Help for a trajectory algorithm

Questions
1

Anyone can help me with an algorithm? I do not know if exist there something like that…
In the image each color represents a trajectory

gest.jpg
gest.jpg512×203 10.1 KB

And I want transform this into a simple and smooth trajectory, like the red points on next image.

gest2.jpg
gest2.jpg512×203 10.3 KB

Any help? Thanks

2

One simple way would be to calculate a moving average:

data = Table[{i, Sin[i]} + RandomReal[.3, {2}], {i, 0, 2*Pi, .1}, {4}];

ListPlot[data, Epilog -> Line[MovingAverage[Join @@ data, 50]]]

Capture.PNG
Capture.PNG716×556 17.3 KB

3

Thanks, nice help! :wink:

4

Bruno, you can also conveniently change the length of the list of elements you want to test through with Manipulate function. Simply replace the second argument in the ListPlot function with a dynamic variable “k” and wrap it with the Manipulate function (k is from 5 to 100 with step lenght = 1):

Now you can customize how smooth the data should be.
Copiable code:

data=Table[{i,Sin[i]}+RandomReal[.3,{2}],{i,0,2*Pi,.1},{4}];
Manipulate[
ListPlot[data,Epilog->Line[MovingAverage[Join@@data,k]]]
,{k,5,100,1}]