# How to plot particle trajectories and normalise to 0,0 origin?

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Amadeus Xu on 25 Nov 2020
Hi all,
I have data of lots of single particle trajectories that run for different lengths of time which I'd like to be able to plot them onto a 2D graph, with all the trajectory start positions normalised to 0,0 origin, so the plot looks a bit like the following: My data is in an excel sheet with PARTICLE_ID, Time, X and Y co-ordinate (see attached testdata.xlsx file for example of 5 particle trajectories)
After importing the data as a matrix, I presume I must use mat2cell to convert the matrix to smaller cell arrays, with each cell array representing the data different particle trajectories? Currently I have the following code:
C = mat2cell(testdata, [59 56 240 56 10], )
C =
5×1 cell array
{ 59×4 double} % trajectory 1
{ 56×4 double} % trajectory 2
{240×4 double} % trajectory 3
{ 56×4 double} % trajectory 4
{ 10×4 double} % trajectory 5
However, if I have a file with >100s of trajectories, how would I code this so I don't have to manually specify the cell array sizes for each trajectory?
Then the next question is how do I normalise all the particle trajectory coordinates so that they begin at the origin 0,0?
Pier Giorgio Petrolini on 25 Nov 2020
Hello Amadeus, I tried to solve your problem in the following way :
1) Convert the dataset in a table;
2) Find all the points of the trajectory of the same particle;
3) Scale all the points of the trajectory ( I assumed the the starting point of the trajectory of a certain particle was the first value recorded of the particle dataset under consideration i don't know if it is a correct assumption but you can easily change it in the code);
4) Plot the scaled values of the trajectory.
% Import the data
Clear temporary variables
clear opts
% Count unique values in "PARTICLE_ID" column
n = unique(testdata.PARTICLE_ID)
ParticleNumber = numel(n)
% Plot each scaled trajectory
for i = 1:ParticleNumber
table = testdata(testdata.PARTICLE_ID == i,:); % Isolate single particle trajetory
color = {'k' 'r' 'b' 'g' 'c'};
xmin = table.X(1); % Zero point on x-axis
ymin = table.Y(1); % Zero point on y-axis
table.Scaled_x = table.X-xmin; % Scaled values on x-axis
table.Scaled_y = table.Y-ymin; % Scaled values on y-axis
plot(table.Scaled_x, table.Scaled_y, color{i})
xlabel('x')
ylabel('y')
legend
hold on
end
In the attached file "untitled.1.png" you can find the plot that was generated by this code.
I really hope it helps. Kind regards,
PGP

Star Strider on 25 Nov 2020
This will normalise everycell to begin at (0,0):
[Uid,~,ix] = unique(testdata(:,1));
tally = accumarray(ix, ones(size(ix)));
C = mat2cell(testdata, tally, )
figure
hold on
for k = 1:size(C,1)
plot(C{k}(:,3)-C{k}(1,3), C{k}(:,4)-C{k}(1,4))
end
grid
plot([0 0], ylim, 'k')
plot(xlim, [0 0], 'k')
hold off
xlabel('x')
ylabel('y')
Note that the arguments to mat2cell were not correct, so I added code to create the correct argument. The unique call is not absolutely necessary here since the IDs go from 1 to 5, however I included it in the event that is not the situation in other files. This also requires that the IDs be consecutive. Code to correct for that would be required if that is not the situation on other files. .
ADJE JEREMIE ALAGBE on 21 Jul 2021
Hi, @Star Strider, any idea on this after additional details? Thank you!

Steve Eddins on 25 Nov 2020
Here is one way you could do it. Read in the whole Excel file as a table. Then, in a loop, extract the particle data for each trajectory, subtract the first X-Y location, and plot it.
ans =
8×4 table
PARTICLE_ID TIME X Y
___________ ____ ______ ______
1 42 40.831 69.093
1 43 40.865 69.034
1 44 40.861 69.039
1 45 40.887 69.043
1 46 40.857 69.045
1 47 40.859 69.07
1 48 40.826 69.189
1 49 40.864 69.655
>> N = max(T.PARTICLE_ID)
N =
5
>> hold on
>> for k = 1:N
Tk = T(T.PARTICLE_ID == k,:);
plot(Tk.X - Tk.X(1), Tk.Y - Tk.Y(1))
end
>> hold off
>> axis equal ADJE JEREMIE ALAGBE on 19 Jul 2021
I have a dataset that seems to have some similarities with @Amadeus Xu's dataset, but when I tried to apply @Star Strider and @Steve Eddins's solutions to my dataset it works but there were also some excessive lines that should not be present in the plot, so I guess I still need some additional line of code to make it perfetct.
The dataset is attached in excel file 15_device76.xlsx. It's a set of data collected at an approach of a freeway intersection by a radar detector. It has 9 columns as follows: deviceno (the number given to each device, radar, here there is only one radar which is numbered 76), timestamp (at every second, the radar detects all vehicles in the detection area and collects their information, including each vehicle's position, speed, and attributes an id to each vehicle, which means same instant or timestamp can contain many vehicles, and a same vehicle can be detected in the next second and so on if it's still in the detection area), unixtime, ID (each vehicle is given an id by the radar; the vehicles are circularly number from 1 to 255, which means after the number reaches 255 it restarts numbering the following vehicles from 1 to 255, and so on), Length (vehicle length), YPos (the vehicle's Y-coordinate in the radar coordinate system, with radar as origin), XPos (the vehicle's X-coordinate), YSpeed (the vehicle's speed in Y-direction), and XSpeed (the vehicle's speed in X-direction). The following image is the plot I got. I tried to take a single range of the dataset that now only contains the firt 1-255 range of vehicle ID trajectories data (see attached 15_device76_1.xlsx file) and plot it by using the fllowing code from @Steve Eddins:
N = max(T.ID)
hold on
for k = 1:N
Tk = T(T.ID == k,:);
plot(Tk.yPos, Tk.XPos)
end
hold off
xlabel('y')
ylabel('x')
It works perfectly as you can see in the image bellow, however I don't know how to continue plotting all other successive 1-255 ranges on the same plot, as my original file contains a very large amount of vehicle trajectory data to visualize. This is the issue I'm facing.
I would greatly appreciate a solution from you to my problem. Thank you all in advance! Pier Giorgio Petrolini on 25 Nov 2020
Hello Amadeus, I tried to solve your problem in the following way :
1) Convert the dataset in a table;
2) Find all the points of the trajectory of the same particle;
3) Scale all the points of the trajectory ( I assumed the the starting point of the trajectory of a certain particle was the first value recorded of the particle dataset under consideration i don't know if it is a correct assumption but you can easily change it in the code);
4) Plot the scaled values of the trajectory.
% Import the data
Clear temporary variables
clear opts
% Count unique values in "PARTICLE_ID" column
n = unique(testdata.PARTICLE_ID)
ParticleNumber = numel(n)
% Plot each scaled trajectory
for i = 1:ParticleNumber
table = testdata(testdata.PARTICLE_ID == i,:); % Isolate single particle trajetory
color = {'k' 'r' 'b' 'g' 'c'};
xmin = table.X(1); % Zero point on x-axis
ymin = table.Y(1); % Zero point on y-axis
table.Scaled_x = table.X-xmin; % Scaled values on x-axis
table.Scaled_y = table.Y-ymin; % Scaled values on y-axis
plot(table.Scaled_x, table.Scaled_y, color{i})
xlabel('x')
ylabel('y')
legend
hold on
end
In the attached file "untitled.1.png" you can find the plot that was generated by this code.
I really hope it helps. Kind regards,
PGP