:13 and 23:17. I was able to build an animation that flows from time 23:00 to 0:00 and shows at the right time the event by plotting a disc of a specified magnitude at the specified coordinates.


data = {{{2012, 3, 19, 23, 9}, 44.891, 12.202, 2.6, 2.5, 
3541187340}, {{2012, 3, 19, 23, 13}, 44.898, 11.258, 6.2, 4.1,
3541187580}, {{2012, 3, 19, 23, 17}, 44.186, 11.496, 4.2, 2.2,
3541187820}};

Each event is specified by its time of occurrence, x and y coordinates, magnitude 1, magnitude 2, absolute time. First, I specified the start and end time of the animation in absolute time and build a list of times from start to end in steps of one minute:


start = AbsoluteTime[{2012, 3, 19, 23, 0, 0}];
end = AbsoluteTime[{2012, 3, 20, 0, 0, 0}];
time = Table[start + 60*i, {i, 0, (end - start)/60}];


For my convenience I reshuffled my data:


d3 = Table[{data[[i, 6]], data[[i, 2]], data[[i, 3]], data[[i, 4]], 
data[[i, 5]]}, {i, Length[data]}];

and checked which values in the 'time' list are taken by the time of my events:


doubles = 
Flatten[Table[Position[time, d3[[All, 1]][[i]]], {i, Length[d3]}]];

Lastly, I inserted my events in the 'time' list:



d4 = ReplacePart[time, 
Table[doubles[[i]] -> d3[[i]], {i, Length[d3]}]];

I can then generate my frames:


frames = Animate[If[Length[d4[[i]]] > 1,
Graphics[{
White,
Rectangle[{10, 43}, {13, 46}],
Red, Disk[d4[[i, {3, 2}]], d4[[i, 5]]/10],
Black,

Text[Style[
DateString[
DateList[d4[[i, 1]]], {"Day", " ", "MonthNameShort", " ",
"Year", " ", "Hour", ":", "Minute"}],
FontFamily -> "Helvetica", FontSize -> 20], {10.8, 45.85}]
}],
Graphics[{
White,
Rectangle[{10, 43}, {13, 46}],
Black,

Text[Style[
DateString[
DateList[d4[[i]]], {"Day", " ", "MonthNameShort", " ", "Year",
" ", "Hour", ":", "Minute"}], FontFamily -> "Helvetica",
FontSize -> 20], {10.8, 45.85}]
}]
], {i, Range[Length[d4]]}, AnimationRate -> 20];

Export["animation.gif", frames, "DisplayDurations" -> .03]


enter image description here


However, what I would like to achieve is a more complicated animation: once an event is plotted at the right time I would like to then present it also on subsequent frames, but slowly dimming (decreasing Opacity) for a specified time window. At the end of the animation all events would be thus dimmed and superimposed.


I simplified a lot the example I provided, real data might span over several days and contain hundreds of events.



Answer



You could do something like this. Here, duration is the time in seconds it takes for the disk to fade away.


signal[data_, duration_][t_] := Piecewise[{{{}, t < data[[-1]]},
{{Opacity[1 - (t - data[[-1]])/duration],
Disk[data[[{3, 2}]], data[[5]]/10]},
data[[-1]] <= t < data[[-1]] + duration},
{{}, t >= data[[-1]] + duration}}]


With[{tmin = AbsoluteTime[{2012, 3, 19, 23, 0}],
tmax = AbsoluteTime[{2012, 3, 20, 0, 0}],
duration = 3600},
tab = Table[Graphics[{
{White, Rectangle[{10, 43}, {13, 46}]},
Text[Style[DateString[
t, {"Day", " ", "MonthNameShort", " ", "Year", " ", "Hour",
":", "Minute"}], FontFamily -> "Helvetica",
FontSize -> 20], {10.8, 45.85}],

{Red, signal[#, duration][t] & /@ data}}],
{t, tmin, tmax, 60}]];

Export["image.gif", tab, "DisplayDurations" -> .03]

movie


Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...