Interpolating between two 3d time dependent positions

I'm trying to interpolate between 3d position values seperated by a 1 minute timestep. I have an array of position data <x,y,z> of size [500,000 x 3]. Each row of 3 values <x,y,z> represents a point in 3d space at a specific time (ex. 2 minutes). I'm trying to interpolate between each value so that I have a timestep in my data of 1 second. So I want to generate 59 pts between minute 1 and minute 2. For example: If t1 = 1min, <x1,y1,z1> = <1,1,1> and t2 = 2min, <x2,y2,z2> = <2,2,2>, then t3 = 1min 30 seconds and <x3,y3,z3> might equal ~ <1.5,1.5,1.5> using a linear interpolation method. My inclination is to use interpn(). Could anyone direct me how to set this up?

[Tahariet Sharon]

I have the same problem, only that instead of 3 points in space I have a whole 3D matrix in space at a given point.

I have 10 points in time for different configuations of the 3D matrix, and I want to interpolate several time points between each data point. How to go about this?

Answer 1

[Adam Danz]

There are multiple ways to do this. Here I show how to put your (x,y,z) coordinates into a timeseries and use resample to interpolate the 3D coordinates.

Main functions

• timeseries
• resample

Create an mx3 matrix of [x,y,z] coordinates

xyz is the only input in this demo. The rest of the demo can be copy-pasted.

th = linspace(0,31.5,50)';
xyz = [sin(th),cos(th),th];

Create a timeseries object at 2-minute intervals and interpolate at 60-sec intervals

Create an mx1 vector of time stamps at 2-minute intervals

timestamps = (0:2:size(xyz,1)*2-1)'; % minutes; col vector!x

Create a timeseries object

ts = timeseries(xyz, timestamps, 'Name', 'XYZdata'); % name optional
ts.TimeInfo.Units = 'Minutes';

Create an nx1 vector of time stamps at 1-second resolution. The vector spans the range of timestamps in your raw-data.

timestampsInterp = ts.Time(1) : 1/60 : ts.Time(end);

Interpolate, or resample at the new timestamps created above. Interpolation is linear by default; see the timeseries interpolation method in ts.DataInfo.Interpolation. See other interpolation options in resample>interpmethod and timeseries>DataInfo.

tsInt = resample(ts,timestampsInterp);

Extract the interpolated xyz data to an nx3 matrix (xyzInt). Note that this step could be skipped and you could work with the interpolated timeseries object directly.

xyzInt = tsInt.Data;

Plot the original and interpolated data

If you're planning on plotting your data, you may want to plot a subsection of the data since it is much larger than these demo data and will take a long time to render and will comsume much memory.

figure()
plot3(xyz(:,1),xyz(:,2),xyz(:,3),'bo','LineWidth',2,'DisplayName','Original (2-min)')
hold on
plot3(xyzInt(:,1),xyzInt(:,2),xyzInt(:,3),'r.','MarkerSize',3,'DisplayName','Interpolated (1-sec)')
grid on
legend('Location','SouthOutside')

Store the new interpolated data in a timetable

This, of course, is optional but it will be useful if you're planning on doing further time-based analysis.

TT = array2timetable(tsInt.Data,...
    'RowTimes',seconds(tsInt.Time*60), ...
    'VariableNames', {'x','y','z'});
head(TT) % view the first few rows

ans = 8×3 timetable
    Time         x           y           z    
    _____    _________    _______    _________

    0 sec            0          1            0
    1 sec    0.0049957    0.99834    0.0053571
    2 sec    0.0099914    0.99667     0.010714
    3 sec     0.014987    0.99501     0.016071
    4 sec     0.019983    0.99335     0.021429
    5 sec     0.024979    0.99168     0.026786
    6 sec     0.029974    0.99002     0.032143
    7 sec      0.03497    0.98836       0.0375

[Adam Danz]

Another approach may be to convert the data to a timetable at 2 min intervals and use retime to interpolate to seconds.

[Tahariet Sharon]

I have the same problem, only that instead of 3 points in space I have a whole 3D matrix in space at a given point.

I have 10 points in time for different configuations of the 3D matrix, and I want to interpolate several time points between each data point. How to go about this?