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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


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