Interpolation x,y from time

Hi all, I have several variables

time           x       y
31977674  200  195
31978007  204  198
31978341  200  195
31978674  200  195
31979008  200  195
31979341  201  196
31979674  201  196
31980008  202  196
31980341  202  196
31980674  203  196
......

Presume in this case x,y are positions of say a ball rolling around at a given time. I now have a set of new times without x,y co-ordinates, none of the times match times already existing, so I have gone through the time list and find the two closest to that value (either side.)

So for example: given 31977674 = (200,195) and 31978007 = (204,198) what position am I at with a time 3197900?

I guess I need to use some sort of interpolation function but I'm struggling to see how to apply it in this case. I looked up interp2 in the help:

   Vq = interp2(X,Y,V,Xq,Yq) returns interpolated values of a function of two variables at specific query points using linear interpolation. The results always pass through the original sampling of the function. X and Y contain the coordinates of the sample points. V contains the corresponding function values at each sample point. Xq and Yq contain the coordinates of the query points.

But Xq and Yq are the 'co-ordinates of the query points' - I seem to want the opposite of this, I want the points given the time!

Apologies If I have misunderstood, the help is much appreciated.

Answer 1

[Star Strider]

Use interp1 and pass both the x and y columns to interpolate both at the same time:

I call your matrix ‘M’ here:

M = [31977674  200  195
31978007  204  198
31978341  200  195
31978674  200  195
31979008  200  195
31979341  201  196
31979674  201  196
31980008  202  196
31980341  202  196
31980674  203  196];

xynew = interp1(M(:,1), M(:,2:3), 31979000)

produces:

xynew =

     200   195

The values on either side of it aren’t changing, so it has the same values as its immediate neighbors. (I had a bit of a problem at first because there was a zero missing from your interpolation point.)

For two points between x and y values that are changing, the results are a bit more apparent:

xynew = interp1(M(:,1), M(:,2:3), [31978225; 31979225])

produces:

xynew =

     201.3892   196.0419
     200.6517   195.6517

[Montgomery]

Just tested this and it is exactly what I am after, perfect answer. :-) Also thank you for your examples, especially the second one it really cleared everything up.

[Star Strider]

My pleasure!